\bibfield  {author} {\bibinfo {author} {\bibfnamefont {A.}~\bibnamefont
{Mishra}}, \bibinfo {author} {\bibfnamefont {T.}~\bibnamefont {Albash}}, \
and\ \bibinfo {author} {\bibfnamefont {D.~A.}\ \bibnamefont {Lidar}},\
}\bibfield  {title} {\enquote {\bibinfo {title} {Finite temperature quantum
annealing solving exponentially small gap problem with non-monotonic success
probability},}\ }\href {https://doi.org/10.1038/s41467-018-05239-9}
{\bibfield  {journal} {\bibinfo  {journal} {Nature Communications}\ }\textbf
{\bibinfo {volume} {9}},\ \bibinfo {pages} {2917} (\bibinfo {year}
{2018})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Feynman}\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {R.}~\bibnamefont
{Feynman}}\ and\ \bibinfo {author} {\bibfnamefont {F.}~\bibnamefont
{Vernon}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {The theory of a
general quantum system interacting with a linear dissipative system},}\
}\href {https://doi.org/10.1016/0003-4916(63)90068-X} {\bibfield  {journal}
{\bibinfo  {journal} {Annals of Physics}\ }\textbf {\bibinfo {volume} {24}},\
\bibinfo {pages} {118 -- 173} (\bibinfo {year} {1963})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Caldeira}\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {A.}~\bibnamefont
{Caldeira}}\ and\ \bibinfo {author} {\bibfnamefont {A.}~\bibnamefont
{Leggett}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Quantum
tunnelling in a dissipative system},}\ }\href
{http://dx.doi.org/10.1016/0003-4916(83)90202-6} {\bibfield  {journal}
{\bibinfo  {journal} {Annals of Physics}\ }\textbf {\bibinfo {volume}
{149}},\ \bibinfo {pages} {374 -- 456} (\bibinfo {year} {1983})}\BibitemShut
\bibitem [{\citenamefont {Makarov}\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {D.~E.}\ \bibnamefont
{Makarov}}\ and\ \bibinfo {author} {\bibfnamefont {N.}~\bibnamefont
{Makri}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Path integrals
for dissipative systems by tensor multiplication. condensed phase quantum
dynamics for arbitrarily long time},}\ }\href
{https://doi.org/10.1016/0009-2614(94)00275-4} {\bibfield  {journal}
{\bibinfo  {journal} {Chemical Physics Letters}\ }\textbf {\bibinfo {volume}
{221}},\ \bibinfo {pages} {482 -- 491} (\bibinfo {year} {1994})}\BibitemShut
\bibitem [{\citenamefont {Sim}(2001)}]{Eunji:2001}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {E.}~\bibnamefont
{Sim}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Quantum dynamics
for a system coupled to slow baths: On-the-fly filtered propagator method},}\
}\href {https://doi.org/10.1063/1.1394208} {\bibfield  {journal} {\bibinfo
{journal} {The Journal of Chemical Physics}\ }\textbf {\bibinfo {volume}
{115}},\ \bibinfo {pages} {4450--4456} (\bibinfo {year} {2001})}\BibitemShut
\bibitem [{\citenamefont {{K. Kraus}}(1983)}]{Kraus:book}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibnamefont {{K. Kraus}}},\ }\href
{https://doi.org/10.1007/3-540-12732-1} {\emph {\bibinfo {title} {{States,
Effects, and Operations}}}}\ (\bibinfo  {publisher} {{Springer}},\ \bibinfo
{address} {{Berlin}},\ \bibinfo {year} {1983})\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Dominy}\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {J.~M.}\ \bibnamefont
{Dominy}}\ and\ \bibinfo {author} {\bibfnamefont {D.~A.}\ \bibnamefont
{Lidar}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Beyond complete
positivity},}\ }\href {http://dx.doi.org/10.1007/s11128-015-1228-1}
{\bibfield  {journal} {\bibinfo  {journal} {{Quant. Inf. Proc.}}\ }\textbf
{\bibinfo {volume} {15}},\ \bibinfo {pages} {1349} (\bibinfo {year}
{2016})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Gorini}\ \emph {et~al.}(1978)\citenamefont {Gorini},
\citenamefont {Frigerio}, \citenamefont {Verri}, \citenamefont
{Kossakowski},\ and\ \citenamefont {Sudarshan}}]{gorini_properties_1978}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {V.}~\bibnamefont
{Gorini}}, \bibinfo {author} {\bibfnamefont {A.}~\bibnamefont {Frigerio}},
\bibinfo {author} {\bibfnamefont {M.}~\bibnamefont {Verri}}, \bibinfo
{author} {\bibfnamefont {A.}~\bibnamefont {Kossakowski}}, \ and\ \bibinfo
{author} {\bibfnamefont {E.~C.~G.}\ \bibnamefont {Sudarshan}},\ }\bibfield
{title} {\enquote {\bibinfo {title} {Properties of quantum {Markovian} master
equations},}\ }\href {http://dx.doi.org/10.1016/0034-4877(78)90050-2}
{\bibfield  {journal} {\bibinfo  {journal} {Reports on Mathematical Physics}\
}\textbf {\bibinfo {volume} {13}},\ \bibinfo {pages} {149--173} (\bibinfo
{year} {1978})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {{S. Nakajima}}(1958)}]{Nakajima:58}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibnamefont {{S. Nakajima}}},\
}\bibfield  {title} {\enquote {\bibinfo {title} {{On Quantum Theory of
Transport Phenomena : Steady Diffusion}},}\ }\href
{https://doi.org/10.1143/PTP.20.948} {\bibfield  {journal} {\bibinfo
{journal} {Prog. Theor. Phys.}\ }\textbf {\bibinfo {volume} {20}},\ \bibinfo
{pages} {948} (\bibinfo {year} {1958})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Zwanzig}(1960)}]{Zwanzig:60a}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {R.}~\bibnamefont
{Zwanzig}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {{Ensemble
Method in the Theory of Irreversibility}},}\ }\href
{https://doi.org/10.1063/1.1731409} {\bibfield  {journal} {\bibinfo
{journal} {J. Chem. Phys.}\ }\textbf {\bibinfo {volume} {33}},\ \bibinfo
{pages} {1338} (\bibinfo {year} {1960})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Redfield}(1965)}]{Redfield:66}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {A.}~\bibnamefont
{Redfield}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {The theory of
relaxation processes},}\ }in\ \href
{https://doi.org/10.1016/B978-1-4832-3114-3.50007-6} {\emph {\bibinfo
{booktitle} {Advances in Magnetic Resonance}}},\ \bibinfo {series} {Advances
in Magnetic and Optical Resonance}, Vol.~\bibinfo {volume} {1},\ \bibinfo
{editor} {edited by\ \bibinfo {editor} {\bibfnamefont {J.~S.}\ \bibnamefont
{Waugh}}}\ (\bibinfo  {publisher} {Academic Press},\ \bibinfo {year} {1965})\
pp.\ \bibinfo {pages} {1 -- 32}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Bacon}\ \emph {et~al.}(1999)\citenamefont {Bacon},
\citenamefont {Lidar},\ and\ \citenamefont {Whaley}}]{PhysRevA.60.1944}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {D.}~\bibnamefont
{Bacon}}, \bibinfo {author} {\bibfnamefont {D.~A.}\ \bibnamefont {Lidar}}, \
and\ \bibinfo {author} {\bibfnamefont {K.~B.}\ \bibnamefont {Whaley}},\
}\bibfield  {title} {\enquote {\bibinfo {title} {Robustness of
decoherence-free subspaces for quantum computation},}\ }\href
{http://dx.doi.org/10.1103/PhysRevA.60.1944} {\bibfield  {journal} {\bibinfo
{journal} {Phys. Rev. A}\ }\textbf {\bibinfo {volume} {60}},\ \bibinfo
{pages} {1944--1955} (\bibinfo {year} {1999})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {van Wonderen}\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {A.~J.}\ \bibnamefont
{van Wonderen}}\ and\ \bibinfo {author} {\bibfnamefont {K.}~\bibnamefont
{Lendi}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Virtues and
limitations of markovian master equations with a time-dependent generator},}\
}\href {http://dx.doi.org/10.1023/A:1018671424739} {\bibfield  {journal}
{\bibinfo  {journal} {J. Stat. Phys.}\ }\textbf {\bibinfo {volume} {100}},\
\bibinfo {pages} {633--658} (\bibinfo {year} {2000})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Lidar}\ \emph {et~al.}(2001)\citenamefont {Lidar},
\citenamefont {Bihary},\ and\ \citenamefont {Whaley}}]{Lidar200135}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {D.~A.}\ \bibnamefont
{Lidar}}, \bibinfo {author} {\bibfnamefont {Z.}~\bibnamefont {Bihary}}, \
and\ \bibinfo {author} {\bibfnamefont {K.}~\bibnamefont {Whaley}},\
}\bibfield  {title} {\enquote {\bibinfo {title} {From completely positive
maps to the quantum \uppercase{M}arkovian semigroup master equation},}\
}\href {http://dx.doi.org/10.1016/S0301-0104(01)00330-5} {\bibfield
{journal} {\bibinfo  {journal} {Chem. Phys.}\ }\textbf {\bibinfo {volume}
{268}},\ \bibinfo {pages} {35} (\bibinfo {year} {2001})}\BibitemShut
\bibitem [{\citenamefont {{S. Daffer, K. Wodkiewicz, J.D. Cresser, J.K.
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibnamefont {{S. Daffer, K.
Wodkiewicz, J.D. Cresser, J.K. McIver}}},\ }\bibfield  {title} {\enquote
{\bibinfo {title} {{Depolarizing channel as a completely positive map with
memory}},}\ }\href {https://doi.org/10.1103/PhysRevA.70.010304} {\bibfield
{journal} {\bibinfo  {journal} {Phys. Rev. A}\ }\textbf {\bibinfo {volume}
{70}},\ \bibinfo {pages} {{010304(R)}} (\bibinfo {year} {2004})}\BibitemShut
\bibitem [{\citenamefont {Shabani}\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {A.}~\bibnamefont
{Shabani}}\ and\ \bibinfo {author} {\bibfnamefont {D.~A.}\ \bibnamefont
{Lidar}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Completely
positive post-markovian master equation via a measurement approach},}\ }\href
{https://doi.org/10.1103/PhysRevA.71.020101} {\bibfield  {journal} {\bibinfo
{journal} {Phys. Rev. A}\ }\textbf {\bibinfo {volume} {71}},\ \bibinfo
{pages} {020101(R)} (\bibinfo {year} {2005})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {{S. Maniscalco and F.
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibnamefont {{S. Maniscalco and F.
