††thanks: Editor and topical group convener††thanks: Editor and topical group
convener††thanks: Editor and topical group convener

#  Report of the Snowmass 2021 Theory Frontier Topical Group on
Quantum Information Science for HEP

Simon Catterall<EMAIL_ADDRESS>Department of Physics, Syracuse University,
Syracuse NY 13244, USA  Roni Harnik<EMAIL_ADDRESS>Theory Division, Fermi
National Accelerator Laboratory, Batavia, IL 60510, USA  Superconducting
Quantum Materials and Systems Center (SQMS), Fermi National Accelerator
Laboratory, Batavia, IL 60510, USA  Veronika E. Hubeny<EMAIL_ADDRESS>Center for Quantum Mathematics and Physics (QMAP)
Department of Physics & Astronomy, University of California, Davis CA, USA
Christian W. Bauer  Ernest Orlando Lawrence Berkeley National Laboratory, &
Berkeley Center for Theoretical Physics,
Department of Physics, University of California, Berkeley, CA 94720, USA
Asher Berlin  Theory Division, Fermi National Accelerator Laboratory, Batavia,
IL 60510, USA  Zohreh Davoudi  Maryland Center for Fundamental Physics and
Department of Physics, University of Maryland, College Park, MD 20742, USA
Institute for Robust Quantum Simulation, University of Maryland, College Park,
Maryland 20742, USA  Thomas Faulkner  Department of Physics, University of
Illinois Urbana-Champaign, Urbana, IL 61801, USA  Thomas Hartman  Department
of Physics, Cornell University, Ithaca NY, USA  Matthew Headrick  Martin
Fisher School of Physics, Brandeis University, Waltham MA, USA  Yonatan F.
Kahn  Department of Physics, University of Illinois Urbana-Champaign, Urbana,
IL 61801, USA  Illinois Center for Advanced Studies of the Universe,
University of Illinois Urbana-Champaign, Urbana, IL 61801, USA
Superconducting Quantum Materials and Systems Center (SQMS), Fermi National
Accelerator Laboratory, Batavia, IL 60510, USA  Henry Lamm  Theory Division,
Fermi National Accelerator Laboratory, Batavia, IL 60510, USA  Yannick Meurice
Department of Physics and Astronomy, University of Iowa, Iowa City, Iowa
52242, USA  Surjeet Rajendran  Department of Physics and Astronomy, The Johns
Hopkins University, Baltimore, MD 21218, USA  Mukund Rangamani  Center for
Quantum Mathematics and Physics (QMAP)
Department of Physics & Astronomy, University of California, Davis CA, USA
Brian Swingle  Martin Fisher School of Physics, Brandeis University, Waltham
MA, USA

###### Abstract

We summarise current and future applications of quantum information science to
theoretical high energy physics. Three main themes are identified and
discussed; quantum simulation, quantum sensors and formal aspects of the
connection between quantum information and gravity. Within these themes, there
are important research questions and opportunities to address them in the
years and decades ahead. Efforts in developing a diverse quantum workforce are
also discussed. This work summarises the subtopical area Quantum Information
for HEP TF10 which forms part of the Theory Frontier report for the Snowmass
2021 planning process.

—

_Submitted to the Proceedings of the US Community Study_

_on the Future of Particle Physics (Snowmass 2021)_

###### Contents

  1. I Executive Summary
  2. II Quantum Simulation for High Energy Physics
    1. II.1 Towards simulation of QCD and  other gauge theories
    2. II.2 Tensor networks
    3. II.3 Simple holographic lattice models
    4. II.4 Future near-term goals
  3. III Theory for Quantum Sensing of Fundamental Physics
    1. III.1 Fundamental physics targets
    2. III.2 Theory for sensing experiments
    3. III.3 Outlook
  4. IV Formal Aspects of Quantum Information and Fundamental Physics
    1. IV.1 Change of perspective
    2. IV.2 Recent developments
    3. IV.3 Outlook
  5. V Quantum Workforce Development
  6. VI Acknowledgements

##  I Executive Summary

Ideas and methods of quantum information science have found wide application
to theoretical high energy physics in recent years. This report divides those
aspects into three main themes; quantum simulation, quantum sensors and the
application of ideas in quantum information to formal aspects of quantum field
theories (QFTs) and gravity.

Understanding the theoretical aspects of quantum information in quantum
gravity and quantum field theories has catalyzed vibrant cross-disciplinary
collaborations (e.g. between the lattice gauge theory and quantum gravity
communities) and revealed new phenomena and organizational principles. There
are many types of avenues for exploration, ranging from the concrete (e.g.
what happens dynamically in a particular system), to organizational (e.g. what
attribute of a given system is relevant or useful in characterizing it), to
exploratory (e.g. how does these various attributes’ behavior depend on the
system), to mathematical (e.g. how does one actually define a certain quantity
or meaningfully generalize it from its original formulation). Although the
central focus is different in each of these avenues, they are interlinked, and
progress in one informs the others. This has opened up a vast and wonderful
new theoretical playground.

Complementary to these formal developments there have been extensive efforts
to develop the framework and algorithms needed to simulate QFTs on quantum
computers. The difficulties in simulating quantum theories classically
motivate simulation on a quantum computer Feynman (1982); Jordan  _et al._
(2018); Carena  _et al._ (2020). Quantum simulation has the potential to
explore non-perturbative physics in theories and regimes that have previously
been inaccessible to classical computing. Examples include probing the real
time dynamics of hadronic collisions and associated non-perturbative phenomena
such as fragmentation and hadronization in particle colliders, the
determination of the neutron star equation of state from finite density QCD,
measuring the viscosity of the QCD quark-gluon plasma, or simulating chiral
fermions in beyond-the-Standard-Model (BSM) theories.

Current efforts are centered about understanding the best truncation schemes
for gauge theories, and the development of efficient classical Hamiltonian
simulation methods such as tensor networks in higher dimensions including
fermions and their role in developing efficient quantum simulation algorithms.
Theoretical work in HEP is needed to identify the simplest paths that will
bring us closer to simulating the QFTs of interest to particle physicists.
These efforts should, in addition, provide interesting benchmarks for the
quantum computing community as devices are being developed. Indeed, HEP
theorists have developed active collaborations with quantum hardware
developers both in universities and private companies.

The third strand of this report focuses on the development of quantum sensors.
Here there is an opportunity, even in the near term, to leverage the
technology that is developed for QIS to directly search for new physics,
including searching for new particles, dark matter, and gravitational waves.
Theorists have been instrumental in making interesting connections between
quantum sensing technologies and fundamental physics.

In addition to research at the HEP-QIS interface, there is a need to develop
and train a workforce in that US which is diverse and well-versed in the tools
of quantum information science. To this end, HEP theorists are involved in
workforce development efforts Bauer  _et al._ (2022) which we will comment
upon.

This synergy between QIS and HEP benefits both fields. HEP theorists will be
needed to build new bridges and establish existing connections between
fundamental physics and quantum science. The research directions presented in
this summary are relatively new, but are ambitious. New surprises are surely
ahead.

##  II Quantum Simulation for High Energy Physics

There are a wide variety of problems in high energy physics that cannot be
addressed using classical computation. These include real time scattering
processes, finite density strongly interacting matter and theories of BSM
physics that incorporate supersymmetry or chiral fermions. Monte Carlo
simulation of the path integral representing these quantum systems fails as a
computational method because of the infamous sign problem. Hamiltonian
approaches using classical computation suffer from the fact that the relevant
Hilbert spaces grow exponentially with the number of degrees of freedom which
rapidly renders them beyond the reach of classical computers. In contrast, a
quantum computer is capable, in principle, of representing dynamics on such
spaces with a number of quantum bits that increases only linearly with the
number of degrees of freedom. Furthermore quantum operations ideally retain
quantum correlations and effectively perform massively parallel computations
on the encoded wavefunction.

However the practical application of quantum computers to such problems faces
several immediate problems. First, the quantum field theories (QFTs) that
describe such systems possess an infinite numbers of degrees of freedom. Thus
before one can contemplate simulating such a system with a quantum computer
one must first truncate the theory. In classical Monte Carlo simulation one
introduces a lattice in spacetime as part of this process. For quantum
computation one also needs to effect a truncation in the field space. This
latter truncation or digitization should preserve as much symmetry as
possible. This is particularly true in the case of gauge theories where
violations of gauge symmetry have the potential to ruin unitarity and
consistency of the theory. Furthermore, the truncated theory should retain a
simple local encoding in terms of the elementary quantum bits or qubits that
form the building blocks of the quantum computer.

Recent work has also been devoted to the problem of simulating scattering from
first principles. It is believed that all relevant scattering and
hadronization processes can be simulated on a quantum computer using resources
that scale only polynomially with the system size Jordan  _et al._ (2012).
Quantum simulations potentially offer an ab initio method for understanding
these non-perturbative phenomena that are crucial for interpreting the results
of collider experiments Bauer  _et al._ (2021a).

Parton distribution functions (PDFs) involve a matrix element of two quark
fields separated by a light-like direction, which can not be calculated using
traditional lattice field theory techniques directly due to a sign problem,
although several indirect methods have been successfully developed in recent
years Constantinou  _et al._ (2022). Quantum computers give rise to the
possibility to compute the matrix element relevant for the PDFs directly and
from first principles. Several proposals have been put forward in recent years
to demonstrate how PDFs can be accessed on a quantum computer Lamm  _et al._
(2020a); Echevarria  _et al._ (2021); Li  _et al._ (2021); Mueller  _et al._
(2020); Qian  _et al._ (2021). At this stage, it is not clear what the
realistic computational resource requirements are for computing PDFs and
hadronic tensor to given accuracy, as the complete algorithms, including that
needed for preparation of hadronic states in QCD on a quantum computer, are
either non-existing or premature. PDFs can also be computed using effective
field theories describing the collinear and soft physics in jet-like collider
events Bauer  _et al._ (2021a). Another example of important long-distance
effects in collider events is collinear radiation, which traditionally is
described by parton-shower algorithms see e.g., Ref. Bauer and Schwartz
(2007). The very nature of a probabilistic Markov-Chain algorithm makes
including quantum-interference effects challenging, since collider events
typically contain a very large number of final-state particles. This problem,
therefore, is also a suitable candidate for quantum simulation. A quantum
algorithm has been developed in Ref. Bauer  _et al._ (2021b) that reproduces
the regular parton shower, while by computing all possible amplitudes at the
same time, it also includes quantum-interference effects, see also Refs.
Williams  _et al._ (2021); Gustafson  _et al._ (2022) for more progress.

