be daunting, hence needing more optimal Gaussian-state generations Bauer  _et
al._ (2021b). Additionally, various techniques have been proposed to design
minimal and maximally expressive quantum circuits for the NISQ era (e.g.,
Refs. Sim  _et al._ (2019); Funcke  _et al._ (2021)) and to split large
quantum circuits into small circuits executable on NISQ devices (e.g., Ref.
Peng  _et al._ (2020)). Finally, gauge-invariant simulation of gauge theories
may save qubit resources but locality of interactions may be lost. Many
digital simulations of lattice gauge-theory simulations on the NISQ hardware
to date Martinez  _et al._ (2016); Klco  _et al._ (2018); Nguyen  _et al._
(2021a); Klco  _et al._ (2020); A Rahman  _et al._ (2021); Ciavarella  _et
al._ (2021) have been enabled by fully (when possible) or partially removing
the redundant degrees of freedom (via appropriate gauge transformation or by
solving the Gauss’s law) or by imposing symmetries. This simplified simulation
can also reduce leakage to the unphysical sector of the gauge theories due to
algorithm and hardware errors. Taking full advantage of such strategies for
simulating the gauge theories of the SM, while paying attention to the
resulting time complexity of the simulation, will be essential in the
resource-limited era of quantum computing.

###  X.0.2 Error mitigation for NISQ computing

Given that in the NISQ era operations are noisy and the system is not error
corrected, error mitigation is required to make sense of the measurements.
There are two general types of errors that can affect a quantum simulation.
The first is called readout error, and is responsible for the fact that the
measurement of a qubit does not reproduce the amplitude of the qubit before
the measurement. The reason for such an error is often due to decoherence that
happens on the time scale required to measure a qubit. The second is called a
gate error, and arises due to imperfect implementation of quantum operators
(gates). On current publically-accessible machines, readout errors typically
dominate, with error rates between 1 and 10%, and the largest gate errors
occur in entangling operators, such as the CNOT operation, with a typical
error rate slightly below 1%. However, since gate errors accumulate with the
number of gates in an algorithm, gate errors become dominant for longer
circuits.

There are several techniques that have been proposed over the years to
mitigate these errors. Readout errors can be measured relatively easily by
preparing a system in a given state and recording the measurement of this
state. This results in a readout-error matrix. Note that given that the number
of possible states is exponential in the number of qubits, the size of this
matrix, and therefore the computing resources to determine it, scale
exponentially with the number of qubits. However, given this matrix, one can
invert it using a variety of techniques Kandala  _et al._ (2017); Song  _et
al._ (2017); Chen  _et al._ (2019); Geller and Sun (2020); Nachman and Geller
(2021); Wei  _et al._ (2020); Hamilton  _et al._ (2020); Maciejewski  _et al._
(2020); Nachman  _et al._ (2020); Maciejewski  _et al._ (2020), where the last
method is directly related to techniques developed for detector unfolding in
HEP collider physics. This corrects a given measurement on average. Recently a
technique using active readout error correction, where each qubit to be
measured is encoded into multiple qubits using repetition or hamming codes,
have been developed Günther  _et al._ (2021); Hicks  _et al._ (2022). This
allows for readout-error correction for each individual measurement. Examples
of other approaches to readout errors are discussed in Refs. Kandala  _et al._
(2019b); Funcke  _et al._ (2020); Nation  _et al._ (2021).

Gate errors depend on the details of their implementation in the quantum
simulator, and most of the commercial systems available do not provide enough
details to directly mitigate the errors introduced. One often distinguishes
between stochastic and coherent errors. Coherent errors preserve state purity.
They are typically small mis-calibrations in control parameters. Coherent
errors usually produce similar errors in consecutive executions of a quantum
circuit and lead to a systematic bias in the output. Stochastic errors can be
understood as either coherent errors with randomly varying control parameters
or as processes that entangle the system with its environment. Stochastic
errors can often be modeled as depolarizing noise. A method for converting
coherent errors into incoherent errors is randomized compiling Wallman and
Emerson (2016); Li and Benjamin (2017); Cai and Benjamin (2019); Cai  _et al._
(2020). The dominant gate error is typically found in gates that introduce
entanglement between qubits, and a common universal gate introducing such
entanglement is the CNOT gate.