Petruccione}}},\ }\bibfield  {title} {\enquote {\bibinfo {title}
{{Non-Markovian dynamics of a qubit}},}\ }\href
{https://doi.org/10.1103/PhysRevA.73.012111} {\bibfield  {journal} {\bibinfo
{journal} {Phys. Rev. A}\ }\textbf {\bibinfo {volume} {73}},\ \bibinfo
{pages} {012111} (\bibinfo {year} {2006})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Piilo}\ \emph {et~al.}(2008)\citenamefont {Piilo},
\citenamefont {Maniscalco}, \citenamefont {H{\"a}rk{\"o}nen},\ and\
\citenamefont {Suominen}}]{piilo2008non}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {J.}~\bibnamefont
{Piilo}}, \bibinfo {author} {\bibfnamefont {S.}~\bibnamefont {Maniscalco}},
\bibinfo {author} {\bibfnamefont {K.}~\bibnamefont {H{\"a}rk{\"o}nen}}, \
and\ \bibinfo {author} {\bibfnamefont {K.-A.}\ \bibnamefont {Suominen}},\
}\bibfield  {title} {\enquote {\bibinfo {title} {Non-markovian quantum
jumps},}\ }\href {https://doi.org/10.1103/PhysRevLett.100.180402} {\bibfield
{journal} {\bibinfo  {journal} {Physical Review Letters}\ }\textbf {\bibinfo
{volume} {100}},\ \bibinfo {pages} {180402--} (\bibinfo {year}
{2008})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Breuer}\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {H.-P.}\ \bibnamefont
{Breuer}}\ and\ \bibinfo {author} {\bibfnamefont {B.}~\bibnamefont
{Vacchini}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Quantum
semi-markov processes},}\ }\href
{https://doi.org/10.1103/PhysRevLett.101.140402} {\bibfield  {journal}
{\bibinfo  {journal} {Physical Review Letters}\ }\textbf {\bibinfo {volume}
{101}},\ \bibinfo {pages} {140402--} (\bibinfo {year} {2008})}\BibitemShut
\bibitem [{\citenamefont {Whitney}(2008)}]{Whitney:2008aa}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {R.~S.}\ \bibnamefont
{Whitney}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Staying
positive: going beyond lindblad with perturbative master equations},}\ }\href
{https://doi.org/10.1088/1751-8113/41/17/175304} {\bibfield  {journal}
{\bibinfo  {journal} {Journal of Physics A: Mathematical and Theoretical}\
}\textbf {\bibinfo {volume} {41}},\ \bibinfo {pages} {175304} (\bibinfo
{year} {2008})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Wu}\ \emph {et~al.}(2009)\citenamefont {Wu},
\citenamefont {Kurizki},\ and\ \citenamefont {Brumer}}]{Wu09}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {L.-A.}\ \bibnamefont
{Wu}}, \bibinfo {author} {\bibfnamefont {G.}~\bibnamefont {Kurizki}}, \ and\
\bibinfo {author} {\bibfnamefont {P.}~\bibnamefont {Brumer}},\ }\bibfield
{title} {\enquote {\bibinfo {title} {Master equation and control of an open
quantum system with leakage},}\ }\href
{https://doi.org/10.1103/PhysRevLett.102.080405} {\bibfield  {journal}
{\bibinfo  {journal} {Physical Review Letters}\ }\textbf {\bibinfo {volume}
{102}},\ \bibinfo {pages} {080405--} (\bibinfo {year} {2009})}\BibitemShut
\bibitem [{\citenamefont {Chru\ifmmode \acute{s}\else
\'{s}\fi{}ci\ifmmode~\acute{n}\else \'{n}\fi{}ski}\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {D.}~\bibnamefont
{Chru\ifmmode \acute{s}\else \'{s}\fi{}ci\ifmmode~\acute{n}\else
\'{n}\fi{}ski}}\ and\ \bibinfo {author} {\bibfnamefont {A.}~\bibnamefont
{Kossakowski}},\ }\bibfield  {title} {\enquote {\bibinfo {title}
{Non-markovian quantum dynamics: Local versus nonlocal},}\ }\href
{https://doi.org/10.1103/PhysRevLett.104.070406} {\bibfield  {journal}
{\bibinfo  {journal} {Phys. Rev. Lett.}\ }\textbf {\bibinfo {volume} {104}},\
\bibinfo {pages} {070406} (\bibinfo {year} {2010})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Albash}\ \emph {et~al.}(2012)\citenamefont {Albash},
\citenamefont {Boixo}, \citenamefont {Lidar},\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {T.}~\bibnamefont
{Albash}}, \bibinfo {author} {\bibfnamefont {S.}~\bibnamefont {Boixo}},
\bibinfo {author} {\bibfnamefont {D.~A.}\ \bibnamefont {Lidar}}, \ and\
\bibinfo {author} {\bibfnamefont {P.}~\bibnamefont {Zanardi}},\ }\bibfield
{title} {\enquote {\bibinfo {title} {{Quantum adiabatic Markovian master
equations}},}\ }\href {http://dx.doi.org/10.1088/1367-2630/14/12/123016}
{\bibfield  {journal} {\bibinfo  {journal} {New J. of Phys.}\ }\textbf
{\bibinfo {volume} {14}},\ \bibinfo {pages} {123016} (\bibinfo {year}
{2012})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Mozgunov}(2016)}]{Mozgunov:2016aa}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {E.}~\bibnamefont
{Mozgunov}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Local master
equation for small temperatures},}\ }\href {http://arXiv.org/abs/1611.04188}
{\bibfield  {journal} {\bibinfo  {journal} {arXiv:1611.04188}\ } (\bibinfo
{year} {2016})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Smirnov}\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {A.~Y.}\ \bibnamefont
{Smirnov}}\ and\ \bibinfo {author} {\bibfnamefont {M.~H.}\ \bibnamefont
{Amin}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Theory of open
quantum dynamics with hybrid noise},}\ }\href
{https://doi.org/10.1088/1367-2630/aae79c} {\bibfield  {journal} {\bibinfo
{journal} {New Journal of Physics}\ }\textbf {\bibinfo {volume} {20}},\
\bibinfo {pages} {103037} (\bibinfo {year} {2018})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Dann}\ \emph {et~al.}(2018)\citenamefont {Dann},
\citenamefont {Levy},\ and\ \citenamefont {Kosloff}}]{Kosloff:2018}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {R.}~\bibnamefont
{Dann}}, \bibinfo {author} {\bibfnamefont {A.}~\bibnamefont {Levy}}, \ and\
\bibinfo {author} {\bibfnamefont {R.}~\bibnamefont {Kosloff}},\ }\bibfield
{title} {\enquote {\bibinfo {title} {Time-dependent markovian quantum master
equation},}\ }\href {\doibase 10.1103/PhysRevA.98.052129} {\bibfield
{journal} {\bibinfo  {journal} {Phys. Rev. A}\ }\textbf {\bibinfo {volume}
{98}},\ \bibinfo {pages} {052129} (\bibinfo {year} {2018})}\BibitemShut
\bibitem [{\citenamefont {Venuti}\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {L.~C.}\ \bibnamefont
{Venuti}}\ and\ \bibinfo {author} {\bibfnamefont {D.~A.}\ \bibnamefont
{Lidar}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Error reduction
in quantum annealing using boundary cancellation: Only the end matters},}\
}\href {\doibase 10.1103/PhysRevA.98.022315} {\bibfield  {journal} {\bibinfo
{journal} {Phys. Rev. A}\ }\textbf {\bibinfo {volume} {98}},\ \bibinfo
{pages} {022315} (\bibinfo {year} {2018})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {McCauley}\ \emph {et~al.}(2019)\citenamefont
{McCauley}, \citenamefont {Cruikshank}, \citenamefont {Bondar},\ and\
\citenamefont {Jacobs}}]{McCauley:19}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {G.}~\bibnamefont
{McCauley}}, \bibinfo {author} {\bibfnamefont {B.}~\bibnamefont
{Cruikshank}}, \bibinfo {author} {\bibfnamefont {D.~I.}\ \bibnamefont
{Bondar}}, \ and\ \bibinfo {author} {\bibfnamefont {K.}~\bibnamefont
{Jacobs}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Completely
positive, accurate master equation for weakly-damped quantum systems across
all regimes},}\ }\href {https://arxiv.org/abs/1906.08279} {\bibfield
{journal} {\bibinfo  {journal} {arXiv:1906.08279}\ } (\bibinfo {year}
{2019})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Benatti}\ \emph {et~al.}(2009)\citenamefont
{Benatti}, \citenamefont {Floreanini},\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {F.}~\bibnamefont
{Benatti}}, \bibinfo {author} {\bibfnamefont {R.}~\bibnamefont {Floreanini}},
\ and\ \bibinfo {author} {\bibfnamefont {U.}~\bibnamefont {Marzolino}},\
}\bibfield  {title} {\enquote {\bibinfo {title} {Environment-induced
entanglement in a refined weak-coupling limit},}\ }\href
{https://doi.org/10.1209/0295-5075/88/20011} {\bibfield  {journal} {\bibinfo
{journal} {{EPL} (Europhysics Letters)}\ }\textbf {\bibinfo {volume} {88}},\
\bibinfo {pages} {20011} (\bibinfo {year} {2009})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Benatti}\ \emph {et~al.}(2010)\citenamefont
{Benatti}, \citenamefont {Floreanini},\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {F.}~\bibnamefont
{Benatti}}, \bibinfo {author} {\bibfnamefont {R.}~\bibnamefont {Floreanini}},
\ and\ \bibinfo {author} {\bibfnamefont {U.}~\bibnamefont {Marzolino}},\
}\bibfield  {title} {\enquote {\bibinfo {title} {Entangling two unequal atoms
through a common bath},}\ }\href {https://doi.org/10.1103/PhysRevA.81.012105}
{\bibfield  {journal} {\bibinfo  {journal} {Phys. Rev. A}\ }\textbf {\bibinfo
{volume} {81}},\ \bibinfo {pages} {012105} (\bibinfo {year}
{2010})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Merkli}(2020)}]{Merkli_2019}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {M.}~\bibnamefont
{Merkli}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Quantum
markovian master equations: Resonance theory shows validity for all time
scales},}\ }\href {\doibase https://doi.org/10.1016/j.aop.2019.167996}
{\bibfield  {journal} {\bibinfo  {journal} {Annals of Physics}\ }\textbf
{\bibinfo {volume} {412}},\ \bibinfo {pages} {167996} (\bibinfo {year}
{2020})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Majenz}\ \emph {et~al.}(2013)\citenamefont {Majenz},
\citenamefont {Albash}, \citenamefont {Breuer},\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {C.}~\bibnamefont
{Majenz}}, \bibinfo {author} {\bibfnamefont {T.}~\bibnamefont {Albash}},
\bibinfo {author} {\bibfnamefont {H.-P.}\ \bibnamefont {Breuer}}, \ and\
\bibinfo {author} {\bibfnamefont {D.~A.}\ \bibnamefont {Lidar}},\ }\bibfield
{title} {\enquote {\bibinfo {title} {Coarse graining can beat the
rotating-wave approximation in quantum markovian master equations},}\ }\href
{https://doi.org/10.1103/PhysRevA.88.012103} {\bibfield  {journal} {\bibinfo
{journal} {Phys. Rev. A}\ }\textbf {\bibinfo {volume} {88}},\ \bibinfo
{pages} {012103--} (\bibinfo {year} {2013})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Cubitt}\ \emph {et~al.}(2015)\citenamefont {Cubitt},
\citenamefont {Lucia}, \citenamefont {Michalakis},\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {T.~S.}\ \bibnamefont
{Cubitt}}, \bibinfo {author} {\bibfnamefont {A.}~\bibnamefont {Lucia}},
\bibinfo {author} {\bibfnamefont {S.}~\bibnamefont {Michalakis}}, \ and\
\bibinfo {author} {\bibfnamefont {D.}~\bibnamefont {Perez-Garcia}},\
}\bibfield  {title} {\enquote {\bibinfo {title} {Stability of local quantum
dissipative systems},}\ }\href {https://doi.org/10.1007/s00220-015-2355-3}
{\bibfield  {journal} {\bibinfo  {journal} {Communications in Mathematical
Physics}\ }\textbf {\bibinfo {volume} {337}},\ \bibinfo {pages} {1275--1315}
(\bibinfo {year} {2015})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Knill}(2005)}]{Knill:05}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {E.}~\bibnamefont
{Knill}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Quantum computing
with realistically noisy devices},}\ }\href
{http://dx.doi.org/10.1038/nature03350} {\bibfield  {journal} {\bibinfo
{journal} {Nature}\ }\textbf {\bibinfo {volume} {434}},\ \bibinfo {pages}
{39--44} (\bibinfo {year} {2005})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Alicki}\ \emph {et~al.}(2006)\citenamefont {Alicki},
\citenamefont {Lidar},\ and\ \citenamefont {Zanardi}}]{PhysRevA.73.052311}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {R.}~\bibnamefont
{Alicki}}, \bibinfo {author} {\bibfnamefont {D.~A.}\ \bibnamefont {Lidar}}, \
and\ \bibinfo {author} {\bibfnamefont {P.}~\bibnamefont {Zanardi}},\
}\bibfield  {title} {\enquote {\bibinfo {title} {Internal consistency of
fault-tolerant quantum error correction in light of rigorous derivations of
the quantum markovian limit},}\ }\href
{http://dx.doi.org/10.1103/PhysRevA.73.052311} {\bibfield  {journal}
{\bibinfo  {journal} {Phys. Rev. A}\ }\textbf {\bibinfo {volume} {73}},\
\bibinfo {pages} {052311} (\bibinfo {year} {2006})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Lidar}(2019)}]{Lidar:2019aa}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {D.~A.}\ \bibnamefont
{Lidar}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Lecture notes on
the theory of open quantum systems},}\ }\href
{https://arxiv.org/abs/1902.00967} {\bibfield  {journal} {\bibinfo  {journal}
{arXiv preprint arXiv:1902.00967}\ } (\bibinfo {year} {2019})}\BibitemShut
\bibitem [{\citenamefont {Albash}\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {T.}~\bibnamefont
{Albash}}\ and\ \bibinfo {author} {\bibfnamefont {D.~A.}\ \bibnamefont
{Lidar}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Decoherence in
adiabatic quantum computation},}\ }\href
{https://doi.org/10.1103/PhysRevA.91.062320} {\bibfield  {journal} {\bibinfo
{journal} {Phys. Rev. A}\ }\textbf {\bibinfo {volume} {91}},\ \bibinfo
{pages} {062320--} (\bibinfo {year} {2015})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {{\v{Z}}nidari{\v{c}}}(2010)}]{Znidaric:10}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {M.}~\bibnamefont
{{\v{Z}}nidari{\v{c}}}},\ }\bibfield  {title} {\enquote {\bibinfo {title}
{Dephasing-induced diffusive transport in the anisotropic heisenberg
model},}\ }\href {https://doi.org/10.1088/1367-2630/12/4/043001} {\bibfield
{journal} {\bibinfo  {journal} {New Journal of Physics}\ }\textbf {\bibinfo
{volume} {12}},\ \bibinfo {pages} {043001} (\bibinfo {year}
{2010})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Medvedyeva}\ \emph {et~al.}(2016)\citenamefont
{Medvedyeva}, \citenamefont {Prosen},\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {M.~V.}\ \bibnamefont
{Medvedyeva}}, \bibinfo {author} {\bibfnamefont {T.}~\bibnamefont {Prosen}},
\ and\ \bibinfo {author} {\bibfnamefont {M.}~\bibnamefont
{\v{Z}nidari\v{c}}},\ }\bibfield  {title} {\enquote {\bibinfo {title}
{Influence of dephasing on many-body localization},}\ }\href
{https://doi.org/10.1103/PhysRevB.93.094205} {\bibfield  {journal} {\bibinfo
{journal} {Phys. Rev. B}\ }\textbf {\bibinfo {volume} {93}},\ \bibinfo
{pages} {094205} (\bibinfo {year} {2016})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {{R. Bhatia}}(1997)}]{Bhatia:book}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibnamefont {{R. Bhatia}}},\
}\href@noop {} {\emph {\bibinfo {title} {{Matrix Analysis}}}},\ \bibinfo
{series} {{Graduate Texts in Mathematics}}\ No.\ \bibinfo {number} {169}\
(\bibinfo  {publisher} {Springer-Verlag},\ \bibinfo {address} {{New York}},\
\bibinfo {year} {1997})\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Gaspard}\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {P.}~\bibnamefont
{Gaspard}}\ and\ \bibinfo {author} {\bibfnamefont {M.}~\bibnamefont
{Nagaoka}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Slippage of
initial conditions for the redfield master equation},}\ }\href
{https://doi.org/10.1063/1.479867} {\bibfield  {journal} {\bibinfo  {journal}
{Journal of Chemical Physics}\ }\textbf {\bibinfo {volume} {111}},\ \bibinfo
{pages} {5668--5675} (\bibinfo {year} {1999})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Vidal}(2003)}]{Vidalsolo:03}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {G.}~\bibnamefont
{Vidal}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Efficient
classical simulation of slightly entangled quantum computations},}\ }\href
{https://doi.org/10.1103/PhysRevLett.91.147902} {\bibfield  {journal}
{\bibinfo  {journal} {Phys. Rev. Lett.}\ }\textbf {\bibinfo {volume} {91}},\
\bibinfo {pages} {147902} (\bibinfo {year} {2003})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Verstraete}\ \emph {et~al.}(2004)\citenamefont
{Verstraete}, \citenamefont {Garcia-Ripoll},\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {F.}~\bibnamefont
{Verstraete}}, \bibinfo {author} {\bibfnamefont {J.~J.}\ \bibnamefont
{Garcia-Ripoll}}, \ and\ \bibinfo {author} {\bibfnamefont {J.~I.}\
\bibnamefont {Cirac}},\ }\bibfield  {title} {\enquote {\bibinfo {title}
{Matrix product density operators: Simulation of finite-temperature and
dissipative systems},}\ }\href
{https://doi.org/10.1103/PhysRevLett.93.207204} {\bibfield  {journal}
{\bibinfo  {journal} {Phys. Rev. Lett.}\ }\textbf {\bibinfo {volume} {93}},\
\bibinfo {pages} {207204} (\bibinfo {year} {2004})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {{E. H. Lieb and D.W. Robinson}}(1972)}]{Lieb:72}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibnamefont {{E. H. Lieb and D.W.