There are two related approaches to quantum simulation that have been explored
which can be loosely termed analog and digital simulation. In both cases one
maps the physical system of interest to hardware whose quantum dynamics is
capable of solving or simulating the original theory. In the case of analog
simulation the hardware is tailored to the problem at hand and requires
substantial modification to solve a different problem. The digital case more
closely corresponds to a classical computer with elementary unitary quantum
gates acting on quantum states represented by qubits, or qudits (in cases
where the hardware allows for more than a binary representation). It is
possible to show, in analogy with classical logic, that any quantum
computation can be carried out with just a handful of one and two qubit or
qudit gates.

A quantum circuit then plays the role of the program that describes the
precise sequence of gates and the configuration of qubits that are needed to
simulate a given Hamiltonian. Like in classical computing, it should be
possible to change the circuit relatively easily in a high level programming
language to solve new problems in a manner which is agnostic about the
underlying hardware. There are many types of hardware platform that are
currently being investigated for quantum simulation including ultra cold atoms
in optical lattices Zohar  _et al._ (2016); Bermudez  _et al._ (2010);
Laflamme  _et al._ (2016); Meurice (2011); Bazavov  _et al._ (2015);
Tagliacozzo  _et al._ (2013a), trapped ions Davoudi  _et al._ (2020a); Monroe
_et al._ (2021); Nguyen  _et al._ (2022) including a proposal to construct
such a trapped ion machine using a storage ring Brooks (2022), superconducting
circuits on a chip Martinez  _et al._ (2016a); Lamm  _et al._ (2019);
Raychowdhury and Stryker (2020a); Gustafson  _et al._ (2019a), superconducting
bulk cavities Alam  _et al._ (2022); Kurkcuoglu  _et al._ (2021) and
configurable Rydberg atom arrays Keesling  _et al._ (2019); Bernien  _et al._
(2017); Notarnicola  _et al._ (2020); Celi  _et al._ (2020); Surace  _et al._
(2020); Meurice (2021a). Gate fidelities, coherence times, the number of
available qubits, and the feasibility for qudit encodings, all vary
significantly across these difference platforms and at this time it is not
clear which type of platform(s) will ultimately prove most effective for the
quantum simulation of high energy physics theories.

Figure 1 which is taken from a recent Snowmass white paper et al. (2007) gives
an overview of the physics drives, methodologies and strategies that are being
employed in the application of quantum simulation to high energy physics.

Figure 1: Physics drives, methodologies and strategies for quantum simulation
in HEP, from et al. (2007).

A variety of approaches are currently being explored for Hamiltonian
simulation such as the original Kogut-Susskind formulation of Hamiltonian
lattice gauge theory Kogut and Susskind (1975), efforts to find optimal bases
for truncation such as those derived from tensor networks Liu  _et al._
(2013); Meurice  _et al._ (2022a, b), pre-potential and loop-string-hadron
formulations Mathur  _et al._ (2010); Raychowdhury and Stryker (2020a),
quantum link models Wiese (2013, 2021), and qubit regularizations Bhattacharya
_et al._ (2020). A great deal of work is focused on strategies to retain gauge
invariance even in the presence of basis truncation, correct for finite time
step errors and reduce the effects of noise. A detailed review of these topics
can be found in a recent white paper Bauer  _et al._ (2022).

Once one has fixed the truncation scheme it is straightforward to implement a
discrete time evolution operator via Suzuki-Trotter decomposition which
factorizes the unitary rotations associated with different non-commuting parts
of the Hamiltonian. The optimal decomposition of terms to simulatable terms,
the ordering of such terms, and the amount of errors one expects from
digitization schemes constitute an area of research for both general
Hamiltonians and the Hamiltonian of gauge theories of Standard Model, see
e.g., Refs. Shaw  _et al._ (2020); Ciavarella  _et al._ (2021a); Paulson  _et
al._ (2021); Kan and Nam (2021); Nguyen  _et al._ (2022). The basic elements
of a digital circuit are single-qubit rotations (Pauli operators) and CNOT
gates acting on a pair of qubits which flip the target qubit when the control
qubit is in the $\ket{1}$ state.

The general aim of the field in recent years has been to explore the different
approaches to quantum simulation for a variety of simple QFTs with the goal of
figuring out the best truncation schemes and evolution algorithms that can
ultimately be scaled to gauge theories including fermions in (3+1) dimensions.
It is particularly important in this regard to understand the limitations of
what is possible on NISQ era machines which possess limited numbers of qubits
and no error correction.

Paralleling these developments in quantum simulation of QFTs there is strong
evidence (see section III) of a holographic connection between strongly
entangled quantum systems and gravity. This is visible in the original AdS/CFT
correspondence Maldacena (1998), the Ryu-Takayanagi proposal for entanglement
entropy in holographic systems Ryu and Takayanagi (2006a) and applying ideas
in quantum entanglement to black holes in AdS spacetime Van Raamsdonk (2010).
These topics and other more recent work are summarized in a recent Snowmass
white paper Faulkner  _et al._ (2022). Efforts are also underway to explore
these ideas using classical and ultimately quantum simulation of spin and
gauge models on discrete tessellations of hyperbolic space (Wick rotated AdS
space) Asaduzzaman  _et al._ (2020, 2021). Such models are also closely
connected to MERA tensor network models that have been proposed for building
highly entangled ground states of many body systems Evenbly and Vidal (2011)
and play an important role in certain proposals for quantum error correction
Pastawski  _et al._ (2015).

###  II.1 Towards simulation of QCD and
other gauge theories

Gauge theories are one of the pillars of the standard model. Strongly coupled
gauge theories are a target for exploration with high performance computing,
using both classical methods - lattice QCD (LQCD) and, in the future, with
quantum devices. However to make use of future quantum computers requires the
development of new ways to represent QFTs that can be mapped to quantum
hardware and new algorithms to carry out simulations that go well beyond what
has been done with classical computers.

A natural starting point for gauge theory is the Kogut-Susskind formulation of
Hamiltonian lattice gauge theory Kogut and Susskind (1975) (though there are
alternatives as are described below). Even with a Hamiltonian one wishes to
simulate, there are interesting conceptual challenges need to be resolved to
make such simulations feasible in the future, as well as technical problems at
the interface of theory and design. HEP theorists are clearly critical to
address the challenges in this new field. In some cases the decades of
accumulated knowledge in LQCD can be leveraged, yet some problems are
inherently related to quantum simulation and require completely new ideas.

#### Discretization of space:

To turn the infinite-dimensional Hilbert space of quantum field theories into
finite-dimensional system that quantum computers can simulate, one necessary
step is to discretize continuous spatial dimensions into a finite-volume
lattice Kogut (1983); Kogut and Susskind (1975); Kogut (1979), inevitably
leading to discretization errors and finite-volume effects. Such
discretization reduces spacetime symmetries and introduce new operators that
modifies the nonperturbative renormalization. Investigations of approaching
the infinite-volume and continuum limits of certain QFTs have recently emerged
Carena  _et al._ (2021); Briceño  _et al._ (2021) and deserve more studies.
Most gauge theory studies consider the Kogut-Susskind Hamiltonian Kogut and
Susskind (1975), Hamiltonians with reduced discretization errors Luo  _et al._
(1999); Carlsson and McKellar (2001); Spitz and Berges (2019) will improve the
convergence towards the infinite-volume and continuum theories, which allows
quantum simulations at larger lattice spacings and smaller lattices for the
same error. Recently, quantum simulations of these improved Hamiltonians has
been initiated Carena  _et al._ (2022) where the corresponding time-evolution
operators are derived together with the construction of the quantum circuits
for a general gauge theory. Studies on the finite-volume technology in lattice
calculations have been shown powerful to access physical observables Luscher
(1986); Briceno  _et al._ (2018); Davoudi (2018); Bulava  _et al._ (2022),
which will potentially enable the mapping between the finite and infinite-
volume physics in quantum simulations of field theories.