Among the common noise-mitigation techniques for CNOT errors (but which can be
also used for other gate errors) are zero-noise extrapolation (ZNE) and its
variants Li and Benjamin (2017); Temme  _et al._ (2017); Kandala  _et al._
(2019a); Klco  _et al._ (2018); He  _et al._ (2020); Sun  _et al._ (2021a);
Bauer  _et al._ (2021c). ZNE magnifies the noise in the system either by
changing the gate operation time or by replacing each CNOT gate by a larger
odd number of CNOT gates. Since applying two CNOT gates in direct succession
amounts to an identity operation (${\rm CNOT}^{2}=\mathbbm{1}$), this does not
change the circuit in the noiseless limit, but it increases the amount of
noise. This allows to measure the result of the circuit at different noise
levels, which can be used to extrapolate the measurement to the noiseless
limit. For the dominant depolarizing-error channel, one can prove that this
techniques reduces the noise level in a quantifiable way, with the amount
depending on the order of the extrapolation used He  _et al._ (2020). Other
techniques have been proposed which either require knowledge of the noise
model or use circuits to measure it Endo  _et al._ (2018, 2019); Otten and
Gray (2019a, b); Strikis  _et al._ (2021); Urbanek  _et al._ (2021). Another
interesting idea is to use the symmetries of the simulated system to control
and mitigate errors Bonet-Monroig  _et al._ (2018); Otten  _et al._ (2019). An
interesting question that requires more study is whether gauge invariance in
gauge-field theories can be used to detect and mitigate errors in the quantum
simulators Stryker (2019); Raychowdhury and Stryker (2020b).

While noise mitigation is not a requirement that is specific to simulations
for HEP applications, the HEP community might be able to contribute to this
important problem. For decades, high-energy physicists have mastered the
science of distinguishing tiny elusive signals from dominant background noise,
and of sheltering sensitive particle detectors and readout instruments from
environmental noise. It is conceivable that further noise-suppression
techniques at the level of the hardware, and noise-mitigation schemes at the
level of algorithms, can emerge from communications and collaborations among
the two communities in the comping decade(s).

###  X.0.3 Quantum annealers

Quantum annealers are non-universal quantum optimizer machines. Annealers
Johnson  _et al._ (2011) with more than 5000 qubits and associated simulators
(with white noise) are accessible via cloud, and their performance is being
benchmarked across a wide range of problems, from commercial optimization
problems, to finance, to applied mathematics, biology, materials, nuclear
physics, and HEP. One niche target for quantum annealers is to find optimal or
near-optimal solutions to NP-hard problems, although their ultimate
performance relative to classical competitors is unknown. In HEP research, the
types of problems being addressed include track reconstruction in the analysis
of collider data, e.g. Refs. Mott  _et al._ (2017); Zlokapa  _et al._ (2021);
Bapst  _et al._ (2020) and real-time simulations of elementary components
required for QFTs A Rahman  _et al._ (2021); Illa and Savage (2022). Annealers
use time-dependent adiabatic switching to minimize the quadratic unconstrained
binary optimization (QUBO) cost function, or mappings to an Ising model,
constructed to address the problem of interest, including eigenstates and
energies, real-time dynamics using the Feynman Clock algorithm, and problems
that are NP-Hard (or NP-complete), such as max-cut problems.

The quantum devices have extensive hardware controls (e.g., controlling
parameters of the annealing process) that require higher-level expertise and
allocations of device time to gain experience with. The D-Wave systems have a
low bar for entry to new users, with extensive documentation available online,
including tutorials. Algorithms that have been developed and integrated into
HEP computational efforts, such as lattice QCD, have been found to be valuable
to working with the annealing systems A Rahman  _et al._ (2021); Illa and
Savage (2022). Beyond optimizations for classical NP-Hard problems, a
challenge currently faced in addressing classes of HEP problems is the
dimensionality of their QUBO representations. The need for binary-string
representations of complex numbers defining wavefunctions provides a challenge
to the scale of problems that can be embedded on the device. With next-
generation annealers having increased qubit connectivity and more qubits,
larger problem instances can be addressed, but paths for tackling problems at
scale (beyond pre-conditioning) remain to be established.