Robinson}}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {The finite
group velocity of quantum spin systems},}\ }\href
{https://doi.org/10.1007/BF01645779} {\bibfield  {journal} {\bibinfo
{journal} {{Commun. Math. Phys.}}\ }\textbf {\bibinfo {volume} {28}},\
\bibinfo {pages} {251} (\bibinfo {year} {1972})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {{Haah}}\ \emph {et~al.}(2018)\citenamefont {{Haah}},
\citenamefont {{Hastings}}, \citenamefont {{Kothari}},\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {J.}~\bibnamefont
{{Haah}}}, \bibinfo {author} {\bibfnamefont {M.}~\bibnamefont {{Hastings}}},
\bibinfo {author} {\bibfnamefont {R.}~\bibnamefont {{Kothari}}}, \ and\
\bibinfo {author} {\bibfnamefont {G.~H.}\ \bibnamefont {{Low}}},\ }\bibfield
{title} {\enquote {\bibinfo {title} {Quantum algorithm for simulating real
time evolution of lattice hamiltonians},}\ }in\ \href
{https://doi.org/10.1109/FOCS.2018.00041} {\emph {\bibinfo {booktitle} {2018
IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS)}}}\
(\bibinfo {year} {2018})\ pp.\ \bibinfo {pages} {350--360}\BibitemShut
\bibitem [{\citenamefont {Pichler}\ \emph {et~al.}(2010)\citenamefont
{Pichler}, \citenamefont {Daley},\ and\ \citenamefont {Zoller}}]{Pichler:10}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {H.}~\bibnamefont
{Pichler}}, \bibinfo {author} {\bibfnamefont {A.~J.}\ \bibnamefont {Daley}},
\ and\ \bibinfo {author} {\bibfnamefont {P.}~\bibnamefont {Zoller}},\
}\bibfield  {title} {\enquote {\bibinfo {title} {Nonequilibrium dynamics of
bosonic atoms in optical lattices: Decoherence of many-body states due to
spontaneous emission},}\ }\href {https://doi.org/10.1103/PhysRevA.82.063605}
{\bibfield  {journal} {\bibinfo  {journal} {Phys. Rev. A}\ }\textbf {\bibinfo
{volume} {82}},\ \bibinfo {pages} {063605} (\bibinfo {year}
{2010})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {{L.-M Duan and G.-C. Guo}}(1998)}]{Duan:98}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibnamefont {{L.-M Duan and G.-C.
Guo}}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {{Reducing
decoherence in quantum-computer memory with all quantum bits coupling to the
same environment}},}\ }\href {https://doi.org/10.1103/PhysRevA.57.737}
{\bibfield  {journal} {\bibinfo  {journal} {Phys. Rev. A}\ }\textbf {\bibinfo
{volume} {57}},\ \bibinfo {pages} {737} (\bibinfo {year} {1998})}\BibitemShut
\bibitem [{\citenamefont {Zanardi}\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {P.}~\bibnamefont
{Zanardi}}\ and\ \bibinfo {author} {\bibfnamefont {M.}~\bibnamefont
{Rasetti}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Noiseless
quantum codes},}\ }\href {https://doi.org/10.1103/PhysRevLett.79.3306}
{\bibfield  {journal} {\bibinfo  {journal} {{Phys.~Rev.~Lett.}}\ }\textbf
{\bibinfo {volume} {79}},\ \bibinfo {pages} {3306--3309} (\bibinfo {year}
{1997})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Lidar}\ \emph {et~al.}(1998)\citenamefont {Lidar},
\citenamefont {Chuang},\ and\ \citenamefont {Whaley}}]{Lidar:1998fk}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {D.~A.}\ \bibnamefont
{Lidar}}, \bibinfo {author} {\bibfnamefont {I.~L.}\ \bibnamefont {Chuang}}, \
and\ \bibinfo {author} {\bibfnamefont {K.~B.}\ \bibnamefont {Whaley}},\
}\bibfield  {title} {\enquote {\bibinfo {title} {Decoherence-free subspaces
for quantum computation},}\ }\href
{https://doi.org/10.1103/PhysRevLett.81.2594} {\bibfield  {journal} {\bibinfo
{journal} {Phys. Rev. Lett.}\ }\textbf {\bibinfo {volume} {81}},\ \bibinfo
{pages} {2594--2597} (\bibinfo {year} {1998})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Lidar}\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {D.~A.}\ \bibnamefont
{Lidar}}\ and\ \bibinfo {author} {\bibfnamefont {K.~B.}\ \bibnamefont
{Whaley}},\ }\enquote {\bibinfo {title} {Decoherence-free subspaces and
subsystems},}\ in\ \href {https://www.springer.com/us/book/9783540402237}
{\emph {\bibinfo {booktitle} {Irreversible Quantum Dynamics}}},\ \bibinfo
{series} {Lecture Notes in Physics}, Vol.\ \bibinfo {volume} {622},\ \bibinfo
{editor} {edited by\ \bibinfo {editor} {\bibfnamefont {F.}~\bibnamefont
{Benatti}}\ and\ \bibinfo {editor} {\bibfnamefont {R.}~\bibnamefont
{Floreanini}}}\ (\bibinfo  {publisher} {Springer},\ \bibinfo {address}
{Berlin},\ \bibinfo {year} {2003})\ p.~\bibinfo {pages} {83}\BibitemShut
\bibitem [{\citenamefont {{P.G. Kwiat, A.J. Berglund, J.B. Altepeter, and A.G.
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibnamefont {{P.G. Kwiat, A.J.
Berglund, J.B. Altepeter, and A.G. White}}},\ }\bibfield  {title} {\enquote
{\bibinfo {title} {{Experimental Verification of Decoherence-Free
Subspaces}},}\ }\href {https://doi.org/10.1126/science.290.5491.498}
{\bibfield  {journal} {\bibinfo  {journal} {Science}\ }\textbf {\bibinfo
{volume} {290}},\ \bibinfo {pages} {498} (\bibinfo {year}
{2000})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Viola}\ \emph {et~al.}(2001)\citenamefont {Viola},
\citenamefont {Fortunato}, \citenamefont {Pravia}, \citenamefont {Knill},
\citenamefont {Laflamme},\ and\ \citenamefont {Cory}}]{Viola:2001sp}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {L.}~\bibnamefont
{Viola}}, \bibinfo {author} {\bibfnamefont {E.~M.}\ \bibnamefont
{Fortunato}}, \bibinfo {author} {\bibfnamefont {M.~A.}\ \bibnamefont
{Pravia}}, \bibinfo {author} {\bibfnamefont {E.}~\bibnamefont {Knill}},
\bibinfo {author} {\bibfnamefont {R.}~\bibnamefont {Laflamme}}, \ and\
\bibinfo {author} {\bibfnamefont {D.~G.}\ \bibnamefont {Cory}},\ }\bibfield
{title} {\enquote {\bibinfo {title} {Experimental realization of noiseless
subsystems for quantum information processing},}\ }\href
{https://doi.org/10.1126/science.1064460} {\bibfield  {journal} {\bibinfo
{journal} {Science}\ }\textbf {\bibinfo {volume} {293}},\ \bibinfo {pages}
{2059--2063} (\bibinfo {year} {2001})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Kielpinski}\ \emph {et~al.}(2001)\citenamefont
{Kielpinski}, \citenamefont {Meyer}, \citenamefont {Rowe}, \citenamefont
{Sackett}, \citenamefont {Itano}, \citenamefont {Monroe},\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {D.}~\bibnamefont
{Kielpinski}}, \bibinfo {author} {\bibfnamefont {V.}~\bibnamefont {Meyer}},
\bibinfo {author} {\bibfnamefont {M.~A.}\ \bibnamefont {Rowe}}, \bibinfo
{author} {\bibfnamefont {C.~A.}\ \bibnamefont {Sackett}}, \bibinfo {author}
{\bibfnamefont {W.~M.}\ \bibnamefont {Itano}}, \bibinfo {author}
{\bibfnamefont {C.}~\bibnamefont {Monroe}}, \ and\ \bibinfo {author}
{\bibfnamefont {D.~J.}\ \bibnamefont {Wineland}},\ }\bibfield  {title}
{\enquote {\bibinfo {title} {A decoherence-free quantum memory using trapped
ions},}\ }\href {https://doi.org/10.1126/science.1057357} {\bibfield
{journal} {\bibinfo  {journal} {Science}\ }\textbf {\bibinfo {volume}
{291}},\ \bibinfo {pages} {1013--1015} (\bibinfo {year} {2001})}\BibitemShut
\bibitem [{\citenamefont {Ollerenshaw}\ \emph {et~al.}(2003)\citenamefont
{Ollerenshaw}, \citenamefont {Lidar},\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {J.~E.}\ \bibnamefont
{Ollerenshaw}}, \bibinfo {author} {\bibfnamefont {D.~A.}\ \bibnamefont
{Lidar}}, \ and\ \bibinfo {author} {\bibfnamefont {L.~E.}\ \bibnamefont
{Kay}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Magnetic resonance
realization of decoherence-free quantum computation},}\ }\href
{http://dx.doi.org/10.1103/PhysRevLett.91.217904} {\bibfield  {journal}
{\bibinfo  {journal} {Phys. Rev. Lett.}\ }\textbf {\bibinfo {volume} {91}},\
\bibinfo {pages} {217904} (\bibinfo {year} {2003})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Viola}\ and\ \citenamefont {Lloyd}(1998)}]{Viola:98}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {L.}~\bibnamefont
{Viola}}\ and\ \bibinfo {author} {\bibfnamefont {S.}~\bibnamefont {Lloyd}},\
}\bibfield  {title} {\enquote {\bibinfo {title} {Dynamical suppression of
decoherence in two-state quantum systems},}\ }\href
{http://dx.doi.org/10.1103/PhysRevA.58.2733} {\bibfield  {journal} {\bibinfo
{journal} {Phys. Rev. A}\ }\textbf {\bibinfo {volume} {58}},\ \bibinfo
{pages} {2733--2744} (\bibinfo {year} {1998})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Zanardi}(1999)}]{Zanardi:1999fk}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {P.}~\bibnamefont
{Zanardi}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Symmetrizing
evolutions},}\ }\href {http://dx.doi.org/10.1016/S0375-9601(99)00365-5}
{\bibfield  {journal} {\bibinfo  {journal} {Physics Letters A}\ }\textbf
{\bibinfo {volume} {258}},\ \bibinfo {pages} {77--82} (\bibinfo {year}
{1999})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Lidar}\ and\ \citenamefont
\BibitemOpen
\bibinfo {editor} {\bibfnamefont {D.}~\bibnamefont {Lidar}}\ and\ \bibinfo
{editor} {\bibfnamefont {T.}~\bibnamefont {Brun}},\ eds.,\ \href
{http://www.cambridge.org/9780521897877} {\emph {\bibinfo {title} {Quantum
Error Correction}}}\ (\bibinfo  {publisher} {Cambridge University Press},\
\bibinfo {address} {{Cambridge, UK}},\ \bibinfo {year} {2013})\BibitemShut
\bibitem [{\citenamefont {Suter}\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {D.}~\bibnamefont
{Suter}}\ and\ \bibinfo {author} {\bibfnamefont {G.~A.}\ \bibnamefont
{{\'A}lvarez}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Colloquium:
Protecting quantum information against environmental noise},}\ }\href
{https://doi.org/10.1103/RevModPhys.88.041001} {\bibfield  {journal}
{\bibinfo  {journal} {Reviews of Modern Physics}\ }\textbf {\bibinfo {volume}
{88}},\ \bibinfo {pages} {041001--} (\bibinfo {year} {2016})}\BibitemShut
\bibitem [{\citenamefont {Ng}\ \emph {et~al.}(2011)\citenamefont {Ng},
\citenamefont {Lidar},\ and\ \citenamefont {Preskill}}]{Ng:2011dn}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {H.~K.}\ \bibnamefont
{Ng}}, \bibinfo {author} {\bibfnamefont {D.~A.}\ \bibnamefont {Lidar}}, \
and\ \bibinfo {author} {\bibfnamefont {J.}~\bibnamefont {Preskill}},\
}\bibfield  {title} {\enquote {\bibinfo {title} {Combining dynamical
decoupling with fault-tolerant quantum computation},}\ }\href
{https://doi.org/10.1103/PhysRevA.84.012305} {\bibfield  {journal} {\bibinfo
{journal} {Phys. Rev. A}\ }\textbf {\bibinfo {volume} {84}},\ \bibinfo
{pages} {012305--} (\bibinfo {year} {2011})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Szczygielski}\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {K.}~\bibnamefont
{Szczygielski}}\ and\ \bibinfo {author} {\bibfnamefont {R.}~\bibnamefont
{Alicki}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Markovian theory
of dynamical decoupling by periodic control},}\ }\href
{https://doi.org/10.1103/PhysRevA.92.022349} {\bibfield  {journal} {\bibinfo
{journal} {Physical Review A}\ }\textbf {\bibinfo {volume} {92}},\ \bibinfo
{pages} {022349--} (\bibinfo {year} {2015})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Gough}\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {J.~E.}\ \bibnamefont
{Gough}}\ and\ \bibinfo {author} {\bibfnamefont {H.~I.}\ \bibnamefont
{Nurdin}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Can quantum
markov evolutions ever be dynamically decoupled?}}\ }in\ \href