#### Digitization of Fields:

In addition to the use of spatial lattices and discretization in time digital
simulations require truncation of the local Hilbert space at each lattice
point. Digitization represents the task of formulating, representing, and
encoding truncations for QFTs suitable for digital quantum computers. Some
natural encodings exist for fermionic degrees of freedom Jordan and Wigner
(1928); Bravyi and Kitaev (2002); Chen and Kapustin (2019). Further proposals
discuss how to map lattice fermions (e.g. Wilson and staggered) onto these
encodings Muschik  _et al._ (2017) or use gauge symmetry to eliminate the
fermions Zohar and Cirac (2018, 2019). The relative merits of each approach
are only beginning to be understood. The question of gauge boson digitization
is murkier, with complicated tradeoffs Hackett  _et al._ (2019); Alexandru
_et al._ (2019); Singh and Chandrasekharan (2019); Singh (2019); Davoudi  _et
al._ (2020b); Bhattacharya  _et al._ (2020); Alexandru  _et al._ (2022);
Barata  _et al._ (2020); Kreshchuk  _et al._ (2020a); Ji  _et al._ (2020).
Digitizing may reduce symmetries – either explicitly or through finite
truncations Zohar  _et al._ (2013a). Care must be taken as the regulated
theory may not have the original theory as its continuum limit Hasenfratz and
Niedermayer (2001a); Caracciolo  _et al._ (2001a); Hasenfratz and Niedermayer
(2001b); Patrascioiu and Seiler (1998); Krcmar  _et al._ (2016); Caracciolo
_et al._ (2001b). A particularly illustrative example of the complications
between truncations and renormalization can be found in Ref. Wilson  _et al._
(1994). Prominent proposals for digitization can be broadly classified
Gustafson  _et al._ (2020) into: Casimir dynamics Zohar  _et al._ (2012a,
2013b, 2013a); Zohar and Burrello (2015); Zohar  _et al._ (2016, 2017); Klco
_et al._ (2020); Ciavarella  _et al._ (2021b) potentially with auxillary
fields Bender  _et al._ (2018a), conformal truncation Liu and Xin (2020),
discrete groups (e.g. $D_{4}$ as a subgroup of SU(2) or $S_{1080}$ as a
subgroup of SU(3)) Hackett  _et al._ (2019); Alexandru  _et al._ (2019);
Yamamoto (2021); Ji  _et al._ (2020); Haase  _et al._ (2020), dual variables
Bazavov  _et al._ (2019, 2015); Zhang  _et al._ (2018); Unmuth-Yockey  _et
al._ (2018); Unmuth-Yockey (2019), light-front kinematics Kreshchuk  _et al._
(2020b, c), the pre-potential and loop-string-hadron formulation Mathur  _et
al._ (2010); Raychowdhury and Stryker (2020a, b); Davoudi  _et al._ (2020b),
quantum link models Wiese (2014); Luo  _et al._ (2019); Brower  _et al._
(2019); Mathis  _et al._ (2020), and qubit regularization Singh (2019); Singh
and Chandrasekharan (2019); Buser  _et al._ (2020). In tensorial
reformulations discussed in II.B, symmetry-preserving Meurice (2019, 2020)
truncations are applied to character expansions and provide controllable
finite dimensional approximations.

#### State preparation:

Given a digitization, the next obstacle is initializing strongly-coupled
quantum states in terms of fundamental fields. Much of the literature
emphasized ground-state preparation Peruzzo  _et al._ (2014); Kokail  _et al._
(2018); Abrams and Lloyd (1999); Nielsen and Chuang (2000); Wiebe and Granade
(2016); Farhi  _et al._ (2000, 2001); Kaplan  _et al._ (2017); Ciavarella and
Chernyshev (2022); Farrell  _et al._ (2022); Atas  _et al._ (2021, 2022) but
thermal and particle states have been investigated Bilgin and Boixo (2010);
Jordan  _et al._ (2012, 2014a); García-Álvarez  _et al._ (2015); Jordan  _et
al._ (2014b); Hamed Moosavian and Jordan (2018); Lamm and Lawrence (2018);
Gustafson  _et al._ (2019b, 2021a); Harmalkar  _et al._ (2020); Gustafson and
Lamm (2021); Jordan  _et al._ (2018); Klco and Savage (2019); Riera  _et al._
(2012); Brandão and Kastoryano (2019); Clemente  _et al._ (2020); Motta  _et
al._ (2020); de Jong  _et al._ (2021); Gustafson  _et al._ (2021b); Davoudi
_et al._ (2022). For methods which construct states using regulated theories,
careful study of the renormalization needed to properly match onto the
physical limit is required Maiani and Testa (1990); Bruno and Hansen (2020).

#### Time propagation:

Propagating for a time $t$ requires the application of a unitary operator
$\mathcal{U}(t)=e^{-iHt}$, which generically cannot be implemented exactly on
a quantum computer and needs to be approximated. A common method is
trotterization, whereby
$\mathcal{U}(t)\approx(\prod_{i}e^{iH_{i}t/N})^{N}\equiv(e^{-iH^{\prime}t/N})^{N}$
where $H=\sum_{i}H_{i}$ is a sum of $k$-local terms $H_{i}$, and $H^{\prime}$
is an approximation of $H$ defined via this relation, which is generally hard
to deduce. The renormalization of lattice field theory in Minkoswki spacetime
due to trotterization is to introduce a temporal lattice spacing and new
operators depending upon it Carena  _et al._ (2021). For some $H$, this allows
for efficient simulations Jordan  _et al._ (2012, 2014a, 2018); García-Álvarez
_et al._ (2015); Jordan  _et al._ (2014b); Hamed Moosavian and Jordan (2018);
Bender  _et al._ (2018a); Haah  _et al._ (2018); Du  _et al._ (2020); Childs
_et al._ (2021) and the errors from using $H^{\prime}$ can be reduced via
scale settings Carena  _et al._ (2021). Another way to reduce trotterization
error might be using Hamiltonians with reduced lattice artifacts Luo  _et al._
(1999); Carlsson and McKellar (2001); Bulava  _et al._ (2022); Carena  _et
al._ (2022). Other approximations of $\mathcal{U}(t)$ exist: QDRIFT Campbell
(2019), variational approaches Cirstoiu  _et al._ (2020); Gibbs  _et al._
(2021); Yao  _et al._ (2020), Taylor series Berry  _et al._ (2015), use of
nonlinear effects to increase the Trotter step Meurice (2021b); Gustafson  _et
al._ (2021a) and qubitization Low and Chuang (2019). Initial resource
comparisons have been performed for various gauge theories, see Refs. Shaw
_et al._ (2020); Ciavarella  _et al._ (2021a); Paulson  _et al._ (2021); Kan
and Nam (2021); Nguyen  _et al._ (2022).

#### Observables:

It is straightforward to evaluate the expectation values of instantaneous
Hermitian operators. Observables that depend on time-separated operators (such
as parton distribution functions Lamm  _et al._ (2020a); Kreshchuk  _et al._
(2020b); Echevarria  _et al._ (2020), particle decays Ciavarella (2020), and
viscosity Cohen  _et al._ (2021)) are more challenging. Naively, the first
measurement collapses the state, preventing further evolution. Ways to
overcome this have been proposed, including ancillary probe-and-control qubits
Pedernales  _et al._ (2014); Ortiz  _et al._ (2001); Lamm  _et al._ (2019,
2020a); Gustafson and Lamm (2021) and phase estimation Abrams and Lloyd
(1999); Roggero and Carlson (2018). For time-separated matrix elements, it is
still not known how to perform nonperturbative renormalization like RI/SMOM
Martinelli  _et al._ (1995); Aoki  _et al._ (2008); Sturm  _et al._ (2009) on
quantum computers.

#### Gauge invariance and errors:

Noisy quantum devices can also be viewed as introducing new operators. The
best-studied examples of this are related to gauge-violating operators
Stannigel  _et al._ (2014); Stryker (2019); Halimeh and Hauke (2019); Lamm
_et al._ (2020b); Tran  _et al._ (2020); Halimeh  _et al._ (2020a); Halimeh
and Hauke (2020); Halimeh  _et al._ (2020b, c); Van Damme  _et al._ (2020);
Kasper  _et al._ (2020); Halimeh  _et al._ (2021). Which operators are
introduced and which symmetries are broken are both hardware and digitization
dependent. In tensorial reformulations discussed in II.B, the full integration
over the gauge fields provides manifestly gauge-invariant discrete
reformulations.

—

Analog quantum simulations provide another potentially promising path to
quantum simulation of QFTs. Such simulators may naturally exhibit fermionic
and bosonic degrees of freedom, or provide tunable interactions between larger
local Hilbert. Nonetheless, one needs to engineer the interactions of these
degrees of freedom to represent the dynamics of the QFT Hamiltonians of
interest, which is generally a challenging task in current platforms. For
example, simulating the dynamics of both Abelian and non-Abelian gauge
theories in 2+1 and higher dimensions have proven hard Zohar  _et al._
(2012b); Zohar and Reznik (2011); Zohar  _et al._ (2013c); Tagliacozzo  _et
al._ (2013b); Ott  _et al._ (2021); González-Cuadra  _et al._ (2022) given
either higher-body interactions or non-local interactions depending on the
representation of the Hamiltonian. Some progress has been reported in recent
years, but a first implementation of complete building blocks of a lattice
gauge theory with high fidelity remains an important goal of the program in
the coming decade. Rigorous error-bound analysis, error corrections, and
verifiability will need to be developed for analog simulations as well.

The role of hardware implementation and benchmarks in guiding the course of
developments in quantum simulation cannot be overstated. Many recent
experiments and implementations of a variety of QFT problems on a range of
quantum platforms in both analog and digital modes (see e.g., Refs. Martinez
_et al._ (2016b); Klco  _et al._ (2018); Nguyen  _et al._ (2022); Kokail  _et
al._ (2019); Lu  _et al._ (2019); Alam  _et al._ (2021); Klco  _et al._
(2020); Atas  _et al._ (2021); Ciavarella  _et al._ (2021a); Ciavarella and
Chernyshev (2022); Xu and Xue (2021); Mildenberger  _et al._ (2022); Schweizer
_et al._ (2019); Görg  _et al._ (2019); Mil  _et al._ (2019); Yang  _et al._
(2020); Zhou  _et al._ (2022) have generated a platform for communications and
collaborations with experts in quantum hardware technology. It has also
generated proposals and experiments dedicated to developing simulators
suitable for QFTs, see e.g., Refs. Hauke  _et al._ (2013); Davoudi  _et al._
(2020a); Surace  _et al._ (2020); Macridin  _et al._ (2018); Davoudi  _et al._
(2021); Casanova  _et al._ (2011); Zohar  _et al._ (2013b); Banerjee  _et al._
(2013); Dasgupta and Raychowdhury (2022); Zohar  _et al._ (2013d). This is a
critical path as otherwise theory and algorithmic developments will be
disconnected from the reality of hardware. To achieve meaningful progress, a
series of models from low-dimensional theories and simpler gauge groups need
to be identified and progressively made more complex to follow, or ideally,
guide, hardware developments. Finally, hybrid classical-quantum approaches to
quantum simulation should be taken advantage of in both near and far terms
Bender  _et al._ (2018b); Davoudi  _et al._ (2021); González-Cuadra  _et al._
(2022). See Ref. Bauer  _et al._ (2022) for more references and context.