###  X.0.4 Benchmarking for HEP

In the context of quantum simulation of HEP, the principles of locality and
unitarity that played a crucial role in the establishment of the SM also
guarantees that dynamics of QFTs of relevance to nature can be factorized into
unitary building blocks that act on a finite Hilbert space independent of the
size of the system. This is the central argument for quantum advantage in
quantum simulation of physical systems Lloyd (1996). Developing, optimizing,
and testing these building blocks is a near-term task that can be started with
existing NISQ devices following the roadmap discussed in Sec. VI. In this
context, error mitigation, device comparisons, and benchmarking are essential
for making progress.

In particular, it is important to introduce metrics to assess the progress
made and compare devices. This is an essential aspect of the hardware and
software developments that allows to match applications to platforms that best
implement them. Indices have been proposed to compare mitigated real-time
evolution with the exact Trotter evolution for different quantum devices
Gustafson  _et al._ (2021c). Furthermore, sophisticated methods such as cycle
benchmarking Erhard  _et al._ (2019) have been developed to characterize the
systematic errors of NISQ devices and applied to the quantum Ising model
Yeter-Aydeniz  _et al._ (2022b) with a specific IBMQ machine.

The HEP community will continue to develop and apply new NISQ-tailored
simulation algorithms in the coming years. It would be interesting to see what
the limit of NISQ computing is for HEP applications and whether one can
anticipate any quantum advantage in HEP in the NISQ era of quantum computing.

##  Appendix XI Simulator requirements: Software and compilers

Early investments by DOE HEP have enabled research into algorithms and
applications for the study of HEP problems on the NISQ devices. These early
explorations have been critical to understanding how quantum computers may be
used to solve challenging physics problems. Experiences with these early
science explorations have demonstrated the need to expand the programmability
of quantum-computing devices for testing new and creative quantum algorithms.

###  XI.0.1 Current state of software and compilers

A variety of low-level quantum-computing programming languages akin to
assembler-level programming models in classical computing have been developed
over the past decade, and several of those have been used recently to program
actual hardware devices. They are low-level programming languages that work
well for knowledgeable experts. Widely used software systems include the IBM’s
Qiskit Anis  _et al._ (2021), Xanadu’s Strawberry Fields Killoran  _et al._
(2019), Google’s Cirq Developers (2021), and Microsoft’s $Q\\#$ language Svore
_et al._ (2018).

Transpilers and early low-level compilers are being developed to optimize the
user-generated operations—generally referred to as circuits—into a shorter and
more efficient set that can be translated to pulses and other fundamental
operations needed to execute on quantum hardware. Transpilation tools utilize
multiple pathways to optimize performance utilizing a wide variety of methods,
including graph optimization Sivarajah  _et al._ (2020), unitary synthesis
Younis  _et al._ (2021), and ZX-Calculus van de Wetering (2020) to name a few.
Many of these tools also incorporate hardware-specific knowledge, such as
topologies and error rates to deliver the best performance possible. Full
error correction is simply not feasible for near-term quantum computers due to
limits in scale and the levels of noise. Nearly all scientific simulations
require (mostly) non-automated application of error-mitigation approaches to
achieve reliable results Endo  _et al._ (2021); He  _et al._ (2020); Urbanek
_et al._ (2021); Kandala  _et al._ (2019a); Huggins  _et al._ (2021b).

To ease the programmability for quantum computers, higher-level programming
frameworks will be needed. Some efforts have led to OpenFermion McClean  _et
al._ (2020) for materials and chemical sciences and Pennylane Bergholm  _et
al._ (2018) that is primarily focused on machine learning. Within the DOE,
efforts are underway in the Office of Advanced Scientific Computing Research
to develop a software toolkit that includes higher-level programming models
Nguyen  _et al._ (2021c). No higher-level programming models suitable for HEP
are currently available, though homegrown tools are being developed at various
institutions.