{https://doi.org/10.1109/CDC.2017.8264587} {\emph {\bibinfo {booktitle} {2017
IEEE 56th Annual Conference on Decision and Control (CDC)}}}\ (\bibinfo
{year} {2017})\ pp.\ \bibinfo {pages} {6155--6160}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Addis}\ \emph {et~al.}(2015)\citenamefont {Addis},
\citenamefont {Ciccarello}, \citenamefont {Cascio}, \citenamefont {Palma},\
and\ \citenamefont {Maniscalco}}]{Addis:2015aa}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {C.}~\bibnamefont
{Addis}}, \bibinfo {author} {\bibfnamefont {F.}~\bibnamefont {Ciccarello}},
\bibinfo {author} {\bibfnamefont {M.}~\bibnamefont {Cascio}}, \bibinfo
{author} {\bibfnamefont {G.~M.}\ \bibnamefont {Palma}}, \ and\ \bibinfo
{author} {\bibfnamefont {S.}~\bibnamefont {Maniscalco}},\ }\bibfield  {title}
{\enquote {\bibinfo {title} {Dynamical decoupling efficiency versus quantum
non-markovianity},}\ }\href
{http://dx.doi.org/10.1088/1367-2630/17/12/123004} {\bibfield  {journal}
{\bibinfo  {journal} {New Journal of Physics}\ }\textbf {\bibinfo {volume}
{17}},\ \bibinfo {pages} {123004} (\bibinfo {year} {2015})}\BibitemShut
\bibitem [{\citenamefont {Arenz}\ \emph {et~al.}(2018)\citenamefont {Arenz},
\citenamefont {Burgarth}, \citenamefont {Facchi},\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {C.}~\bibnamefont
{Arenz}}, \bibinfo {author} {\bibfnamefont {D.}~\bibnamefont {Burgarth}},
\bibinfo {author} {\bibfnamefont {P.}~\bibnamefont {Facchi}}, \ and\ \bibinfo
{author} {\bibfnamefont {R.}~\bibnamefont {Hillier}},\ }\bibfield  {title}
{\enquote {\bibinfo {title} {Dynamical decoupling of unbounded
hamiltonians},}\ }\bibfield  {booktitle} {\emph {\bibinfo {booktitle}
{Journal of Mathematical Physics}},\ }\href
{https://doi.org/10.1063/1.5016495} {\bibfield  {journal} {\bibinfo
{journal} {Journal of Mathematical Physics}\ }\textbf {\bibinfo {volume}
{59}},\ \bibinfo {pages} {032203} (\bibinfo {year} {2018})}\BibitemShut
\bibitem [{\citenamefont {Li}\ \emph {et~al.}(2018)\citenamefont {Li},
\citenamefont {Hall},\ and\ \citenamefont {Wiseman}}]{Li:2018aa}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {L.}~\bibnamefont
{Li}}, \bibinfo {author} {\bibfnamefont {M.~J.~W.}\ \bibnamefont {Hall}}, \
and\ \bibinfo {author} {\bibfnamefont {H.~M.}\ \bibnamefont {Wiseman}},\
}\bibfield  {title} {\enquote {\bibinfo {title} {Concepts of quantum
non-markovianity: A hierarchy},}\ }\bibfield  {booktitle} {\emph {\bibinfo
{booktitle} {Concepts of quantum non-Markovianity: A hierarchy}},\ }\href
{https://doi.org/10.1016/j.physrep.2018.07.001} {\bibfield  {journal}
{\bibinfo  {journal} {Physics Reports}\ }\textbf {\bibinfo {volume} {759}},\
\bibinfo {pages} {1--51} (\bibinfo {year} {2018})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {de~Vega}\ \emph {et~al.}(2010)\citenamefont
{de~Vega}, \citenamefont {Ba{\~n}uls},\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {I.}~\bibnamefont
{de~Vega}}, \bibinfo {author} {\bibfnamefont {M.~C.}\ \bibnamefont
{Ba{\~n}uls}}, \ and\ \bibinfo {author} {\bibfnamefont {A.}~\bibnamefont
{P{\'e}rez}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Effects of
dissipation on an adiabatic quantum search algorithm},}\ }\href
{https://doi.org/10.1088/1367-2630/12/12/123010} {\bibfield  {journal}
{\bibinfo  {journal} {New J. of Phys.}\ }\textbf {\bibinfo {volume} {12}},\
\bibinfo {pages} {123010} (\bibinfo {year} {2010})}\BibitemShut {NoStop}%
\bibitem [{url()}]{urlCode}%
\BibitemOpen
\href@noop {} {}\bibinfo {howpublished}
{\url{https://github.com/mvjenia/CGMEcode}},\ \bibinfo {note} {code for the
numerical section of the paper}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Isserlis}(1916)}]{Isserlis:1916}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {L.}~\bibnamefont
{Isserlis}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {On certain
probable errors and correlation coefficients of multiple frequency
distributions with skew regression},}\ }\href
{https://doi.org/10.1093/biomet/11.3.185} {\bibfield  {journal} {\bibinfo
{journal} {Biometrika}\ }\textbf {\bibinfo {volume} {11}},\ \bibinfo {pages}
{185} (\bibinfo {year} {1916})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Albash}\ \emph {et~al.}(2013)\citenamefont {Albash},
\citenamefont {Lidar}, \citenamefont {Marvian},\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {T.}~\bibnamefont
{Albash}}, \bibinfo {author} {\bibfnamefont {D.~A.}\ \bibnamefont {Lidar}},
\bibinfo {author} {\bibfnamefont {M.}~\bibnamefont {Marvian}}, \ and\
\bibinfo {author} {\bibfnamefont {P.}~\bibnamefont {Zanardi}},\ }\bibfield
{title} {\enquote {\bibinfo {title} {Fluctuation theorems for quantum
processes},}\ }\href {https://doi.org/10.1103/PhysRevE.88.032146} {\bibfield
{journal} {\bibinfo  {journal} {Phys. Rev. E}\ }\textbf {\bibinfo {volume}
{88}},\ \bibinfo {pages} {032146--} (\bibinfo {year} {2013})}\BibitemShut
\bibitem [{\citenamefont {Albash}\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {T.}~\bibnamefont
{Albash}}\ and\ \bibinfo {author} {\bibfnamefont {D.~A.}\ \bibnamefont
{Lidar}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Adiabatic quantum
computation},}\ }\href {https://doi.org/10.1103/RevModPhys.90.015002}
{\bibfield  {journal} {\bibinfo  {journal} {Reviews of Modern Physics}\
}\textbf {\bibinfo {volume} {90}},\ \bibinfo {pages} {015002--} (\bibinfo
{year} {2018})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Alicki}\ \emph {et~al.}(2007)\citenamefont {Alicki},
\citenamefont {Fannes},\ and\ \citenamefont {Horodecki}}]{Alicki:07a}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {R.}~\bibnamefont
{Alicki}}, \bibinfo {author} {\bibfnamefont {M.}~\bibnamefont {Fannes}}, \
and\ \bibinfo {author} {\bibfnamefont {M.}~\bibnamefont {Horodecki}},\
}\bibfield  {title} {\enquote {\bibinfo {title} {A statistical mechanics view
on kitaev's proposal for quantum memories},}\ }\href
{http://dx.doi.org/10.1088/1751-8113/40/24/012} {\bibfield  {journal}
{\bibinfo  {journal} {Journal of Physics A: Mathematical and Theoretical}\
}\textbf {\bibinfo {volume} {40}},\ \bibinfo {pages} {6451--6467} (\bibinfo
{year} {2007})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Bombin}(2010)}]{Bombin:2010aa}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {H.}~\bibnamefont
{Bombin}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Topological
subsystem codes},}\ }\href {https://doi.org/10.1103/PhysRevA.81.032301}
{\bibfield  {journal} {\bibinfo  {journal} {Physical Review A}\ }\textbf
{\bibinfo {volume} {81}},\ \bibinfo {pages} {032301--} (\bibinfo {year}
{2010})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Altshuler}\ \emph {et~al.}(2010)\citenamefont
{Altshuler}, \citenamefont {Krovi},\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {B.}~\bibnamefont
{Altshuler}}, \bibinfo {author} {\bibfnamefont {H.}~\bibnamefont {Krovi}}, \
and\ \bibinfo {author} {\bibfnamefont {J.}~\bibnamefont {Roland}},\
}\bibfield  {title} {\enquote {\bibinfo {title} {Anderson localization makes
adiabatic quantum optimization fail},}\ }\href
{https://doi.org/10.1073/pnas.1002116107} {\bibfield  {journal} {\bibinfo
{journal} {Proceedings of the National Academy of Sciences}\ }\textbf
{\bibinfo {volume} {107}},\ \bibinfo {pages} {12446--12450} (\bibinfo {year}
{2010})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Reed}\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {M.}~\bibnamefont
{Reed}}\ and\ \bibinfo {author} {\bibfnamefont {B.}~\bibnamefont {Simon}},\
}\href {https://books.google.com/books?id=14XvAAAAMAAJ} {\emph {\bibinfo
{title} {{Methods of Modern Mathematical Physics: Fourier analysis,
self-adjointness}}}},\ Vol.~\bibinfo {volume} {2}\ (\bibinfo  {publisher}
{Academic Press},\ \bibinfo {year} {1975})\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Alzer}(1997)}]{Alzer:1997}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {H.}~\bibnamefont
{Alzer}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {On some
inequalities for the incomplete gamma function},}\ }\href
{https://doi.org/10.1090/S0025-5718-97-00814-4} {\bibfield  {journal}
{\bibinfo  {journal} {Mathematics of Computation}\ }\textbf {\bibinfo
{volume} {66}},\ \bibinfo {pages} {771} (\bibinfo {year} {1997})}\BibitemShut
\end{thebibliography}%

\nocite{apsrev41Control}
%merlin.mbs apsrev4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked
%Control: key (0)
%Control: author (72) initials jnrlst
%Control: editor formatted (1) identically to author
%Control: production of article title (0) allowed
%Control: page (1) range
%Control: year (0) verbatim
%Control: production of eprint (0) enabled
\begin{thebibliography}{82}%
\makeatletter
\providecommand \@ifxundefined [1]{%
\@ifx{#1\undefined}
\providecommand \@ifnum [1]{%
\ifnum #1\expandafter \@firstoftwo
\else \expandafter \@secondoftwo
\fi
\providecommand \@ifx [1]{%
\ifx #1\expandafter \@firstoftwo
\else \expandafter \@secondoftwo
\fi
\providecommand \natexlab [1]{#1}%
\providecommand \enquote  [1]{``#1''}%
\providecommand \bibnamefont  [1]{#1}%
\providecommand \bibfnamefont [1]{#1}%
\providecommand \citenamefont [1]{#1}%
\providecommand \href@noop [0]{\@secondoftwo}%
\providecommand \href [0]{\begingroup \@sanitize@url \@href}%
\providecommand \@href[1]{\@@startlink{#1}\@@href}%
\providecommand \@@href[1]{\endgroup#1\@@endlink}%
\providecommand \@sanitize@url [0]{\catcode `\\12\catcode `\$12\catcode
`\&12\catcode `\#12\catcode `\^12\catcode `\_12\catcode `\%12\relax}%
\providecommand \@@startlink[1]{}%
\providecommand \@@endlink[0]{}%
\providecommand \url  [0]{\begingroup\@sanitize@url \@url }%
\providecommand \@url [1]{\endgroup\@href {#1}{\urlprefix }}%
\providecommand \urlprefix  [0]{URL }%
\providecommand \Eprint [0]{\href }%
\providecommand \doibase [0]{http://dx.doi.org/}%
\providecommand \selectlanguage [0]{\@gobble}%
\providecommand \bibinfo  [0]{\@secondoftwo}%
\providecommand \bibfield  [0]{\@secondoftwo}%
\providecommand \translation [1]{[#1]}%
\providecommand \BibitemOpen [0]{}%
\providecommand \bibitemStop [0]{}%
\providecommand \bibitemNoStop [0]{.\EOS\space}%
\providecommand \EOS [0]{\spacefactor3000\relax}%
\providecommand \BibitemShut  [1]{\csname bibitem#1\endcsname}%
\let\auto@bib@innerbib\@empty
\bibitem [{\citenamefont {Alicki}\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {R.}~\bibnamefont
{Alicki}}\ and\ \bibinfo {author} {\bibfnamefont {K.}~\bibnamefont {Lendi}},\
}\href {https://doi.org/10.1007/3-540-18276-4} {\emph {\bibinfo {title}
{Quantum {Dynamical} {Semigroups} and {Applications}}}}\ (\bibinfo
{publisher} {Springer Science \& Business Media},\ \bibinfo {year}
{2007})\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Breuer}\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {H.-P.}\ \bibnamefont
{Breuer}}\ and\ \bibinfo {author} {\bibfnamefont {F.}~\bibnamefont
{Petruccione}},\ }\href
{https://doi.org/10.1093/acprof:oso/9780199213900.001.0001} {\emph {\bibinfo
{title} {The Theory of Open Quantum Systems}}}\ (\bibinfo  {publisher}
{Oxford University Press},\ \bibinfo {address} {Oxford},\ \bibinfo {year}
{2002})\BibitemShut {NoStop}%
\bibitem [{\citenamefont {{C.W. Gardiner and P.
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibnamefont {{C.W. Gardiner and P.