LQCD began around the time the computing became available to the scientific
community and developed to its current mature state alongside the increase in
computing power. These decades of experience can be leveraged as quantum
computers develop. The challenges of simulating gauge theories, with an eye
towards QCD, will be a rich area of research in the decades ahead.

###  II.2 Tensor networks

Tensor network methods are playing an increasingly important role in several
branches of physics and in quantum information science. In the context of HEP,
tensor networks have appeared as ways to reformulate lattice gauge theory
models to obtain a fully discrete formulation that is suitable for quantum
computation and coarse graining methods. Tensor networks also provide tools to
understand entanglement in conformal field theories and their connection to
gravity Meurice  _et al._ (2022a).

In the context of lattice gauge theory, tensors can be seen as the
translationally invariant, local building blocks of exact discretizations of
the path integral. They encode both the local and global symmetries of the
original model. It is easy to design approximations (truncations) that
preserve these symmetries and to design simplified models that should have the
same correct universal continuum limit as the original model. Developing these
building blocks and optimizing the approximations for NISQ machines and
classical computers are important tasks for the near-term future. Tensor
networks can also be used to perform classical simulations of quantum
circuits. This is useful for developing and testing quantum computing
algorithms and quantum computational advantage.

Tensor networks have their origins in condensed matter physics where they
provide a suitable truncated basis for constructing the low lying energy
eigenstates of strongly interacting many body systems. In particular matrix
product states and the DMRG algorithm provide very accurate ground state
wavefunctions for one dimensional systems White (1992); Bañuls  _et al._
(2020); Cirac  _et al._ (2021). The annual lattice conferences have helped
foster interactions among the communities involved Bañuls  _et al._ (2014);
Meurice  _et al._ (2014a); Van Acoleyen  _et al._ (2014); Shimizu and
Kuramashi (2014); Saito  _et al._ (2014); Unmuth-Yockey  _et al._ (2014);
Meurice  _et al._ (2014b) and the number of contributions has grown steadily
with the years Bañuls  _et al._ (2018). Current applications to particle
physics include the Schwinger and Thirring models and gauge theories in
$(2+1)$ dimensions - see Bañuls and Cichy (2020) and references therein. The
basic idea is to express the ground state wavefunction as the trace of a
product of local tensors which are functions of a set of parameters. Varying
these parameters allows for a good estimation of the ground state.

Tensor network formulations can also be constructed for Euclidean path
integrals and in conjunction with the tensor renormalization group (TRG) have
been used to provide classical simulations of two dimensional models including
both gauge fields, scalars and fermions such as the non-abelian Higgs,
Schwinger and Gross-Neveu models provide classical simulations of lattice
field theory models including spin models, gauge theories, scalars and
fermions, the non-abelian Higgs, the Schwinger and Gross-Neveu models Meurice
_et al._ (2022a, b). For more extensive sets of references and a road-map (the
“Kogut sequence”), Typically the local Boltzmann factors are expanded on
characters of the group and the original fields integrated out exactly
yielding a discrete tensor representation that can form a starting point for
quantum simulation. Furthermore, it can be shown that truncation of these
tensors to a finite number of representations does not break any symmetries.
These tensor networks can be coarse grained using renormalization group ideas
to allow computation of a variety of observable including the free energy.
Fig. 2 shows an example of this procedure for the two dimensional Ising model

Figure 2:  A coarse-graining step for a tensor network. Circles represent
tensors, and closed indices should be contracted. From Ref. Meurice  _et al._
(2022b).

Recently, improved renormalization group methods (loop-TNR and ATRG
algorithms—see Ref. Meurice  _et al._ (2022b)) have been developed that are
capable of yielding accurate results for three dimensional $U(1)$ gauge theory
and scalar theories in four dimensions Akiyama  _et al._ (2020). To handle
fermions a Grassmann tensor renormalization group has also been developed
which can keep track of any signs arising from the fermions Kadoh  _et al._
(2018).

###  II.3 Simple holographic lattice models

Figure 3: Sample configuration for Ising model on 2d hyperbolic disk

The original AdS/CFT correspondence provided strong evidence for a duality
between gravity in anti-deSitter space and strongly coupled quantum field
theories living at the boundary of that space Maldacena (1998). Subsequently
ideas from quantum information science have served to strengthen this
holographic connection between gravity and entangled quantum systems—see a
recent Snowmass review Faulkner  _et al._ (2022). Typically this
correspondence is studied in the limit where the bulk gravitational
fluctuations are vanishing. Quantum simulation can be used in principle to
probe this duality in more general regimes. A significant amount of work has
been done using classical simulation over the last decade to check holography
see Refs. Cotler  _et al._ (2017); Berkowitz  _et al._ (2016); Hanada  _et
al._ (2016); Catterall  _et al._ (2020); Catterall and Wiseman (2008);
Catterall  _et al._ (2018); Hanada  _et al._ (2014). However the next frontier
in testing the holographic dictionary will likely come from quantum
simulation.

Motivated by this a variety of simple scalar, Ising and fermion matter systems
have been simulated on tessellations of hyperbolic space (Wick rotated anti-
deSitter space) in two and three dimensions Asaduzzaman  _et al._ (2020,
2021); Brower  _et al._ (2019). Results like the RT formula for the
entanglement entropy arises naturally via lattice strong coupling expansions.
An example Ising configuration generated by a Monte Carlo algorithm is shown
in fig. 3. In spite of the fact that the discrete spaces are only invariant
under a subgroup of the continuum isometry group the boundary theories are
seen to exhibit power law correlations as expected for a conformal field
theory. Furthermore it is possible to include dynamical gravity effects by
allowing the tessellation to fluctuate. Preliminary results in this case
suggest the existence of both conformal and non-conformal phases depending on
the size of the gravitational fluctuations Asaduzzaman and Catterall (2021).

Extending this approach to a Hamiltonian formulation allows for quantum
simulation and would allow a connection to be made to tensor network models of
quantum error correction Pastawski  _et al._ (2015). The central idea of
holographic error correction is that the quantum state of qubits residing deep
inside the bulk of such a tessellated hyperbolic space is robust to errors in
the quantum state of the boundary qubits.

###  II.4 Future near-term goals

Both the algorithms and hardware needed for quantum simulation are progressing
rapidly and so any projection for the next decade will necessarily be somewhat
uncertain. Nevertheless the successes that have been achieved so far suggest
some interesting goals may be achievable with the next five to ten years.
These include:

  * •

Simulation of quantum circuits representing gauge theories coupled to Dirac
fermions in (1+1) and (2+1) dimensions on small lattices with control over
time-digitization errors.

  * •

Classical tensor-network calculations of similar systems for validation
purposes. Use of tensor networks for initial state preparation.

  * •

Classical and quantum simulation of gauge theories and fermions formulated on
discretizations of two and three dimensional hyperbolic space. Studies of
quantum error correction on such networks.

  * •

Identifying and implementing problems that can provide qualitative
understanding of non-equilibrium dynamics of strong interactions, including
mechanisms for equilibration and thermalization, starting from small prototype
models and using potentially analog simulators with larger Hilbert spaces, as
well as classical Hamiltonian-simulation methods such as tensor networks, see
e.g., Refs. Mueller  _et al._ (2022); Zhou  _et al._ (2022); de Jong  _et al._
(2021); Pichler  _et al._ (2016); Zache  _et al._ (2019); Desaules  _et al._
(2022).

Crucial to the long term success of these efforts will be the development of
reliable quantum error correction algorithms and hardware. This will in turn
depend partly on the fabrication of systems with many thousands of qubits.
Keeping gate fidelities and decoherence times acceptable at such scales will
be an important mission of the quantum hardware community.

##  III Theory for Quantum Sensing of Fundamental Physics

The emerging ability to manipulate and control the quantum state of a system,
as well as the technological advances that enable it, opens a host of new
opportunities to directly probe fundamental physics and to search for new
physics. Particle theorists are playing a vital role in identifying the
physics opportunities for novel sensing experiments and drawing new
connections between technology and fundamental tests. The theory-experiment-
technology connection in the broadly-defined area of quantum sensing is strong
and mutually beneficial to all these communities. Researchers developing
sensors and systems for “practial” quantum applications in the areas of
superconducting circuits, quantum optics, single photon detection, atomic
physics, or superconducting cavities have been made aware of the utility of
their technology to searching for new physics by particle theorists.
Similarly, HEP theorists have been informed by their experimental colleagues
about state-of-the-art technology, triggering new ideas. This back-and-forth
is particularly strong in universities and labs in the US.

In this section we will present some of the physics targets for quantum sensor
searches and proceed to highlight some of the technologies that theorists,
often in collaboration with experimentalists, have proposed to pursue these
target. We conclude with a a discussion and outlook. Other Snowmass white
papers that deal with sensing with a theory component include Refs. Carney
_et al._ (2022a); Essig  _et al._ (2022).

###  III.1 Fundamental physics targets

Some of the physics questions on which sensing experiments aim to shed light
are central to enhancing our understating of nature. These include:

#### Searching for new particles:

An understanding of which degrees of freedom are included in the rule book of
nature – in other words, which particles exist – has always been at the heart
of fundamental physics. Cosmic rays (in the early 20th century) and collider
experiments (in its later half and into the 21st) have pushed the frontier in
search of heavier particles. New light degrees of freedom that are feebly
interacting, of which neutrinos are an example, are well motivated, and can
exist within a large parameter space Essig  _et al._ (2013). Axions Peccei and
Quinn (1977), axion-like particles, dark photons Holdom (1986), and milli-
charge particles are among the best motivated. Proposed and ongoing sensing
experiments, with strong theory involvement, are making headway in this
search.