###  XI.0.2 HEP programming needs

To advance HEP research on quantum computers, and enable the broader HEP
community to readily participate, models and approaches for programming
quantum computers need to mature to a level in which abstractions and library-
based methods can be adopted to expedite programming and ensure
portability.222See a Snowmass whitepaper on “Quantum Computing Systems and
Software for High-energy Physics Research” Humble  _et al._ (2022) for further
discussions. This will require the development of programming languages,
potentially domain-specific languages, that can readily express the
discretization and complex interactions, such as the need to describe the
coupling of fermions and bosons and open quantum systems, provides key
building blocks, such as non-trivial arithmetic subroutines that are prevalent
in quantum simulating the dynamics of non-Abelian lattice gauge theories, or
large (sparse) matrix inversion for expediting Monte-Carlo-based routines
present in the conventional lattice-gauge-theory program. Considering
programmability needs for digital simulations, it should be noted that there
is a significant overlap with other science domains, including quantum
chemistry and materials, that should be exploited.

In addition to programming languages and libraries, the HEP research community
would benefit from efficient compilers that can take the programs written in
high-level programming languages to efficient low-level code that can be run
efficiently on quantum-computing hardware. Inter-operability of software is a
key feature to ensure low barriers for HEP users to access across different
systems, and avoid being restricted to a single, potentially proprietary
software pathway. Open-source software and tools will be essential for broad
access, and tools that enable researchers to debug, verify, and validate
quantum-computer programs and results will be needed. Last but not least, a
hybrid computing model involving tightly-coupled classical and quantum
hardware could be explored to enable the usual offloading of special-purpose
calculations to a QPU XAC ; Nguyen  _et al._ (2021d).

Much of the discussion in this section has so far focused on digital quantum
computing, along the lines of the field’s usage of classical computers.
However, one could also utilize quantum computers as well-controlled analog
systems, as discussed in Supp. VIII. For example, some recent work has
utilized the cross-resonance effect of a superconducting quantum computer to
replace sequences of one-and two-qubit gate operations Babukhin  _et al._
(2020); Gonzalez-Raya  _et al._ (2021). This very different quantum-computing
paradigm will require that users to effectively engage across the quantum-
computing stack, and to have access to software layers that generate pulses
needed to drive the interactions of relevance to HEP applications, such as
those of lattice gauge theories.

##  Appendix XII Quantum ecosystem: Hardware co-design and accessibility

While it is in principle possible to construct gate-based quantum-computing
algorithms without detailed knowledge of the underlying hardware, the resource
constraints of today’s systems imply severe limitations on the scale of
computations, and imply a need for hardware-aware efficient implementations
and designs that take advantage of a detailed understanding of system
interactions and connectivity, as well as error and decoherence mechanisms.
This favors tightly-coupled collaborative models for executing science
programs, in which hardware providers and domain experts in HEP applications
co-develop scientific agendas. This requirement also motivate the need for
accessible and adjustable devices such that HEP and other domain scientists
can use to benchmark algorithms and test new ideas.

###  XII.0.1 Co-design models and special-purpose devices

In the early days of the conventional lattice field theory program, research
groups at a number of institutions around the world started to successfully
design, build, and run classical-computing hardware dedicated to QCD
simulations. One such development in the U.S. became the precursor to the so
called QCD-on-a-chip (QCDOC) machine, that via technology transfer to IBM
became the underlying design of successful Blue-Gene series of high-
performance supercomputers Boyle  _et al._ (2005, 2004). A similar approach
might prove valuable in the design and deployment of quantum hardware for
lattice-gauge-theory problems. In fact, such a co-design program is even more
relevant in the quantum-computing era as the simulating hardware is itself a
physical system used for a physics application. For example, as mentioned in
Supp. VIII, Rydberg arrays offer the user a degree of flexibility in the
design of the architecture of atom configurations hence model interactions,
trapped ions offer native bosonic degrees of freedom, i.e., phonons
excitations that can be used to encode more efficiently the bosonic fields and
the interactions beyond those possible with only qubits, and cavity QED
hyperbolic lattices can be engineered to simulate physics in curved
geometries, along with many other examples. In the next 5–10 years, scientific
resources should be employed to explore a broad range of co-designed hardware
schemes, fostering a close collaboration between the HEP and the QIS
communities.