Zoller}}},\ }\href {https://www.springer.com/gp/book/9783540223016} {\emph
{\bibinfo {title} {{Quantum Noise}}}},\ \bibinfo {series} {Springer Series in
Synergetics}, Vol.~\bibinfo {volume} {56}\ (\bibinfo  {publisher}
{Springer},\ \bibinfo {address} {Berlin},\ \bibinfo {year}
{2000})\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Davies}(1974)}]{Davies:74}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {E.~B.}\ \bibnamefont
{Davies}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Markovian master
equations},}\ }\href {http://dx.doi.org/10.1007/BF01608389} {\bibfield
{journal} {\bibinfo  {journal} {Communications in Mathematical Physics}\
}\textbf {\bibinfo {volume} {39}},\ \bibinfo {pages} {91--110} (\bibinfo
{year} {1974})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Lindblad}(1976)}]{Lindblad:76}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {G.}~\bibnamefont
{Lindblad}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {On the
generators of quantum dynamical semigroups},}\ }\href
{http://dx.doi.org/10.1007/BF01608499} {\bibfield  {journal} {\bibinfo
{journal} {Comm. Math. Phys.}\ }\textbf {\bibinfo {volume} {48}},\ \bibinfo
{pages} {119--130} (\bibinfo {year} {1976})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Albash}\ \emph
{et~al.}(2015{\natexlab{a}})\citenamefont {Albash}, \citenamefont {Vinci},
\citenamefont {Mishra}, \citenamefont {Warburton},\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {T.}~\bibnamefont
{Albash}}, \bibinfo {author} {\bibfnamefont {W.}~\bibnamefont {Vinci}},
\bibinfo {author} {\bibfnamefont {A.}~\bibnamefont {Mishra}}, \bibinfo
{author} {\bibfnamefont {P.~A.}\ \bibnamefont {Warburton}}, \ and\ \bibinfo
{author} {\bibfnamefont {D.~A.}\ \bibnamefont {Lidar}},\ }\bibfield  {title}
{\enquote {\bibinfo {title} {Consistency tests of classical and quantum
models for a quantum annealer},}\ }\href
{https://doi.org/10.1103/PhysRevA.91.042314} {\bibfield  {journal} {\bibinfo
{journal} {Phys. Rev. A}\ }\textbf {\bibinfo {volume} {91}},\ \bibinfo
{pages} {042314--} (\bibinfo {year} {2015}{\natexlab{a}})}\BibitemShut
\bibitem [{\citenamefont {Boixo}\ \emph {et~al.}(2016)\citenamefont {Boixo},
\citenamefont {Smelyanskiy}, \citenamefont {Shabani}, \citenamefont {Isakov},
\citenamefont {Dykman}, \citenamefont {Denchev}, \citenamefont {Amin},
\citenamefont {Smirnov}, \citenamefont {Mohseni},\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {S.}~\bibnamefont
{Boixo}}, \bibinfo {author} {\bibfnamefont {V.~N.}\ \bibnamefont
{Smelyanskiy}}, \bibinfo {author} {\bibfnamefont {A.}~\bibnamefont
{Shabani}}, \bibinfo {author} {\bibfnamefont {S.~V.}\ \bibnamefont {Isakov}},
\bibinfo {author} {\bibfnamefont {M.}~\bibnamefont {Dykman}}, \bibinfo
{author} {\bibfnamefont {V.~S.}\ \bibnamefont {Denchev}}, \bibinfo {author}
{\bibfnamefont {M.~H.}\ \bibnamefont {Amin}}, \bibinfo {author}
{\bibfnamefont {A.~Y.}\ \bibnamefont {Smirnov}}, \bibinfo {author}
{\bibfnamefont {M.}~\bibnamefont {Mohseni}}, \ and\ \bibinfo {author}
{\bibfnamefont {H.}~\bibnamefont {Neven}},\ }\bibfield  {title} {\enquote
{\bibinfo {title} {Computational multiqubit tunnelling in programmable
quantum annealers},}\ }\href {http://dx.doi.org/10.1038/ncomms10327}
{\bibfield  {journal} {\bibinfo  {journal} {Nat Commun}\ }\textbf {\bibinfo
{volume} {7}} (\bibinfo {year} {2016})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Albash}\ \emph
{et~al.}(2015{\natexlab{b}})\citenamefont {Albash}, \citenamefont {Hen},
\citenamefont {Spedalieri},\ and\ \citenamefont {Lidar}}]{Albash:2015pd}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {T.}~\bibnamefont
{Albash}}, \bibinfo {author} {\bibfnamefont {I.}~\bibnamefont {Hen}},
\bibinfo {author} {\bibfnamefont {F.~M.}\ \bibnamefont {Spedalieri}}, \ and\
\bibinfo {author} {\bibfnamefont {D.~A.}\ \bibnamefont {Lidar}},\ }\bibfield
{title} {\enquote {\bibinfo {title} {Reexamination of the evidence for
entanglement in a quantum annealer},}\ }\href
{https://doi.org/10.1103/PhysRevA.92.062328} {\bibfield  {journal} {\bibinfo
{journal} {Physical Review A}\ }\textbf {\bibinfo {volume} {92}},\ \bibinfo
{pages} {062328--} (\bibinfo {year} {2015}{\natexlab{b}})}\BibitemShut
\bibitem [{\citenamefont {Mishra}\ \emph {et~al.}(2018)\citenamefont {Mishra},
\citenamefont {Albash},\ and\ \citenamefont {Lidar}}]{Mishra:2018}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {A.}~\bibnamefont
{Mishra}}, \bibinfo {author} {\bibfnamefont {T.}~\bibnamefont {Albash}}, \
and\ \bibinfo {author} {\bibfnamefont {D.~A.}\ \bibnamefont {Lidar}},\
}\bibfield  {title} {\enquote {\bibinfo {title} {Finite temperature quantum
annealing solving exponentially small gap problem with non-monotonic success
probability},}\ }\href {https://doi.org/10.1038/s41467-018-05239-9}
{\bibfield  {journal} {\bibinfo  {journal} {Nature Communications}\ }\textbf
{\bibinfo {volume} {9}},\ \bibinfo {pages} {2917} (\bibinfo {year}
{2018})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Feynman}\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {R.}~\bibnamefont
{Feynman}}\ and\ \bibinfo {author} {\bibfnamefont {F.}~\bibnamefont
{Vernon}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {The theory of a
general quantum system interacting with a linear dissipative system},}\
}\href {https://doi.org/10.1016/0003-4916(63)90068-X} {\bibfield  {journal}
{\bibinfo  {journal} {Annals of Physics}\ }\textbf {\bibinfo {volume} {24}},\
\bibinfo {pages} {118 -- 173} (\bibinfo {year} {1963})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Caldeira}\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {A.}~\bibnamefont
{Caldeira}}\ and\ \bibinfo {author} {\bibfnamefont {A.}~\bibnamefont
{Leggett}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Quantum
tunnelling in a dissipative system},}\ }\href
{http://dx.doi.org/10.1016/0003-4916(83)90202-6} {\bibfield  {journal}
{\bibinfo  {journal} {Annals of Physics}\ }\textbf {\bibinfo {volume}
{149}},\ \bibinfo {pages} {374 -- 456} (\bibinfo {year} {1983})}\BibitemShut
\bibitem [{\citenamefont {Makarov}\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {D.~E.}\ \bibnamefont
{Makarov}}\ and\ \bibinfo {author} {\bibfnamefont {N.}~\bibnamefont
{Makri}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Path integrals
for dissipative systems by tensor multiplication. condensed phase quantum
dynamics for arbitrarily long time},}\ }\href
{https://doi.org/10.1016/0009-2614(94)00275-4} {\bibfield  {journal}
{\bibinfo  {journal} {Chemical Physics Letters}\ }\textbf {\bibinfo {volume}
{221}},\ \bibinfo {pages} {482 -- 491} (\bibinfo {year} {1994})}\BibitemShut
\bibitem [{\citenamefont {Sim}(2001)}]{Eunji:2001}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {E.}~\bibnamefont
{Sim}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Quantum dynamics
for a system coupled to slow baths: On-the-fly filtered propagator method},}\
}\href {https://doi.org/10.1063/1.1394208} {\bibfield  {journal} {\bibinfo
{journal} {The Journal of Chemical Physics}\ }\textbf {\bibinfo {volume}
{115}},\ \bibinfo {pages} {4450--4456} (\bibinfo {year} {2001})}\BibitemShut
\bibitem [{\citenamefont {{K. Kraus}}(1983)}]{Kraus:book}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibnamefont {{K. Kraus}}},\ }\href
{https://doi.org/10.1007/3-540-12732-1} {\emph {\bibinfo {title} {{States,
Effects, and Operations}}}}\ (\bibinfo  {publisher} {{Springer}},\ \bibinfo
{address} {{Berlin}},\ \bibinfo {year} {1983})\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Dominy}\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {J.~M.}\ \bibnamefont
{Dominy}}\ and\ \bibinfo {author} {\bibfnamefont {D.~A.}\ \bibnamefont
{Lidar}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Beyond complete
positivity},}\ }\href {http://dx.doi.org/10.1007/s11128-015-1228-1}
{\bibfield  {journal} {\bibinfo  {journal} {{Quant. Inf. Proc.}}\ }\textbf
{\bibinfo {volume} {15}},\ \bibinfo {pages} {1349} (\bibinfo {year}
{2016})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Gorini}\ \emph {et~al.}(1978)\citenamefont {Gorini},
\citenamefont {Frigerio}, \citenamefont {Verri}, \citenamefont
{Kossakowski},\ and\ \citenamefont {Sudarshan}}]{gorini_properties_1978}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {V.}~\bibnamefont
{Gorini}}, \bibinfo {author} {\bibfnamefont {A.}~\bibnamefont {Frigerio}},
\bibinfo {author} {\bibfnamefont {M.}~\bibnamefont {Verri}}, \bibinfo
{author} {\bibfnamefont {A.}~\bibnamefont {Kossakowski}}, \ and\ \bibinfo
{author} {\bibfnamefont {E.~C.~G.}\ \bibnamefont {Sudarshan}},\ }\bibfield
{title} {\enquote {\bibinfo {title} {Properties of quantum {Markovian} master
equations},}\ }\href {http://dx.doi.org/10.1016/0034-4877(78)90050-2}
{\bibfield  {journal} {\bibinfo  {journal} {Reports on Mathematical Physics}\
}\textbf {\bibinfo {volume} {13}},\ \bibinfo {pages} {149--173} (\bibinfo
{year} {1978})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {{S. Nakajima}}(1958)}]{Nakajima:58}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibnamefont {{S. Nakajima}}},\
}\bibfield  {title} {\enquote {\bibinfo {title} {{On Quantum Theory of
Transport Phenomena : Steady Diffusion}},}\ }\href
{https://doi.org/10.1143/PTP.20.948} {\bibfield  {journal} {\bibinfo
{journal} {Prog. Theor. Phys.}\ }\textbf {\bibinfo {volume} {20}},\ \bibinfo
{pages} {948} (\bibinfo {year} {1958})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Zwanzig}(1960)}]{Zwanzig:60a}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {R.}~\bibnamefont
{Zwanzig}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {{Ensemble
Method in the Theory of Irreversibility}},}\ }\href
{https://doi.org/10.1063/1.1731409} {\bibfield  {journal} {\bibinfo
{journal} {J. Chem. Phys.}\ }\textbf {\bibinfo {volume} {33}},\ \bibinfo
{pages} {1338} (\bibinfo {year} {1960})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Redfield}(1965)}]{Redfield:66}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {A.}~\bibnamefont
{Redfield}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {The theory of
relaxation processes},}\ }in\ \href
{https://doi.org/10.1016/B978-1-4832-3114-3.50007-6} {\emph {\bibinfo
{booktitle} {Advances in Magnetic Resonance}}},\ \bibinfo {series} {Advances
in Magnetic and Optical Resonance}, Vol.~\bibinfo {volume} {1},\ \bibinfo
{editor} {edited by\ \bibinfo {editor} {\bibfnamefont {J.~S.}\ \bibnamefont
{Waugh}}}\ (\bibinfo  {publisher} {Academic Press},\ \bibinfo {year} {1965})\
pp.\ \bibinfo {pages} {1 -- 32}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Bacon}\ \emph {et~al.}(1999)\citenamefont {Bacon},
\citenamefont {Lidar},\ and\ \citenamefont {Whaley}}]{PhysRevA.60.1944}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {D.}~\bibnamefont
{Bacon}}, \bibinfo {author} {\bibfnamefont {D.~A.}\ \bibnamefont {Lidar}}, \
and\ \bibinfo {author} {\bibfnamefont {K.~B.}\ \bibnamefont {Whaley}},\
}\bibfield  {title} {\enquote {\bibinfo {title} {Robustness of
decoherence-free subspaces for quantum computation},}\ }\href
{http://dx.doi.org/10.1103/PhysRevA.60.1944} {\bibfield  {journal} {\bibinfo
{journal} {Phys. Rev. A}\ }\textbf {\bibinfo {volume} {60}},\ \bibinfo
{pages} {1944--1955} (\bibinfo {year} {1999})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {van Wonderen}\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {A.~J.}\ \bibnamefont
{van Wonderen}}\ and\ \bibinfo {author} {\bibfnamefont {K.}~\bibnamefont
{Lendi}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Virtues and
limitations of markovian master equations with a time-dependent generator},}\
}\href {http://dx.doi.org/10.1023/A:1018671424739} {\bibfield  {journal}
{\bibinfo  {journal} {J. Stat. Phys.}\ }\textbf {\bibinfo {volume} {100}},\
\bibinfo {pages} {633--658} (\bibinfo {year} {2000})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Lidar}\ \emph {et~al.}(2001)\citenamefont {Lidar},
\citenamefont {Bihary},\ and\ \citenamefont {Whaley}}]{Lidar200135}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {D.~A.}\ \bibnamefont
{Lidar}}, \bibinfo {author} {\bibfnamefont {Z.}~\bibnamefont {Bihary}}, \
and\ \bibinfo {author} {\bibfnamefont {K.}~\bibnamefont {Whaley}},\
}\bibfield  {title} {\enquote {\bibinfo {title} {From completely positive
maps to the quantum \uppercase{M}arkovian semigroup master equation},}\
}\href {http://dx.doi.org/10.1016/S0301-0104(01)00330-5} {\bibfield
{journal} {\bibinfo  {journal} {Chem. Phys.}\ }\textbf {\bibinfo {volume}
{268}},\ \bibinfo {pages} {35} (\bibinfo {year} {2001})}\BibitemShut
\bibitem [{\citenamefont {{S. Daffer, K. Wodkiewicz, J.D. Cresser, J.K.
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibnamefont {{S. Daffer, K.