#### Dark matter:

Our and other galaxies were brought to form by the gravitational pull of dark
matter which still dominates galactic mass. The beyond the standard model
nature of dark matter motivates the search for new degrees of freedom, as in
the previous paragraph, which also make up all or part of our dark matter
halo. New sensing initiatives have originated from the theory community, going
back to Ref. Sikivie (1983), but many new ideas have been put forth recently
(see Refs. Adams  _et al._ (2022); Antypas  _et al._ (2022); Berlin  _et al._
(2022) for Snowmass summaries). Dark matter candidates that can be probed by
quantum sensing setups are remarkably varied, from ultralight wavelike dark
matter (masses of $10^{-21}$ eV to about 1 eV) of which axions Peccei and
Quinn (1977), dark photons Holdom (1986) are the most well-known, to light
WIMP-like particles (in the keV to GeV range), as well as Planck mass
particles and above Carney  _et al._ (2022b).

#### Gravitational waves:

The discovery of gravitational waves (GWs) by LIGO Abbott  _et al._ (2016) has
profound implications, both in confirming the predictions of general
relativity, and in opening a new window for exploring the Universe. Expanding
the range of frequencies in which we can observe GWs is of vital importance,
akin to the detection of light beyond the visible spectrum. Quantum technology
is playing an important role in enabling and enhancing LIGO’s reach.
Furthermore, theorists have put forth ideas for detecting gravitational waves
in a large range of frequencies Berlin  _et al._ (2021a); Domcke  _et al._
(2022); Fedderke  _et al._ (2022, 2021), some of which are being actively
pursued experimentally Berlin  _et al._ (2022).

#### Tests of quantum mechanics:

Quantum mechanics (QM) is an odd theory. Yet, it has withstood many
experimental tests, and hence it is at the very least an excellent
approximation of Nature. Despite its oddity, it has also proven theoretically
very difficult to modify due to constraints imposed by unitarity and causality
Weinberg (1989); Polchinski (1991). High energy theorists are well positioned
to address this because any successful modification of QM would need to be
consistent, or at least embedded within the standard model of particle
physics, a theory which provides an excellent description of nature at high
energies. A modification of quantum mechanics must find a home in quantum
field theory (QFT). Indeed, recently a new nonlinear extension of quantum
mechanics that is inherently unitary and causal has been proposed by HEP
theorists by starting with a modification of QFT and working back to the
consequences for QM Kaplan and Rajendran (2022). This extension, and likely
others that may follow, can be tested experimentally with dedicated quantum
sensing setups Polkovnikov  _et al._ (2022).

#### Tests of gravity in a quantum setting:

Theories of gravity and quantum mechanics have yet to be unified to a single
framework at arbitrarily short lengths scales. From a theoretical point of
view, gravity and quantum theory are compatible within a long distance
effective field theory. Still, given the difficulty in unifying them at short
distance it is interesting to test gravity at laboratory length scales in
situations in which things are manifestly quantum. Theorists have proposed
such tests employing recent advances in atomic physics and opto-mechanical
systems Carney  _et al._ (2022c).

###  III.2 Theory for sensing experiments

In this subsection we demonstrate the role theorists are playing in the arena
of sensing with quantum technology by providing explicit examples of
experimental efforts which were spawned by theory-experiment collaboration as
well as proposals for novel experiments. The takeaway from this list is that
theory is contributing to the development of an innovative and varied research
program in the area of quantum sensing. A similar point has been made more
broadly in Ref. Essig  _et al._ (2022). The list below is by no means complete
(apologies for omissions), but the degree of its incompleteness serves to
strengthen the point that the HEP theory community is making a strong and
broad contribution in proposing innovative ways to search for new physics.

#### Atom interferometers - MAGIS:

Atom interferometers operated in free fall provide an exciting opportunity to
search for gravitational waves in the mid-band (around a Hz, between LIGO and
LISA) as well as for several classes of wavelike dark matter Abe  _et al._
(2021). The flagship experiment in this class, MAGIS 100, a 100 meter network
of interferometers is in design stages Abe  _et al._ (2021) and will be at
Fermilab in the coming years. The initial proposal to search for gravitational
waves with atom interferometers was put forth by a collaboration of HEP
theorists and atomic experimentalists Dimopoulos  _et al._ (2007, 2009);
Graham  _et al._ (2013).

#### Atomic clocks and other atomic experiments:

Atomic physics provides ever increasing precision in time keeping and
frequency determination. The comparison of two atomic clocks, or of an atomic
clock to another high quality device can be sensitive to light bosonic dark
matter, such as a dilaton, as proposed by theorists Derevianko and Pospelov
(2014); Arvanitaki  _et al._ (2015); Stadnik and Flambaum (2015) (and reviewed
in greater detail in Ref. Antypas  _et al._ (2022). Atomic clock technology is
also of interest for future space missions to probe fundamental physics Alonso
_et al._ (2022); Tsai  _et al._ (2021). In addition, precision atomic
spectroscopy and a systematic comparison of transitions among nuclear isotopes
has been shown, again in HEP theory-experiment collaboration, to be sensitive
to new long range forces Berengut  _et al._ (2018).

#### Condensed matter systems for low recoil searches:

The program to detect dark matter directly in the lab has focused for several
decades on dark matter masses above 10 GeV. The leading detectors in this
range, liquid noble element experiments, do not have sensitivity to dark
matter below this range because detection thresholds are above the energy
deposited in dark matter collisions. A need for lower threshold detectors has
thus arisen. Many ideas have been put forth and are pursued experimentally.
Not surprisingly, many such efforts have been spawned by theorists or in a
theory-experiment collaboration. The connection to quantum technology is
simply that the systems that are needed to explore this region of parameter
space are often used to detect single photons or single quanta. Examples
include Skipper CCDs and the SENSEI experiment Crisler  _et al._ (2018) (which
has potential for growth Aguilar-Arevalo  _et al._ (2022)), proposals to use
transition edge sensors Hochberg  _et al._ (2016), a proposal to search for
dark matter with superconducting nano-wires Hochberg  _et al._ (2021), and
magnetic bubble chambers Bunting  _et al._ (2017) (with prototype results in
Ref. Chen  _et al._ (2020)).

#### Cavity based Dark Matter searches:

High quality radio frequency cavities are a key component of the axion
haloscope originally proposed by Sikivie Sikivie (1983) and are currently
being used to search for dark matter axions in the 1-10 GHz mass range Adams
_et al._ (2022). Quantum techniques, such as squeezing (demonstrated in the
HAYSTAC experiment Backes  _et al._ (2021)) and photon counting Dixit  _et
al._ (2021) holds promise to hasten the search in this range. A recent
theoretical analysis showed that squeezing can be distributed over a coherent
network of sensors to provide additional gain in the scan rate Brady  _et al._
(2022).

Recent proposals by theorists and experimentalists have been made to extend
cavity based searches to lower axion masses by leveraging the extremely high
quality of superconducting cavities by considering the upconversion of one
cavity mode to another Berlin  _et al._ (2020a, 2021b); Lasenby (2020) with
interesting potential coverage. R&D is ongoing with theory input to pursue
this goal Berlin  _et al._ (2022); Giaccone  _et al._ (2022).

#### LC resonator DM searches:

Axion, dark photon, and milli-charged particles searches at lower dark matter
masses can be achieved by other resonant systems such as LC circuits. The DM-
Radio experiment Brouwer  _et al._ (2022) was originated by a theory-
experiment collaboration and will search for faint electromagnetic signals
inside a well shielded region employing a squid Chaudhuri  _et al._ (2015).
The ABRACADABRA-10cm experiment Ouellet  _et al._ (2019), which also
originated in the theory community Kahn  _et al._ (2016), proposed a similar
detection strategy employing a toroidal geometry. ABRACADABRA is now merged
with DM-Radio Brouwer  _et al._ (2022). Pushing limits on the QCD axion can be
achieved with quantum limited sensing and a large scale effort. A modest
modification to such setups involves driving electromagnetic fields in a
nearby shielded environment; such a “direct deflection” experiment was
proposed by theorists and would be sensitive to the same class of milli-
charged dark matter models targeted by low-threshold detectors Berlin  _et
al._ (2020b).

#### Searching for new particles with cavities:

High quality cavities can be utilized to search for new degrees of freedom
independently without assuming they make up the dark matter. Dark SRF
(reviewed in Ref. Berlin  _et al._ (2022)) is an ongoing light-shining-
through-wall (LSW) experiment, with theory-experiments collaboration,
searching for dark photons as part of the SQMS center at Fermilab. An ultra
high-Q superconducting RF cavity is excited to the brim with photons, and a
feeble appearance signal is searched for in a nearby cavity which is in tune
with the first. The Dark SRF setup is optimized to search for the longitudinal
polarization of the dark photon, which leads to enhanced sensitivity, as
pointed out in a theoretical paper Graham  _et al._ (2014). Theorists have
also pointed out that the Dark SRF experiment will also be sensitive to very
light milli-charged particles via Schwinger pair production Berlin and Hook
(2020). The Dark SRF experiment will be pushed to the quantum regime in the
coming years Berlin  _et al._ (2022).

Several theoretical proposals have been made to utilize the high quality of
SRF cavities to search for axions. These include two cavities and a conversion
region with a static magnetic field Janish  _et al._ (2019) in an LSW setup, a
two-cavity LSW employing the up-conversion technique Gao and Harnik (2021), or
a single cavity in which two modes are populated, and a third quiet mode is
used as a signal mode Bogorad  _et al._ (2019). The later can in principle
also be sensitive the the standard model Euler-Heisenberg light-by-light
interaction. The feasibility of these various schemes is being studied by
experimentalists and theorists in SQMS Berlin  _et al._ (2022).