Wodkiewicz, J.D. Cresser, J.K. McIver}}},\ }\bibfield  {title} {\enquote
{\bibinfo {title} {{Depolarizing channel as a completely positive map with
memory}},}\ }\href {https://doi.org/10.1103/PhysRevA.70.010304} {\bibfield
{journal} {\bibinfo  {journal} {Phys. Rev. A}\ }\textbf {\bibinfo {volume}
{70}},\ \bibinfo {pages} {{010304(R)}} (\bibinfo {year} {2004})}\BibitemShut
\bibitem [{\citenamefont {Shabani}\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {A.}~\bibnamefont
{Shabani}}\ and\ \bibinfo {author} {\bibfnamefont {D.~A.}\ \bibnamefont
{Lidar}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Completely
positive post-markovian master equation via a measurement approach},}\ }\href
{https://doi.org/10.1103/PhysRevA.71.020101} {\bibfield  {journal} {\bibinfo
{journal} {Phys. Rev. A}\ }\textbf {\bibinfo {volume} {71}},\ \bibinfo
{pages} {020101(R)} (\bibinfo {year} {2005})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {{S. Maniscalco and F.
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibnamefont {{S. Maniscalco and F.
Petruccione}}},\ }\bibfield  {title} {\enquote {\bibinfo {title}
{{Non-Markovian dynamics of a qubit}},}\ }\href
{https://doi.org/10.1103/PhysRevA.73.012111} {\bibfield  {journal} {\bibinfo
{journal} {Phys. Rev. A}\ }\textbf {\bibinfo {volume} {73}},\ \bibinfo
{pages} {012111} (\bibinfo {year} {2006})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Piilo}\ \emph {et~al.}(2008)\citenamefont {Piilo},
\citenamefont {Maniscalco}, \citenamefont {H{\"a}rk{\"o}nen},\ and\
\citenamefont {Suominen}}]{piilo2008non}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {J.}~\bibnamefont
{Piilo}}, \bibinfo {author} {\bibfnamefont {S.}~\bibnamefont {Maniscalco}},
\bibinfo {author} {\bibfnamefont {K.}~\bibnamefont {H{\"a}rk{\"o}nen}}, \
and\ \bibinfo {author} {\bibfnamefont {K.-A.}\ \bibnamefont {Suominen}},\
}\bibfield  {title} {\enquote {\bibinfo {title} {Non-markovian quantum
jumps},}\ }\href {https://doi.org/10.1103/PhysRevLett.100.180402} {\bibfield
{journal} {\bibinfo  {journal} {Physical Review Letters}\ }\textbf {\bibinfo
{volume} {100}},\ \bibinfo {pages} {180402--} (\bibinfo {year}
{2008})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Breuer}\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {H.-P.}\ \bibnamefont
{Breuer}}\ and\ \bibinfo {author} {\bibfnamefont {B.}~\bibnamefont
{Vacchini}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Quantum
semi-markov processes},}\ }\href
{https://doi.org/10.1103/PhysRevLett.101.140402} {\bibfield  {journal}
{\bibinfo  {journal} {Physical Review Letters}\ }\textbf {\bibinfo {volume}
{101}},\ \bibinfo {pages} {140402--} (\bibinfo {year} {2008})}\BibitemShut
\bibitem [{\citenamefont {Whitney}(2008)}]{Whitney:2008aa}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {R.~S.}\ \bibnamefont
{Whitney}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Staying
positive: going beyond lindblad with perturbative master equations},}\ }\href
{https://doi.org/10.1088/1751-8113/41/17/175304} {\bibfield  {journal}
{\bibinfo  {journal} {Journal of Physics A: Mathematical and Theoretical}\
}\textbf {\bibinfo {volume} {41}},\ \bibinfo {pages} {175304} (\bibinfo
{year} {2008})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Wu}\ \emph {et~al.}(2009)\citenamefont {Wu},
\citenamefont {Kurizki},\ and\ \citenamefont {Brumer}}]{Wu09}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {L.-A.}\ \bibnamefont
{Wu}}, \bibinfo {author} {\bibfnamefont {G.}~\bibnamefont {Kurizki}}, \ and\
\bibinfo {author} {\bibfnamefont {P.}~\bibnamefont {Brumer}},\ }\bibfield
{title} {\enquote {\bibinfo {title} {Master equation and control of an open
quantum system with leakage},}\ }\href
{https://doi.org/10.1103/PhysRevLett.102.080405} {\bibfield  {journal}
{\bibinfo  {journal} {Physical Review Letters}\ }\textbf {\bibinfo {volume}
{102}},\ \bibinfo {pages} {080405--} (\bibinfo {year} {2009})}\BibitemShut
\bibitem [{\citenamefont {Chru\ifmmode \acute{s}\else
\'{s}\fi{}ci\ifmmode~\acute{n}\else \'{n}\fi{}ski}\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {D.}~\bibnamefont
{Chru\ifmmode \acute{s}\else \'{s}\fi{}ci\ifmmode~\acute{n}\else
\'{n}\fi{}ski}}\ and\ \bibinfo {author} {\bibfnamefont {A.}~\bibnamefont
{Kossakowski}},\ }\bibfield  {title} {\enquote {\bibinfo {title}
{Non-markovian quantum dynamics: Local versus nonlocal},}\ }\href
{https://doi.org/10.1103/PhysRevLett.104.070406} {\bibfield  {journal}
{\bibinfo  {journal} {Phys. Rev. Lett.}\ }\textbf {\bibinfo {volume} {104}},\
\bibinfo {pages} {070406} (\bibinfo {year} {2010})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Albash}\ \emph {et~al.}(2012)\citenamefont {Albash},
\citenamefont {Boixo}, \citenamefont {Lidar},\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {T.}~\bibnamefont
{Albash}}, \bibinfo {author} {\bibfnamefont {S.}~\bibnamefont {Boixo}},
\bibinfo {author} {\bibfnamefont {D.~A.}\ \bibnamefont {Lidar}}, \ and\
\bibinfo {author} {\bibfnamefont {P.}~\bibnamefont {Zanardi}},\ }\bibfield
{title} {\enquote {\bibinfo {title} {{Quantum adiabatic Markovian master
equations}},}\ }\href {http://dx.doi.org/10.1088/1367-2630/14/12/123016}
{\bibfield  {journal} {\bibinfo  {journal} {New J. of Phys.}\ }\textbf
{\bibinfo {volume} {14}},\ \bibinfo {pages} {123016} (\bibinfo {year}
{2012})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Mozgunov}(2016)}]{Mozgunov:2016aa}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {E.}~\bibnamefont
{Mozgunov}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Local master
equation for small temperatures},}\ }\href {http://arXiv.org/abs/1611.04188}
{\bibfield  {journal} {\bibinfo  {journal} {arXiv:1611.04188}\ } (\bibinfo
{year} {2016})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Smirnov}\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {A.~Y.}\ \bibnamefont
{Smirnov}}\ and\ \bibinfo {author} {\bibfnamefont {M.~H.}\ \bibnamefont
{Amin}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Theory of open
quantum dynamics with hybrid noise},}\ }\href
{https://doi.org/10.1088/1367-2630/aae79c} {\bibfield  {journal} {\bibinfo
{journal} {New Journal of Physics}\ }\textbf {\bibinfo {volume} {20}},\
\bibinfo {pages} {103037} (\bibinfo {year} {2018})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Dann}\ \emph {et~al.}(2018)\citenamefont {Dann},
\citenamefont {Levy},\ and\ \citenamefont {Kosloff}}]{Kosloff:2018}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {R.}~\bibnamefont
{Dann}}, \bibinfo {author} {\bibfnamefont {A.}~\bibnamefont {Levy}}, \ and\
\bibinfo {author} {\bibfnamefont {R.}~\bibnamefont {Kosloff}},\ }\bibfield
{title} {\enquote {\bibinfo {title} {Time-dependent markovian quantum master
equation},}\ }\href {\doibase 10.1103/PhysRevA.98.052129} {\bibfield
{journal} {\bibinfo  {journal} {Phys. Rev. A}\ }\textbf {\bibinfo {volume}
{98}},\ \bibinfo {pages} {052129} (\bibinfo {year} {2018})}\BibitemShut
\bibitem [{\citenamefont {Venuti}\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {L.~C.}\ \bibnamefont
{Venuti}}\ and\ \bibinfo {author} {\bibfnamefont {D.~A.}\ \bibnamefont
{Lidar}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Error reduction
in quantum annealing using boundary cancellation: Only the end matters},}\
}\href {\doibase 10.1103/PhysRevA.98.022315} {\bibfield  {journal} {\bibinfo
{journal} {Phys. Rev. A}\ }\textbf {\bibinfo {volume} {98}},\ \bibinfo
{pages} {022315} (\bibinfo {year} {2018})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {McCauley}\ \emph {et~al.}(2019)\citenamefont
{McCauley}, \citenamefont {Cruikshank}, \citenamefont {Bondar},\ and\
\citenamefont {Jacobs}}]{McCauley:19}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {G.}~\bibnamefont
{McCauley}}, \bibinfo {author} {\bibfnamefont {B.}~\bibnamefont
{Cruikshank}}, \bibinfo {author} {\bibfnamefont {D.~I.}\ \bibnamefont
{Bondar}}, \ and\ \bibinfo {author} {\bibfnamefont {K.}~\bibnamefont
{Jacobs}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Completely
positive, accurate master equation for weakly-damped quantum systems across
all regimes},}\ }\href {https://arxiv.org/abs/1906.08279} {\bibfield
{journal} {\bibinfo  {journal} {arXiv:1906.08279}\ } (\bibinfo {year}
{2019})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Benatti}\ \emph {et~al.}(2009)\citenamefont
{Benatti}, \citenamefont {Floreanini},\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {F.}~\bibnamefont
{Benatti}}, \bibinfo {author} {\bibfnamefont {R.}~\bibnamefont {Floreanini}},
\ and\ \bibinfo {author} {\bibfnamefont {U.}~\bibnamefont {Marzolino}},\
}\bibfield  {title} {\enquote {\bibinfo {title} {Environment-induced
entanglement in a refined weak-coupling limit},}\ }\href
{https://doi.org/10.1209/0295-5075/88/20011} {\bibfield  {journal} {\bibinfo
{journal} {{EPL} (Europhysics Letters)}\ }\textbf {\bibinfo {volume} {88}},\
\bibinfo {pages} {20011} (\bibinfo {year} {2009})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Benatti}\ \emph {et~al.}(2010)\citenamefont
{Benatti}, \citenamefont {Floreanini},\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {F.}~\bibnamefont
{Benatti}}, \bibinfo {author} {\bibfnamefont {R.}~\bibnamefont {Floreanini}},
\ and\ \bibinfo {author} {\bibfnamefont {U.}~\bibnamefont {Marzolino}},\
}\bibfield  {title} {\enquote {\bibinfo {title} {Entangling two unequal atoms
through a common bath},}\ }\href {https://doi.org/10.1103/PhysRevA.81.012105}
{\bibfield  {journal} {\bibinfo  {journal} {Phys. Rev. A}\ }\textbf {\bibinfo
{volume} {81}},\ \bibinfo {pages} {012105} (\bibinfo {year}
{2010})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Merkli}(2020)}]{Merkli_2019}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {M.}~\bibnamefont
{Merkli}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Quantum
markovian master equations: Resonance theory shows validity for all time
scales},}\ }\href {\doibase https://doi.org/10.1016/j.aop.2019.167996}
{\bibfield  {journal} {\bibinfo  {journal} {Annals of Physics}\ }\textbf
{\bibinfo {volume} {412}},\ \bibinfo {pages} {167996} (\bibinfo {year}
{2020})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Majenz}\ \emph {et~al.}(2013)\citenamefont {Majenz},
\citenamefont {Albash}, \citenamefont {Breuer},\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {C.}~\bibnamefont
{Majenz}}, \bibinfo {author} {\bibfnamefont {T.}~\bibnamefont {Albash}},
\bibinfo {author} {\bibfnamefont {H.-P.}\ \bibnamefont {Breuer}}, \ and\
\bibinfo {author} {\bibfnamefont {D.~A.}\ \bibnamefont {Lidar}},\ }\bibfield
{title} {\enquote {\bibinfo {title} {Coarse graining can beat the
rotating-wave approximation in quantum markovian master equations},}\ }\href
{https://doi.org/10.1103/PhysRevA.88.012103} {\bibfield  {journal} {\bibinfo
{journal} {Phys. Rev. A}\ }\textbf {\bibinfo {volume} {88}},\ \bibinfo
{pages} {012103--} (\bibinfo {year} {2013})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Cubitt}\ \emph {et~al.}(2015)\citenamefont {Cubitt},
\citenamefont {Lucia}, \citenamefont {Michalakis},\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {T.~S.}\ \bibnamefont
{Cubitt}}, \bibinfo {author} {\bibfnamefont {A.}~\bibnamefont {Lucia}},
\bibinfo {author} {\bibfnamefont {S.}~\bibnamefont {Michalakis}}, \ and\
\bibinfo {author} {\bibfnamefont {D.}~\bibnamefont {Perez-Garcia}},\
}\bibfield  {title} {\enquote {\bibinfo {title} {Stability of local quantum
dissipative systems},}\ }\href {https://doi.org/10.1007/s00220-015-2355-3}
{\bibfield  {journal} {\bibinfo  {journal} {Communications in Mathematical
Physics}\ }\textbf {\bibinfo {volume} {337}},\ \bibinfo {pages} {1275--1315}
(\bibinfo {year} {2015})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Knill}(2005)}]{Knill:05}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {E.}~\bibnamefont
{Knill}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Quantum computing
with realistically noisy devices},}\ }\href
{http://dx.doi.org/10.1038/nature03350} {\bibfield  {journal} {\bibinfo
{journal} {Nature}\ }\textbf {\bibinfo {volume} {434}},\ \bibinfo {pages}
{39--44} (\bibinfo {year} {2005})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Alicki}\ \emph {et~al.}(2006)\citenamefont {Alicki},
\citenamefont {Lidar},\ and\ \citenamefont {Zanardi}}]{PhysRevA.73.052311}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {R.}~\bibnamefont
{Alicki}}, \bibinfo {author} {\bibfnamefont {D.~A.}\ \bibnamefont {Lidar}}, \
and\ \bibinfo {author} {\bibfnamefont {P.}~\bibnamefont {Zanardi}},\
}\bibfield  {title} {\enquote {\bibinfo {title} {Internal consistency of
fault-tolerant quantum error correction in light of rigorous derivations of
the quantum markovian limit},}\ }\href
{http://dx.doi.org/10.1103/PhysRevA.73.052311} {\bibfield  {journal}
{\bibinfo  {journal} {Phys. Rev. A}\ }\textbf {\bibinfo {volume} {73}},\
\bibinfo {pages} {052311} (\bibinfo {year} {2006})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Lidar}(2019)}]{Lidar:2019aa}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {D.~A.}\ \bibnamefont
{Lidar}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Lecture notes on
the theory of open quantum systems},}\ }\href
{https://arxiv.org/abs/1902.00967} {\bibfield  {journal} {\bibinfo  {journal}
{arXiv preprint arXiv:1902.00967}\ } (\bibinfo {year} {2019})}\BibitemShut
\bibitem [{\citenamefont {Albash}\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {T.}~\bibnamefont
{Albash}}\ and\ \bibinfo {author} {\bibfnamefont {D.~A.}\ \bibnamefont
{Lidar}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Decoherence in
adiabatic quantum computation},}\ }\href
{https://doi.org/10.1103/PhysRevA.91.062320} {\bibfield  {journal} {\bibinfo
{journal} {Phys. Rev. A}\ }\textbf {\bibinfo {volume} {91}},\ \bibinfo
{pages} {062320--} (\bibinfo {year} {2015})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {{\v{Z}}nidari{\v{c}}}(2010)}]{Znidaric:10}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {M.}~\bibnamefont
{{\v{Z}}nidari{\v{c}}}},\ }\bibfield  {title} {\enquote {\bibinfo {title}
{Dephasing-induced diffusive transport in the anisotropic heisenberg
model},}\ }\href {https://doi.org/10.1088/1367-2630/12/4/043001} {\bibfield
{journal} {\bibinfo  {journal} {New Journal of Physics}\ }\textbf {\bibinfo
{volume} {12}},\ \bibinfo {pages} {043001} (\bibinfo {year}
{2010})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Medvedyeva}\ \emph {et~al.}(2016)\citenamefont
{Medvedyeva}, \citenamefont {Prosen},\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {M.~V.}\ \bibnamefont
{Medvedyeva}}, \bibinfo {author} {\bibfnamefont {T.}~\bibnamefont {Prosen}},
\ and\ \bibinfo {author} {\bibfnamefont {M.}~\bibnamefont
{\v{Z}nidari\v{c}}},\ }\bibfield  {title} {\enquote {\bibinfo {title}
{Influence of dephasing on many-body localization},}\ }\href
{https://doi.org/10.1103/PhysRevB.93.094205} {\bibfield  {journal} {\bibinfo
{journal} {Phys. Rev. B}\ }\textbf {\bibinfo {volume} {93}},\ \bibinfo
{pages} {094205} (\bibinfo {year} {2016})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {{R. Bhatia}}(1997)}]{Bhatia:book}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibnamefont {{R. Bhatia}}},\
}\href@noop {} {\emph {\bibinfo {title} {{Matrix Analysis}}}},\ \bibinfo
{series} {{Graduate Texts in Mathematics}}\ No.\ \bibinfo {number} {169}\
(\bibinfo  {publisher} {Springer-Verlag},\ \bibinfo {address} {{New York}},\
\bibinfo {year} {1997})\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Gaspard}\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {P.}~\bibnamefont
{Gaspard}}\ and\ \bibinfo {author} {\bibfnamefont {M.}~\bibnamefont
{Nagaoka}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Slippage of
initial conditions for the redfield master equation},}\ }\href
{https://doi.org/10.1063/1.479867} {\bibfield  {journal} {\bibinfo  {journal}
{Journal of Chemical Physics}\ }\textbf {\bibinfo {volume} {111}},\ \bibinfo
{pages} {5668--5675} (\bibinfo {year} {1999})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Vidal}(2003)}]{Vidalsolo:03}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {G.}~\bibnamefont
{Vidal}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Efficient
classical simulation of slightly entangled quantum computations},}\ }\href
{https://doi.org/10.1103/PhysRevLett.91.147902} {\bibfield  {journal}
{\bibinfo  {journal} {Phys. Rev. Lett.}\ }\textbf {\bibinfo {volume} {91}},\
\bibinfo {pages} {147902} (\bibinfo {year} {2003})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Verstraete}\ \emph {et~al.}(2004)\citenamefont
{Verstraete}, \citenamefont {Garcia-Ripoll},\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {F.}~\bibnamefont
{Verstraete}}, \bibinfo {author} {\bibfnamefont {J.~J.}\ \bibnamefont
{Garcia-Ripoll}}, \ and\ \bibinfo {author} {\bibfnamefont {J.~I.}\
\bibnamefont {Cirac}},\ }\bibfield  {title} {\enquote {\bibinfo {title}
{Matrix product density operators: Simulation of finite-temperature and
dissipative systems},}\ }\href
{https://doi.org/10.1103/PhysRevLett.93.207204} {\bibfield  {journal}
{\bibinfo  {journal} {Phys. Rev. Lett.}\ }\textbf {\bibinfo {volume} {93}},\
\bibinfo {pages} {207204} (\bibinfo {year} {2004})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {{E. H. Lieb and D.W. Robinson}}(1972)}]{Lieb:72}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibnamefont {{E. H. Lieb and D.W.
Robinson}}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {The finite
group velocity of quantum spin systems},}\ }\href
{https://doi.org/10.1007/BF01645779} {\bibfield  {journal} {\bibinfo
{journal} {{Commun. Math. Phys.}}\ }\textbf {\bibinfo {volume} {28}},\
\bibinfo {pages} {251} (\bibinfo {year} {1972})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {{Haah}}\ \emph {et~al.}(2018)\citenamefont {{Haah}},
\citenamefont {{Hastings}}, \citenamefont {{Kothari}},\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {J.}~\bibnamefont
{{Haah}}}, \bibinfo {author} {\bibfnamefont {M.}~\bibnamefont {{Hastings}}},
\bibinfo {author} {\bibfnamefont {R.}~\bibnamefont {{Kothari}}}, \ and\
\bibinfo {author} {\bibfnamefont {G.~H.}\ \bibnamefont {{Low}}},\ }\bibfield
{title} {\enquote {\bibinfo {title} {Quantum algorithm for simulating real
time evolution of lattice hamiltonians},}\ }in\ \href
{https://doi.org/10.1109/FOCS.2018.00041} {\emph {\bibinfo {booktitle} {2018
IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS)}}}\
(\bibinfo {year} {2018})\ pp.\ \bibinfo {pages} {350--360}\BibitemShut
\bibitem [{\citenamefont {Pichler}\ \emph {et~al.}(2010)\citenamefont
{Pichler}, \citenamefont {Daley},\ and\ \citenamefont {Zoller}}]{Pichler:10}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {H.}~\bibnamefont
{Pichler}}, \bibinfo {author} {\bibfnamefont {A.~J.}\ \bibnamefont {Daley}},
\ and\ \bibinfo {author} {\bibfnamefont {P.}~\bibnamefont {Zoller}},\
}\bibfield  {title} {\enquote {\bibinfo {title} {Nonequilibrium dynamics of
bosonic atoms in optical lattices: Decoherence of many-body states due to
spontaneous emission},}\ }\href {https://doi.org/10.1103/PhysRevA.82.063605}
{\bibfield  {journal} {\bibinfo  {journal} {Phys. Rev. A}\ }\textbf {\bibinfo
{volume} {82}},\ \bibinfo {pages} {063605} (\bibinfo {year}
{2010})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {{L.-M Duan and G.-C. Guo}}(1998)}]{Duan:98}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibnamefont {{L.-M Duan and G.-C.
Guo}}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {{Reducing
decoherence in quantum-computer memory with all quantum bits coupling to the
same environment}},}\ }\href {https://doi.org/10.1103/PhysRevA.57.737}
{\bibfield  {journal} {\bibinfo  {journal} {Phys. Rev. A}\ }\textbf {\bibinfo
{volume} {57}},\ \bibinfo {pages} {737} (\bibinfo {year} {1998})}\BibitemShut
\bibitem [{\citenamefont {Zanardi}\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {P.}~\bibnamefont
{Zanardi}}\ and\ \bibinfo {author} {\bibfnamefont {M.}~\bibnamefont
{Rasetti}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Noiseless
quantum codes},}\ }\href {https://doi.org/10.1103/PhysRevLett.79.3306}
{\bibfield  {journal} {\bibinfo  {journal} {{Phys.~Rev.~Lett.}}\ }\textbf
{\bibinfo {volume} {79}},\ \bibinfo {pages} {3306--3309} (\bibinfo {year}
{1997})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Lidar}\ \emph {et~al.}(1998)\citenamefont {Lidar},
\citenamefont {Chuang},\ and\ \citenamefont {Whaley}}]{Lidar:1998fk}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {D.~A.}\ \bibnamefont
{Lidar}}, \bibinfo {author} {\bibfnamefont {I.~L.}\ \bibnamefont {Chuang}}, \
and\ \bibinfo {author} {\bibfnamefont {K.~B.}\ \bibnamefont {Whaley}},\
}\bibfield  {title} {\enquote {\bibinfo {title} {Decoherence-free subspaces
for quantum computation},}\ }\href
{https://doi.org/10.1103/PhysRevLett.81.2594} {\bibfield  {journal} {\bibinfo
{journal} {Phys. Rev. Lett.}\ }\textbf {\bibinfo {volume} {81}},\ \bibinfo
{pages} {2594--2597} (\bibinfo {year} {1998})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Lidar}\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {D.~A.}\ \bibnamefont
{Lidar}}\ and\ \bibinfo {author} {\bibfnamefont {K.~B.}\ \bibnamefont
{Whaley}},\ }\enquote {\bibinfo {title} {Decoherence-free subspaces and
subsystems},}\ in\ \href {https://www.springer.com/us/book/9783540402237}
{\emph {\bibinfo {booktitle} {Irreversible Quantum Dynamics}}},\ \bibinfo
{series} {Lecture Notes in Physics}, Vol.\ \bibinfo {volume} {622},\ \bibinfo
{editor} {edited by\ \bibinfo {editor} {\bibfnamefont {F.}~\bibnamefont
{Benatti}}\ and\ \bibinfo {editor} {\bibfnamefont {R.}~\bibnamefont
{Floreanini}}}\ (\bibinfo  {publisher} {Springer},\ \bibinfo {address}
{Berlin},\ \bibinfo {year} {2003})\ p.~\bibinfo {pages} {83}\BibitemShut
\bibitem [{\citenamefont {{P.G. Kwiat, A.J. Berglund, J.B. Altepeter, and A.G.
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibnamefont {{P.G. Kwiat, A.J.