#### DM Searches with Dielectric Stacks and Dish Antennas:

HEP Theorists have pointed out that both axion and dark photon dark matter can
convert to photons at the surface of a mirror, and that using the appropriate
geometry, the signal can be focused Horns  _et al._ (2013). This broadband
search approach will benefit from single photon detection at the frequency in
question. This idea led to a plethora of experimental efforts, including new
limits, such as Refs. Knirck  _et al._ (2018); Tomita  _et al._ (2020); Brun
_et al._ (2019a); Andrianavalomahefa  _et al._ (2020) (some of which with
strong theory involvement) and planned experiments Liu  _et al._ (2022).

A related detection strategy also proposed by theorists Jaeckel and Redondo
(2013); Millar  _et al._ (2017), is to use the transition between two
dielectric materials to generate photons from dark matter. A repeated
transition, a dielectric layered stack, can be used to enhance the rate. The
MADMAX experiment, a collaboration including theorists, has grown from this
and is already in the prototype phase Brun  _et al._ (2019b).

#### Optics based searches:

Quantum optics is a mature field and a strong driver of progress in QIS.
Optics-based searches for new particles and/or dark matter present interesting
opportunites around the eV scale. The LAMPPOST experiment Chiles  _et al._
(2021), an optics realization of the dielectric stack was first proposed in a
theory paper Baryakhtar  _et al._ (2018). A prototype has already set new
limits on dark photon dark matter.

Optics is also a key tool to search for particles that are not dark matter.
The ALPS experiment Arias  _et al._ (2012), also with strong theory
involvement, is a LSW experiment consisting of two optical cavities on either
side of a wall, one acting as emitter and the other as receiver. The
parametric gain achieved by a receiver cavity was first pointed out in Ref.
Sikivie  _et al._ (2007) in a theory-experiment collaboration.

More recently, nonlinear optics was proposed as a novel tool to search for new
particles by theorists and experimentalists. In a process dubbed dark SPDC, a
pump photon down-converts to a signal photon and an associated dark particle,
either a dark photon or an axion Estrada  _et al._ (2021). A “missing energy
at the optics table”experiment may have parametric advantages, and very
different challenges, compared to light shining through walls experiments.

#### Spin precession experiments:

Some of the most powerful constraints on new physics that violates CP come
from constraints on the (static) electric dipole moments of fundamental
particles Alarcon  _et al._ (2022). The QCD axion, if it is dark matter, will
lead to an oscillation of the neutron electric dipole moment with a frequency
set by the axion mass. Theorists and experimentalists have proposed to search
for this effect by looking for the precession of the polarized nuclear spins
in an electric field in a resonant NMR setup Budker  _et al._ (2014). The
CASPER experiment Jackson Kimball  _et al._ (2020) is pursuing this, as well
as spin precession effects due to direct axion coupling to matter, known as
CASPER-Wind Jackson Kimball  _et al._ (2020) (see also Ref. Gao  _et al._
(2022) for a proposal using superfluid helium-3 and precision readout using
atomic clocks). Using a liquid co-magnetometer, a prototype has already set
limits with theoretical involvement Wu  _et al._ (2019). Other spin precision
experiments, including a spin polarized torsion pendulum, have been shown to
have interesting reach in a theory-experiment collaboration in Graham  _et
al._ (2018).

As a notable example, quantum spin gyroscopes known as noble-alkali co-
magnetometers can also been used to detect the coupling of a gradient of the
axion field to nuclear spins Safronova  _et al._ (2018); Bloch  _et al._
(2020). In a small scale effort dubbed NASDUCK Bloch  _et al._ (2022),
initiated by theorists, new limits on such axion dark matter couplings have
been set.

Similar NMR techniques can also be used to search for the spin dependent long
range force which is mediated by the QCD axion. Again, in strong collaboration
with theorists, the ARIADNE project aims to look for a force between a
Helium-3 polarized sensor and a nearby tungsten target Geraci  _et al._
(2018).

#### Single particle traps:

One area of advance in the quantum regime is the ability to trap and
manipulate the quantum state of a single charged particle, either an ion or
electron. In the realm of fundamental physics, this allows one to study the
properties of single particles. The classic example is the anomalous
gyromagnetic moment of the electron, $(g-2)_{e}$, for which the theory-
experiment comparison represents the most precise test of the standard model
to date Hanneke  _et al._ (2008).

Recently, it was pointed out that a single particle can be a sensitive target
for dark matter direct detection. Millicharged dark matter can cause energy to
be transferred from the laboratory to the cold particle trap at a rate which
is higher than observed Budker  _et al._ (2022); Carney  _et al._ (2021a). In
addition, dark photon dark matter can be resonantly absorbed by a trapped
electron leading to quantum jumps in its axial energy level, as has been shown
in a recent proof of concept experiment Fan  _et al._ (2022).

#### Opto-mechanical sensors:

The ability to bring macroscopic objects to their ground state and sense their
motion at quantum-limited precision is opening new opportunities for sensing.
An array of quantum-limited sensors was proposed by theorists to search for
the gravitational interaction of very heavy dark matter Carney  _et al._
(2020) and for $B-L$ vector boson dark matter Carney  _et al._ (2021b). A
theoretical analysis of going beyond the standard quantum limit was presented
in Ref. Ghosh  _et al._ (2020). An ambitious program, Windchime, was also
proposed Attanasio  _et al._ (2022). Theorists have also analyzed the reach of
torsion balance experiments to some of the same targets in Ref. Graham  _et
al._ (2016) and a dedicated search can make further progress.

###  III.3 Outlook

There are conclusions to draw from this long, yet partial, list of
contributions from theorists to the search for new physics:

  * •

The search for new physics requires us to cast a wide net Hochberg  _et al._
(2022). Theorists are contributing to the search, in particular searches for
new particles, dark matter, and gravitational waves, in a central way.

  * •

Though some of the contributions date back decades, many were made in the past
decade and at an increasing rate. The field of novel ideas to strengthen our
searches for new physics is vibrant and growing.

  * •

Though they may lead to small or large projects, these contributions are
enabled by the vibrant HEP research environment in which theorists and
experimentalists interact, learn and exchange ideas. Maintaining the funding
for research in the US, particularly for theory, is vital in order to reap the
benefits from new innovations. A shortage in funding for small scale efforts
in this genre is a current bottleneck in expanding the search for new physics.

  * •

Not all theory-experiment collaborations are within the scope of quantum
science (see Ref. Essig  _et al._ (2022) for a discussion that is synergistic
to this one, but with a broader scope). However, a large number of quantum and
quantum-related technologies have been identified by theorists and
experimentalists as new tools in the search for new physics. This is not a
coincidence; quantum information science requires isolation and control of
delicate systems as well as reading out the most feeble of signals. These
challenges are shared by the endeavour to look for new physics and this
justifies an investment by the HEP community in the research that connects
quantum technology to fundamental physics. HEP theorists are well poised to
make the needed connections between these fields.

  * •

Gravitational waves have, for a while, been removed from the scope of HEP.
Regardless of how they are detected, GWs are of great interest to the HEP
community. The emergence of new GW detection schemes serves to strengthen this
point further.

##  IV Formal Aspects of Quantum Information and Fundamental Physics

Let us now consider more broadly the theoretical underpinnings of the links
between quantum information science (QIS) and fundamental physics. Within QIS
itself the main directions can be categorized into broad themes of quantum
information theory, quantum computing, and implementations. This section
focuses on the former set, where topics such as entropy, entanglement
measures, quantum error correction, and quantum communication play a prominent
role. These concepts have remarkably enriched theoretical physics, especially
in the context of quantum field theories and quantum gravity.

A particularly fruitful setting at the confluence of these ideas is the
AdS/CFT correspondence Maldacena (1998) (also known as gauge/gravity duality),
which relates a higher-dimensional gravitational theory to a lower-dimensional
non-gravitational one. A cornerstone feature of these dualities is the
specific type of rearrangement (or transmutation) of the degrees of freedom
between the two sides, which allows one to extract genuinely quantum features
on the CFT side from classical ones in the dual AdS, as well as strongly
gravitational effects in AdS from non-gravitational ones in the CFT, with both
pictures nevertheless retaining the requisite degree of locality. Within the
last decade or so, it has become evident that many key quantities of interest
in QI theory actually have a rather simple description on the gravity side,
belying the intricacy of the holographic mapping as well as the operational
definition of the QI construct itself – in some sense, the bulk geometry in
the gravitational theory naturally ‘knows about’ entanglement!

This section will explain how this revelation allowed for a change in
perspective which fueled the vibrant activity in the recent years, then
briefly indicate some of the fascinating resulting developments, and end with
a broad outlook of the big-picture questions that the community is now well
poised to answer over the next decade. Much of the narrative is adapted from
the excellent and pedagogically written white paper Faulkner  _et al._ (2022).
A related theme focused on quantum aspects of black holes and the emergence of
spacetime is nicely summarized in the white paper Bousso  _et al._ (2022).
Other white papers on related topics include Giddings (2022); Meurice  _et
al._ (2022a); Blake  _et al._ (2022). Some useful pedagogical resources on the
subject include Refs. Nielsen and Chuang (2002); Wilde (2013) for an
introduction to quantum information in quantum mechanics, Refs. Haag (2012a);
Ohya and Petz (2004) for algebraic treatment of QFTs, Calabrese and Cardy
(2009) for computation of entanglement in conformally invariant QFTs, and
Refs. Nishioka  _et al._ (2009); Van Raamsdonk (2017); Rangamani and
Takayanagi (2017); Headrick (2019) for reviews of developments in the context
of holography. The referencing in this section will be kept minimal,
restricted to other relevant white papers and to seminal works initiating a
given subject or reviews thereof.

###  IV.1 Change of perspective

With the advent of QIS, the traditional and intuitively natural ways of
organizing physics, e.g. by energy scale or interaction strength, by field
content or observables of interest, or even by its computational tractability,
has been amended by a wholly different perspective of focusing rather on the
information content. Such an approach allows for a description applicable to a
bewildering variety of physical systems, unifying previously disparate avenues
of exploration and simultaneously deepening our understanding.

Of particular significance is the shift of focus towards genuinely quantum
phenomena. Although quantum field theory, providing a framework for explaining
the fundamental laws of nature, is built on quantum mechanics as its central
pillar, the full quantumness is seldom utilized in the traditional approach.
Instead, one typically focuses on observables that can be computed using
correlation functions of local operators, which can then be translated into
physical quantities such as scattering cross-sections and dynamical response
functions. The Wilsonian effective field theory paradigm is also primarily
geared towards identifying relevant operators and understanding their
correlation functions below some cut-off scale. Furthermore, techniques such
as path integrals, the renormalization group, effective theories, symmetries,
and dualities are all primarily geared in textbook treatments towards
computing such correlation functions.

There is, however, more information to be mined by generalizing the framework
to one which is more cognizant of the underlying quantum mechanical structure.
In particular, such a perspective has to account for the fact that composite
quantum mechanical systems exist in tensor product superpositions, which leads
to the essential concept of entanglement. Focusing on these aspects can not
only help us further elucidate the field theory framework, but it also appears
better suited to addressing profound questions in the quantum gravitational
setting.

###  IV.2 Recent developments

The general themes that have been explored in this broad area include
refinement of conventional field-theoretic tools to quantify spatially-ordered
entanglement in QFTs, quantifying measures of entanglement in mixed states,
and the revival of operator algebraic formulations of QFT. In a parallel
development, the geometrization of information theoretic measures in the
context of the holographic AdS/CFT correspondence has played an important role
in furthering our understanding of the holographic dictionary. Additionally,
progress has been made on questions relating to the complexity of state
preparation, which is important for quantum simulations, and it has
furthermore been argued that these ideas have a physics role to play in QFT
and quantum gravity. Many of these developments have been accompanied by novel
insights on the quantum information side, showing that the synergy between the
fields benefits both sides. Here we briefly mention the most important recent
developments and open problems in these areas.

#### Characterizing quantum information:

It has become increasingly evident that the structure of entanglement plays a
key role in understanding many properties of physical systems. Correspondingly
a central goal is to define and quantify the amount of entanglement, with view
towards understanding the organization of entanglement in any given state, in
terms of how it is structured in space and between scales, and how it can be
prepared. This is by no means a simple task. Already in the typical QIS
setting involving finite systems (having Hilbert space of finite dimension
which factorizes into Hilbert spaces of subsystems), there are many distinct
entanglement measures. They are typically based on entropic functions designed
to be meaningful from the point of view of communication, or motivated from a
resource theoretic perspective. Examples include von Neumann entropy (which in
the high energy community is referred to as entanglement entropy), relative
entropy, entanglement of distillation, entanglement cost, entanglement of
purification, etc..

In the setting of interest to high energy physics, formulated in the language
of a QFT and in particular gauge theory, things are far more complicated. Not
only is the Hilbert space infinite-dimensional, but it does not actually
factorize Witten (2018). Nevertheless, one can still define entanglement
entropy and extract its regulator-independent universal features. In the
holographic context this takes a particularly nice form: the entanglement
entropy of a subsystem defined by a spatial region in the CFT is given by the
area of a certain (area-extremizing) surface in the bulk geometry associated
to the specified region. (This prescription is referred to as RT Ryu and
Takayanagi (2006b) in the static context, HRT Hubeny  _et al._ (2007) in the
general dynamical context, and QES Engelhardt and Wall (2015) when certain
quantum corrections are included.) The fact that entanglement entropy is
computed by such a simple geometrical construct provided an early hint at the
intriguing connection between entanglement and geometry which we are still
trying to fathom. The emerging lesson is that in some sense, entanglement
builds spacetime Van Raamsdonk (2009) (sometimes referred to by the slogan
ER=EPR Maldacena and Susskind (2013)). In the holographic context, the bulk
geometry naturally implements a quantum error correcting encoding of the
boundary physics Almheiri  _et al._ (2015).

Hence such geometrization of entanglement has been immensely useful not only
at the practical level (of probing the behavior of entanglement in many
systems of interest) but also at the conceptual level. The QI-based insights
will in turn deepen our understanding of the physical frameworks. For example,
by connecting information quantities to basic data in QFT, we might expect to
be able to put new constraints on the QFT theory space.

#### Symmetry, renormalization group flows, and phases:

Quantum information ideas also interplay with some key non-perturbative
structures in QFT. For example, one can extract statistical properties of
charge fluctuations in localized regions and study different charged sectors
using symmetry resolved entanglement Goldstein and Sela (2018), as well as
formulate order parameters based on the relative entropy which probe
superselection sectors of global charges in QFT Haag (2012b).

Our understanding of effective field theories relies on the fact that dynamics
below some cut-off scale is only sensitive to a handful of relevant parameters
Polchinski (1984). Since from a microscopic viewpoint, the effective
description is attained by tracing out high energy degrees of freedom which is
an intrinsically lossy process, it is natural to expect a measure of the
number of degrees of freedom that is monotonic in energy scale, reaching a
conformal fixed point in the IR. Such functions (dubbed $c$, $F$, and $a$ in
2, 3, and 4 dimensions respectively) have been found Jafferis  _et al._
(2011); Komargodski and Schwimmer (2011) starting with Zamolodchikov’s
c-theorem Zamolodchikov (1986). While the conventional field theory methods
relied on dimension-specific techniques, more recently entropic proofs based
on the Markovian property of the CFT vacuum have been developed Casini  _et
al._ (2017), which provide an interesting overarching principle. One may then
hope that analogous information theoretic perspective will provide similar
monotone functions for higher-dimensional field theories (at least in five and
six dimensions where superconformal critical points exist).

Entanglement and complexity also play an important role in the classification
of IR fixed points of RG flows. In the context of many-body physics, both in
condensed matter examples and engineered systems built from atoms, molecules,
and photons, such fixed points describe distinct phases of matter.
Classification of these phases is a major challenge in many-body physics,
intimately tied to the classification of QFTs. (See also the white papers
Brauner  _et al._ (2022); Cordova  _et al._ (2022) for related reviews.)

#### Dynamics:

The subject of dynamics may be viewed on several levels. The most manifest one
is simply understanding how specific systems evolve in time, and what
universal features such time evolution exhibits. A more primal level concerns
the actual formulation of the quantities of interest in a generic time-
dependent setting. This is especially fruitful in the context of holography,
where the notion of time differs between the two sides. In particular, using
general covariance of the bulk gravitational theory explicitly provides a
useful guiding principle to developing the holographic dictionary by
suggesting natural geometric quantities dual to specific QI or CFT quantities
in the boundary theory. At a deeper level, it is intriguing to observe that
the formulation of the typical QI quantities explored in holography, defined
at a single instant in time, does not manifest the dual bulk general
covariance. Understanding this symmetry in the boundary formulation has been
relatively under-explored, and we may expect to see the insights gained from
harnessing the full power of the gauge/gravity duality come to fruition in the
next decade.

Under time evolution, quantum information tends to spread across many degrees
of freedom. It spreads both spatially, as signals propagate locally through
the system, and internally, among the degrees of freedom at each location.
Over the last decade we have come to better understand the remarkable fact
that the spreading of quantum information obeys universal laws. In a wide
variety of complex systems, including condensed matter, strongly interacting
QFTs, and black holes, information spreads according to general principles and
subject to fundamental bounds imposed by locality and by information-theoretic
inequalities. These bounds play a key role in questions such as how locality
emerges in quantum gravity and how to characterize the dynamics of strongly
correlated materials.

Another important feature is scrambling, a dynamical process which effectively
randomizes the quantum state, which is ubiquitous in chaotic quantum systems
with many degrees of freedom, from the SYK model to black holes and large-$N$
CFTs Sekino and Susskind (2008). A far-reaching new perspective on scrambling,
developed over the last decade, reformulates it in terms of out-of-time-order
correlation functions (OTOCs) Shenker and Stanford (2014), which measure the
effect of small initial time perturbations on later time operators, and hence
can be used to probe the onset of chaos. This in turn carries connections to a
wide range of topics such as emergence of bulk causality in AdS/CFT or bounds
on CFTs from conformal bootstrap.

Vacuum-subtracted energy density in quantum field theory can be negative due
to quantum fluctuations. This negative energy can potentially give rise to
acausal, or otherwise pathological, gravitational dynamics when coupling the
QFT to gravity. For example, traversable wormholes might provide shortcuts
between distant points. The Hawking black hole area theorem and Penrose
singularity theorems rely on assumptions about non-existence of various forms
of negative energy Hawking and Ellis (2011). It is thus important to find
general constraints on such negative energy. Surprisingly, these constraints
have been shown to arise from quantum information considerations applied
directly to the quantum field theory without gravity. For example, the
positivity of relative entropy implies the Bekenstein bound Casini (2008), the
monotonicity of relative entropy gives the averaged null energy condition
(ANEC) Faulkner  _et al._ (2016), the algebraic approach to quantum
information provides a proof for the quantum null energy condition (QNEC
Bousso  _et al._ (2016)), etc.. This story thus connects to the broader
paradigm of gravity from quantum information.

The interaction of a system with an external environment (whose unknown
details are traced over) can be described by a quantum channel acting on an
open quantum system (naturally described by a density matrix). Since such
situations are ubiquitous in physics, it is of broad interest to determine the
general rules to construct effective field theories for these open quantum
systems. One important problem is to ascertain sufficient conditions for a
local effective field theory to emerge. For perturbative dynamics, this is
difficult, since locality relies on the system losing memory of its
interaction with the environment, whereas the relaxation timescale is long at
weak coupling. However holographic systems, where the dynamics is
intrinsically strongly coupled, are fast scrambling and maximally ergodic in
their dynamics, leading to a simple dynamics of probe effective field
theories. Building on developments in real-time AdS/CFT Son and Starinets
(2002); Glorioso  _et al._ (2018), there has been renewed interest and
progress in this subject.