Berglund, J.B. Altepeter, and A.G. White}}},\ }\bibfield  {title} {\enquote
{\bibinfo {title} {{Experimental Verification of Decoherence-Free
Subspaces}},}\ }\href {https://doi.org/10.1126/science.290.5491.498}
{\bibfield  {journal} {\bibinfo  {journal} {Science}\ }\textbf {\bibinfo
{volume} {290}},\ \bibinfo {pages} {498} (\bibinfo {year}
{2000})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Viola}\ \emph {et~al.}(2001)\citenamefont {Viola},
\citenamefont {Fortunato}, \citenamefont {Pravia}, \citenamefont {Knill},
\citenamefont {Laflamme},\ and\ \citenamefont {Cory}}]{Viola:2001sp}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {L.}~\bibnamefont
{Viola}}, \bibinfo {author} {\bibfnamefont {E.~M.}\ \bibnamefont
{Fortunato}}, \bibinfo {author} {\bibfnamefont {M.~A.}\ \bibnamefont
{Pravia}}, \bibinfo {author} {\bibfnamefont {E.}~\bibnamefont {Knill}},
\bibinfo {author} {\bibfnamefont {R.}~\bibnamefont {Laflamme}}, \ and\
\bibinfo {author} {\bibfnamefont {D.~G.}\ \bibnamefont {Cory}},\ }\bibfield
{title} {\enquote {\bibinfo {title} {Experimental realization of noiseless
subsystems for quantum information processing},}\ }\href
{https://doi.org/10.1126/science.1064460} {\bibfield  {journal} {\bibinfo
{journal} {Science}\ }\textbf {\bibinfo {volume} {293}},\ \bibinfo {pages}
{2059--2063} (\bibinfo {year} {2001})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Kielpinski}\ \emph {et~al.}(2001)\citenamefont
{Kielpinski}, \citenamefont {Meyer}, \citenamefont {Rowe}, \citenamefont
{Sackett}, \citenamefont {Itano}, \citenamefont {Monroe},\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {D.}~\bibnamefont
{Kielpinski}}, \bibinfo {author} {\bibfnamefont {V.}~\bibnamefont {Meyer}},
\bibinfo {author} {\bibfnamefont {M.~A.}\ \bibnamefont {Rowe}}, \bibinfo
{author} {\bibfnamefont {C.~A.}\ \bibnamefont {Sackett}}, \bibinfo {author}
{\bibfnamefont {W.~M.}\ \bibnamefont {Itano}}, \bibinfo {author}
{\bibfnamefont {C.}~\bibnamefont {Monroe}}, \ and\ \bibinfo {author}
{\bibfnamefont {D.~J.}\ \bibnamefont {Wineland}},\ }\bibfield  {title}
{\enquote {\bibinfo {title} {A decoherence-free quantum memory using trapped
ions},}\ }\href {https://doi.org/10.1126/science.1057357} {\bibfield
{journal} {\bibinfo  {journal} {Science}\ }\textbf {\bibinfo {volume}
{291}},\ \bibinfo {pages} {1013--1015} (\bibinfo {year} {2001})}\BibitemShut
\bibitem [{\citenamefont {Ollerenshaw}\ \emph {et~al.}(2003)\citenamefont
{Ollerenshaw}, \citenamefont {Lidar},\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {J.~E.}\ \bibnamefont
{Ollerenshaw}}, \bibinfo {author} {\bibfnamefont {D.~A.}\ \bibnamefont
{Lidar}}, \ and\ \bibinfo {author} {\bibfnamefont {L.~E.}\ \bibnamefont
{Kay}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Magnetic resonance
realization of decoherence-free quantum computation},}\ }\href
{http://dx.doi.org/10.1103/PhysRevLett.91.217904} {\bibfield  {journal}
{\bibinfo  {journal} {Phys. Rev. Lett.}\ }\textbf {\bibinfo {volume} {91}},\
\bibinfo {pages} {217904} (\bibinfo {year} {2003})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Viola}\ and\ \citenamefont {Lloyd}(1998)}]{Viola:98}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {L.}~\bibnamefont
{Viola}}\ and\ \bibinfo {author} {\bibfnamefont {S.}~\bibnamefont {Lloyd}},\
}\bibfield  {title} {\enquote {\bibinfo {title} {Dynamical suppression of
decoherence in two-state quantum systems},}\ }\href
{http://dx.doi.org/10.1103/PhysRevA.58.2733} {\bibfield  {journal} {\bibinfo
{journal} {Phys. Rev. A}\ }\textbf {\bibinfo {volume} {58}},\ \bibinfo
{pages} {2733--2744} (\bibinfo {year} {1998})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Zanardi}(1999)}]{Zanardi:1999fk}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {P.}~\bibnamefont
{Zanardi}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Symmetrizing
evolutions},}\ }\href {http://dx.doi.org/10.1016/S0375-9601(99)00365-5}
{\bibfield  {journal} {\bibinfo  {journal} {Physics Letters A}\ }\textbf
{\bibinfo {volume} {258}},\ \bibinfo {pages} {77--82} (\bibinfo {year}
{1999})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Lidar}\ and\ \citenamefont
\BibitemOpen
\bibinfo {editor} {\bibfnamefont {D.}~\bibnamefont {Lidar}}\ and\ \bibinfo
{editor} {\bibfnamefont {T.}~\bibnamefont {Brun}},\ eds.,\ \href
{http://www.cambridge.org/9780521897877} {\emph {\bibinfo {title} {Quantum
Error Correction}}}\ (\bibinfo  {publisher} {Cambridge University Press},\
\bibinfo {address} {{Cambridge, UK}},\ \bibinfo {year} {2013})\BibitemShut
\bibitem [{\citenamefont {Suter}\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {D.}~\bibnamefont
{Suter}}\ and\ \bibinfo {author} {\bibfnamefont {G.~A.}\ \bibnamefont
{{\'A}lvarez}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Colloquium:
Protecting quantum information against environmental noise},}\ }\href
{https://doi.org/10.1103/RevModPhys.88.041001} {\bibfield  {journal}
{\bibinfo  {journal} {Reviews of Modern Physics}\ }\textbf {\bibinfo {volume}
{88}},\ \bibinfo {pages} {041001--} (\bibinfo {year} {2016})}\BibitemShut
\bibitem [{\citenamefont {Ng}\ \emph {et~al.}(2011)\citenamefont {Ng},
\citenamefont {Lidar},\ and\ \citenamefont {Preskill}}]{Ng:2011dn}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {H.~K.}\ \bibnamefont
{Ng}}, \bibinfo {author} {\bibfnamefont {D.~A.}\ \bibnamefont {Lidar}}, \
and\ \bibinfo {author} {\bibfnamefont {J.}~\bibnamefont {Preskill}},\
}\bibfield  {title} {\enquote {\bibinfo {title} {Combining dynamical
decoupling with fault-tolerant quantum computation},}\ }\href
{https://doi.org/10.1103/PhysRevA.84.012305} {\bibfield  {journal} {\bibinfo
{journal} {Phys. Rev. A}\ }\textbf {\bibinfo {volume} {84}},\ \bibinfo
{pages} {012305--} (\bibinfo {year} {2011})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Szczygielski}\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {K.}~\bibnamefont
{Szczygielski}}\ and\ \bibinfo {author} {\bibfnamefont {R.}~\bibnamefont
{Alicki}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Markovian theory
of dynamical decoupling by periodic control},}\ }\href
{https://doi.org/10.1103/PhysRevA.92.022349} {\bibfield  {journal} {\bibinfo
{journal} {Physical Review A}\ }\textbf {\bibinfo {volume} {92}},\ \bibinfo
{pages} {022349--} (\bibinfo {year} {2015})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Gough}\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {J.~E.}\ \bibnamefont
{Gough}}\ and\ \bibinfo {author} {\bibfnamefont {H.~I.}\ \bibnamefont
{Nurdin}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Can quantum
markov evolutions ever be dynamically decoupled?}}\ }in\ \href
{https://doi.org/10.1109/CDC.2017.8264587} {\emph {\bibinfo {booktitle} {2017
IEEE 56th Annual Conference on Decision and Control (CDC)}}}\ (\bibinfo
{year} {2017})\ pp.\ \bibinfo {pages} {6155--6160}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Addis}\ \emph {et~al.}(2015)\citenamefont {Addis},
\citenamefont {Ciccarello}, \citenamefont {Cascio}, \citenamefont {Palma},\
and\ \citenamefont {Maniscalco}}]{Addis:2015aa}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {C.}~\bibnamefont
{Addis}}, \bibinfo {author} {\bibfnamefont {F.}~\bibnamefont {Ciccarello}},
\bibinfo {author} {\bibfnamefont {M.}~\bibnamefont {Cascio}}, \bibinfo
{author} {\bibfnamefont {G.~M.}\ \bibnamefont {Palma}}, \ and\ \bibinfo
{author} {\bibfnamefont {S.}~\bibnamefont {Maniscalco}},\ }\bibfield  {title}
{\enquote {\bibinfo {title} {Dynamical decoupling efficiency versus quantum
non-markovianity},}\ }\href
{http://dx.doi.org/10.1088/1367-2630/17/12/123004} {\bibfield  {journal}
{\bibinfo  {journal} {New Journal of Physics}\ }\textbf {\bibinfo {volume}
{17}},\ \bibinfo {pages} {123004} (\bibinfo {year} {2015})}\BibitemShut
\bibitem [{\citenamefont {Arenz}\ \emph {et~al.}(2018)\citenamefont {Arenz},
\citenamefont {Burgarth}, \citenamefont {Facchi},\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {C.}~\bibnamefont
{Arenz}}, \bibinfo {author} {\bibfnamefont {D.}~\bibnamefont {Burgarth}},
\bibinfo {author} {\bibfnamefont {P.}~\bibnamefont {Facchi}}, \ and\ \bibinfo
{author} {\bibfnamefont {R.}~\bibnamefont {Hillier}},\ }\bibfield  {title}
{\enquote {\bibinfo {title} {Dynamical decoupling of unbounded
hamiltonians},}\ }\bibfield  {booktitle} {\emph {\bibinfo {booktitle}
{Journal of Mathematical Physics}},\ }\href
{https://doi.org/10.1063/1.5016495} {\bibfield  {journal} {\bibinfo
{journal} {Journal of Mathematical Physics}\ }\textbf {\bibinfo {volume}
{59}},\ \bibinfo {pages} {032203} (\bibinfo {year} {2018})}\BibitemShut
\bibitem [{\citenamefont {Li}\ \emph {et~al.}(2018)\citenamefont {Li},
\citenamefont {Hall},\ and\ \citenamefont {Wiseman}}]{Li:2018aa}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {L.}~\bibnamefont
{Li}}, \bibinfo {author} {\bibfnamefont {M.~J.~W.}\ \bibnamefont {Hall}}, \
and\ \bibinfo {author} {\bibfnamefont {H.~M.}\ \bibnamefont {Wiseman}},\
}\bibfield  {title} {\enquote {\bibinfo {title} {Concepts of quantum
non-markovianity: A hierarchy},}\ }\bibfield  {booktitle} {\emph {\bibinfo
{booktitle} {Concepts of quantum non-Markovianity: A hierarchy}},\ }\href
{https://doi.org/10.1016/j.physrep.2018.07.001} {\bibfield  {journal}
{\bibinfo  {journal} {Physics Reports}\ }\textbf {\bibinfo {volume} {759}},\
\bibinfo {pages} {1--51} (\bibinfo {year} {2018})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {de~Vega}\ \emph {et~al.}(2010)\citenamefont
{de~Vega}, \citenamefont {Ba{\~n}uls},\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {I.}~\bibnamefont
{de~Vega}}, \bibinfo {author} {\bibfnamefont {M.~C.}\ \bibnamefont
{Ba{\~n}uls}}, \ and\ \bibinfo {author} {\bibfnamefont {A.}~\bibnamefont
{P{\'e}rez}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Effects of
dissipation on an adiabatic quantum search algorithm},}\ }\href
{https://doi.org/10.1088/1367-2630/12/12/123010} {\bibfield  {journal}
{\bibinfo  {journal} {New J. of Phys.}\ }\textbf {\bibinfo {volume} {12}},\
\bibinfo {pages} {123010} (\bibinfo {year} {2010})}\BibitemShut {NoStop}%
\bibitem [{url()}]{urlCode}%
\BibitemOpen
\href@noop {} {}\bibinfo {howpublished}
{\url{https://github.com/mvjenia/CGMEcode}},\ \bibinfo {note} {code for the
numerical section of the paper}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Isserlis}(1916)}]{Isserlis:1916}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {L.}~\bibnamefont
{Isserlis}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {On certain
probable errors and correlation coefficients of multiple frequency
distributions with skew regression},}\ }\href
{https://doi.org/10.1093/biomet/11.3.185} {\bibfield  {journal} {\bibinfo
{journal} {Biometrika}\ }\textbf {\bibinfo {volume} {11}},\ \bibinfo {pages}
{185} (\bibinfo {year} {1916})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Albash}\ \emph {et~al.}(2013)\citenamefont {Albash},
\citenamefont {Lidar}, \citenamefont {Marvian},\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {T.}~\bibnamefont
{Albash}}, \bibinfo {author} {\bibfnamefont {D.~A.}\ \bibnamefont {Lidar}},
\bibinfo {author} {\bibfnamefont {M.}~\bibnamefont {Marvian}}, \ and\
\bibinfo {author} {\bibfnamefont {P.}~\bibnamefont {Zanardi}},\ }\bibfield
{title} {\enquote {\bibinfo {title} {Fluctuation theorems for quantum
processes},}\ }\href {https://doi.org/10.1103/PhysRevE.88.032146} {\bibfield
{journal} {\bibinfo  {journal} {Phys. Rev. E}\ }\textbf {\bibinfo {volume}
{88}},\ \bibinfo {pages} {032146--} (\bibinfo {year} {2013})}\BibitemShut
\bibitem [{\citenamefont {Albash}\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {T.}~\bibnamefont
{Albash}}\ and\ \bibinfo {author} {\bibfnamefont {D.~A.}\ \bibnamefont
{Lidar}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Adiabatic quantum
computation},}\ }\href {https://doi.org/10.1103/RevModPhys.90.015002}
{\bibfield  {journal} {\bibinfo  {journal} {Reviews of Modern Physics}\
}\textbf {\bibinfo {volume} {90}},\ \bibinfo {pages} {015002--} (\bibinfo
{year} {2018})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Alicki}\ \emph {et~al.}(2007)\citenamefont {Alicki},
\citenamefont {Fannes},\ and\ \citenamefont {Horodecki}}]{Alicki:07a}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {R.}~\bibnamefont
{Alicki}}, \bibinfo {author} {\bibfnamefont {M.}~\bibnamefont {Fannes}}, \
and\ \bibinfo {author} {\bibfnamefont {M.}~\bibnamefont {Horodecki}},\
}\bibfield  {title} {\enquote {\bibinfo {title} {A statistical mechanics view
on kitaev's proposal for quantum memories},}\ }\href
{http://dx.doi.org/10.1088/1751-8113/40/24/012} {\bibfield  {journal}
{\bibinfo  {journal} {Journal of Physics A: Mathematical and Theoretical}\
}\textbf {\bibinfo {volume} {40}},\ \bibinfo {pages} {6451--6467} (\bibinfo
{year} {2007})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Bombin}(2010)}]{Bombin:2010aa}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {H.}~\bibnamefont
{Bombin}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Topological
subsystem codes},}\ }\href {https://doi.org/10.1103/PhysRevA.81.032301}
{\bibfield  {journal} {\bibinfo  {journal} {Physical Review A}\ }\textbf
{\bibinfo {volume} {81}},\ \bibinfo {pages} {032301--} (\bibinfo {year}
{2010})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Altshuler}\ \emph {et~al.}(2010)\citenamefont
{Altshuler}, \citenamefont {Krovi},\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {B.}~\bibnamefont
{Altshuler}}, \bibinfo {author} {\bibfnamefont {H.}~\bibnamefont {Krovi}}, \
and\ \bibinfo {author} {\bibfnamefont {J.}~\bibnamefont {Roland}},\
}\bibfield  {title} {\enquote {\bibinfo {title} {Anderson localization makes
adiabatic quantum optimization fail},}\ }\href
{https://doi.org/10.1073/pnas.1002116107} {\bibfield  {journal} {\bibinfo
{journal} {Proceedings of the National Academy of Sciences}\ }\textbf
{\bibinfo {volume} {107}},\ \bibinfo {pages} {12446--12450} (\bibinfo {year}
{2010})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Reed}\ and\ \citenamefont
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {M.}~\bibnamefont
{Reed}}\ and\ \bibinfo {author} {\bibfnamefont {B.}~\bibnamefont {Simon}},\
}\href {https://books.google.com/books?id=14XvAAAAMAAJ} {\emph {\bibinfo
{title} {{Methods of Modern Mathematical Physics: Fourier analysis,
self-adjointness}}}},\ Vol.~\bibinfo {volume} {2}\ (\bibinfo  {publisher}
{Academic Press},\ \bibinfo {year} {1975})\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Alzer}(1997)}]{Alzer:1997}%
\BibitemOpen
\bibfield  {author} {\bibinfo {author} {\bibfnamefont {H.}~\bibnamefont
{Alzer}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {On some
inequalities for the incomplete gamma function},}\ }\href
{https://doi.org/10.1090/S0025-5718-97-00814-4} {\bibfield  {journal}
{\bibinfo  {journal} {Mathematics of Computation}\ }\textbf {\bibinfo
{volume} {66}},\ \bibinfo {pages} {771} (\bibinfo {year} {1997})}\BibitemShut
\end{thebibliography}%

\end{document}

%% End of file `elsarticle-template-1-num.tex'.