The concept of circuit complexity has also found its way into the holographic
context over the last decade, catalyzed by the observation that its linear
growth under time evolution mimics the growth of the Einstein-Rosen bridge in
a two-sided black hole in the bulk. Several specific geometrical duals of
complexity have been proposed Stanford and Susskind (2014); Brown  _et al._
(2016) and substantiated by a tensor-network picture. A different set of ideas
connecting holography to a notion of complexity is path-integral optimization,
in which the bulk spacetime emerges from minimizing the number of operations
required to prepare the state using a Euclidean path integral Caputa  _et al._
(2017). While each of these proposals does seem to capture important
qualitative features of holographic dualities, it remains to be seen how they
are related to each other and in what regime (if any) they are correct. The
idea that circuit complexity has a simple bulk dual in holographic theories
has also led to a large amount of work attempting to define and quantify this
notion in general field theories, including free ones, as well as in quantum
mechanics.

One of the most notorious open problems in theoretical physics is the black
hole information paradox, highlighting the clash between general relativity
and quantum physics, specifically the thermality of Hawking radiation being
incompatible with the unitarity of quantum evolution. This problem provides an
excellent testing ground for putative formulations of quantum gravity, and
over the last decade, many of the above-mentioned ideas have revitalized
efforts in this direction, engendering significant progress and change of
perspective. This story is the focus of the white paper Bousso  _et al._
(2022) and the earlier pedagogical review Almheiri  _et al._ (2021),
explaining how using holographic entanglement (in particular the QES
prescription) one can recover the Page curve for Hawking evaporation
consistent with unitarity, and the key role played by spacetime wormholes.
These can be studied in a controlled way in low dimensional settings such as
the SYK model and its low-energy limit of JT gravity, though the story is much
less clear for higher-dimensional gravity with propagating gravitational
degrees of freedom. A complementary perspective is offered in the white paper
Giddings (2022) discussing quantum gravity more broadly. This work emphasizes
that gravity requires modifications of the traditional notion of locality
(which hinges on understanding the correct mathematical structure to define a
subsystem in quantum gravity). Further remarks on UV/IR mixing in quantum
gravity and it possible signatures at low energies can be found in the white
paper Berglund  _et al._ (2022). A distinct viewpoint is presented by the
approaches of the fuzzball and microstate geometry programs, reviewed in the
white paper Bena  _et al._ (2022), which give gravitational and quantum
description of horizon-scale microstructure in terms of horizonless objects in
string theory. The vibrant debate revolving around the black hole information
paradox underscores the utility of exploring diverse approaches, in a healthy
symbiosis though which we bootstrap our way towards more complete
understanding.

###  IV.3 Outlook

Despite the remarkable progress in our understanding of quantum information in
fundamental physics, many important questions remain to be addressed.
Fortuitously there is high hope of progress on these over the next few years.

#### What is QFT?:

Notwithstanding its celebrated success as a framework for understanding the
fundamental principles of nature, it is fair to say that we don’t yet fully
understand the nature of QFT Dedushenko (2022). In addition to the growing
role of information-theoretic methods applied to QFT Faulkner  _et al._
(2022), the past decade has also seen new geometric approaches to computing
observables such as scattering amplitudes Bourjaily  _et al._ (2022), further
development of non-perturbative bootstrap techniques Poland and Simmons-Duffin
(2022); Hartman  _et al._ (2022), a better understanding of symmetries and
charges Cordova  _et al._ (2022), and ever deeper connections to many areas of
mathematics Bah  _et al._ (2022). All of these developments have in different
ways lent insights far transcending the standard textbook treatments of QFT.
One natural question is: Which of these ingredients is a defining feature of
the theory? What is the canonical toolkit of a future quantum field theorist,
as presented in a textbook a couple of decades hence? While these questions
might be intangible at present, part of the progress will likely come from
asking questions about the interconnections among these developments. Some of
these are easier to fathom, being already somewhat developed, such as the
connection between symmetry charges and operator algebraic formulations of
QFT. On the other hand, while we have several different proofs of quantities
that are RG monotones ($c$, $F$, and $a$ theorems), as yet we still lack a
unified picture. Nevertheless, understanding how the information theoretic
data in QFTs relates to other observables, and developing further techniques
to extract them, should provide valuable insight towards this goal.

#### Gauge invariance and information:

In theories with gauge-invariant degrees of freedom, the decomposition of
algebras comes with non-trivial centers and related superselection sectors.
Several open questions remain in this context. What is the significance of
algebraic centers for lattice gauge theories in the continuum limit? What is
the role of topological entanglement in gapless theories? How do we describe
gauge theory entanglement in the algebraic approach? What of interacting
theories in the algebraic approach? Does the change in the nature of the von
Neumann algebras, noted in the case of large $N$ confinement-deconfinement
transition Witten (2021), lead to new insights into the dynamics of confining
gauge theories?

#### From fields to gravity and strings:

In the gravitational context, at the semiclassical level we now understand the
relevance of the generalized entropy, an object that combines a Bekenstein-
Hawking-like classical term with a quantum von Neumann entropy. It has played
a crucial role both in the development of gravitational entropy bounds, and in
the recent discussions of the black hole information paradox Bousso  _et al._
(2022). An open problem is to better understand this quantity beyond the
semiclassical regime. How does one pick subregions and define their algebras
in this setting in a relational manner, maintaining diffeomorphism invariance?
How does one define these quantities in string theory? Can the information
theory approach shed light on the question of which effective field theories
can be consistently completed into a quantum theory of gravity, and which lie
in the swampland? In the context of holography, it is interesting to ask about
the information-theoretic nature of QFT wavefunctions. In particular, which
aspects of their entanglement structure are central for the holographic
entropy inequalities, and what does this tell us about quantum gravity? Is
there a principled way to discern which of the various conjectures relating to
complexity are valid, and what they are telling us about the nature of quantum
gravitational wavefunctions?

#### Real-time dynamics and cosmology:

QFT dynamics in cosmological spacetimes shares many characteristics of open
quantum systems. To date, there isn’t a clean description of the effective
dynamics of quantum fields in an open system, and many questions remain to be
addressed. Progress in these directions should help us better formulate the
issues we need to confront in the cosmological context, such as the nature of
observables or the temporal evolution of von Neumann entropy and other
information-theoretic quantities. It would also be interesting to tie these to
the study of cosmological correlators, which has been tackled using bootstrap
methods.

#### Connections:

While the list of interesting, important, and timely questions of course far
exceeds the above sample, it is already evident that the most fruitful
progress is rooted in their interconnection. Physical systems which were
traditionally far beyond the remit of HEP are gradually recognized to underlie
deeper understanding. The encouraging trend of diffusing topical boundaries is
likely to accelerate further progress, which often comes from unexpected
directions. The next decade might well be one of the most exciting ones in
theoretical physics.

t

Figure 4: Students and organizers of the first Quantum Computing Internship
for Physics Undergraduates Program (QCIPU) organized at Fermilab in the summer
of 2021.

##  V Quantum Workforce Development

As quantum information science is becoming an industry, there is an
anticipated need to develop a workforce that is educated in the physics,
language, and tools of QIS Hughes  _et al._ (2021). Emphasizing the need for
diversity in the workforce while the field is in its infancy is important from
the standpoint of equity, as well as to enrich the field with a plethora of
viewpoints. In light of this theorists have taken initiatives that target
students at a variety of levels. Examples include

  * •

References Perry  _et al._ (2019) is a textbook and/or course-module on
quantum computing tailored to advanced high school students or physics
undergraduates authored by a collaboration of HEP theorists and high school
teachers brought together by a science teacher internship at Fermilab. The
course has been successful in classroom setting, as described in Hughes  _et
al._ (2020).

  * •

The Quantum Computing Internship for Physics Undergraduates Program (QCIPU) is
a summer school and internship program which provides training in QIS for
undergraduate students, with an emphasis on physics sophomores and juniors
from under-represented groups. The program is run and organized by Fermilab
theorists, taking place virtually (see Figure 4 and
missinghttps://indico.fnal.gov/event/54760/) in the past two summers, with
plans for in-person programs in the future. Several students from the 2021
program have continued to work on research projects at Fermilab as part of the
internship.

  * •

At the graduate level and beyond, the SQMS center has organized two GGI summer
schools, one (virtual) dedicated to Quantum sensing for fundamental physics,
and a second (in person) on quantum simulation of QFT.

The continued success and further developments of programs such as QCIPU,
especially as we leave the zoom era, will require increased community support,
and devotion of effort and funding.

##  VI Acknowledgements

We thank the authors of snowmass white papers that were submitted to TF10. RH
is much obliged to Ying-Ying Li and Wanqiang Liu for useful discussions.
Fermilab is operated by the Fermi Research Alliance, LLC under contract No.
DE-AC02-07CH11359 with the United States Department of Energy. The work of RH
is also supported by the U.S. Department of Energy, Office of Science,
National Quantum Information Science Research Centers, Superconducting Quantum
Materials and Systems Center (SQMS) under the contract No. DE-AC02-07CH11359.
VH has been supported by the U.S. Department of Energy grant DE-SC0009999. S.C
has been supported under U.S. Department of Energy grants DE-SC0009998 and DE-
SC0019139. ZD is supported the U.S. Department of Energy grant DE-SC0021143,
U.S. Department of Energy’s Quantum Computing Application Teams program under
fieldwork proposal number ERKJ347, and by the National Science Foundation QLCI
grant OMA-2120757.

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