In order for the co-design process to be effective, the interaction between
researchers within institutions that deploy quantum hardware is essential.
This allows to find synergies that can lead to collaborations on the design of
algorithms, protocols, and even devices, with immediate applications. Among
successful examples in the present day is the DOE-funded Advanced Quantum
Testbed aqt  at the LBNL, where internal and external collaborators and users
are engaged in developing benchmarking methods that offer new insights into
noise processes and associated mitigation strategies in quantum hardware. This
was done through an iterative process of protocol execution feeding back into
the external theory teams. To assist in this process, application-specific
circuit synthesis, programming sequences, readout, feedback, and noise
mitigation were employed for maximizing circuit depth and learning outcomes.
Through these and other interlocked collaborations and user interaction, the
depth and breadth of science that can be accomplished through novel technology
can be advanced, enabling science that goes beyond cloud-based quantum-
computing resources.

In addition to DOE programs at the national laboratories, several commercial
hardware service providers now offer in-house services to help design
efficient hardware-cognizant implementations on demand IBM ; Que ; Xan ; QCI ;
Dwa . This will remove the wall between the users and cloud-based services
with preset features and will allow the needs of the domain scientists to be
communicated directly to the hardware and software developers. At the
university setting, experimental efforts have long been in harmony with
theoretical proposals in quantum simulation, and there is a direct
relationship between strong theory groups and strong experimental groups at
the universities. Such a model will potentially be the key to success in
arrangements outside academia as well. For HEP applications, resources and
opportunities in co-design efforts will need to be directed toward systematic
evaluation of the best methods to simulate Hamiltonians of relevance to HEP
efficiently and accurately, design and perform state-preparation and state-
tomography in strongly-interacting QFTs, understand the role of decoherence
mechanisms, and how best to incorporate symmetries and gauge and scale
invariance, or take advantage of them to mitigate or correct the errors.

###  XII.0.2 Hardware-access model

In the rapidly-evolving landscape at the interface between HEP and QIS, it is
important for the HEP community to identify optimal ways to have access to
state-of-the-art programmable quantum computers or quantum-simulation
experiments. In the coming years, the ability to access multiple platforms
with a variety of architectures would lead to rapid progress on target
problems in HEP, as each platform would be most suitable for particular
problems. As already mentioned, this access could be through existing
experimental setups, either located in universities and national laboratories
or by contracting private companies. At the software and compiler front, the
most popular frameworks for programming universal quantum computers such as
Qiskit, Cirq, and pyQuil have so far been offered as free and open-source
resources. This has been critical for the HEP community, and will be important
that this tradition continues as these packages become more advanced and gain
commercial value. By making quantum machines available to researchers,
companies can ensure competitiveness in the future, which is a practice now
pursued by several countries, see e.g., Ref. Pollet ; Gougard ; Flinders .
Finally, it is also often necessary to run relatively large simulations on
classical computers, as numerical tests and benchmarks in the quantum-
simulation problems is a necessity. It is conceivable that these calculations
start to require a non-negligible time at High Performance Computing (HPC)
facilities, and this requirement should be recognized ahead of time.

One successful model for how accessibility of resources in HEP can be ensured
is the USQCD-collaboration model. USQCD usq  is a meta collaboration of the
majority of U.S. lattice gauge theorists. It has benefited from dedicated
hardware at Brookhaven National Laboratory, Fermi National Accelerator
Laboratory, and Thomas Jefferson National Accelerator Facility, and provides
access to these resources for the members via proposal solicitation and a
rigorous review process. It also makes community-wide bids for time on
leadership-class computing facilities managed by the DOE, which has led to
successful acquisition of computing time for large-scale lattice-QCD projects
over the years. One could envisage a meta collaboration of U.S. HEP-QIS
theorists whose main goal would be to strengthen individual efforts and
coordinate their access to different hardware platforms available at national
labs or commercial sites. It would also facilitate communications between
people developing QC hardware and the needs of the theorists developing
algorithms and software for HEP applications. USQCD has also been successful
in bringing up a collaborative algorithm-development team feeding into
independent and basically competing individual groups. It can be thought of as
a “virtual U.S. lab” that could be emulated for the QIS community. It is also
important to identify the most pressing needs of the potential users. For
these reasons, the communication between the HEP researchers and
experimentalists developing new computational platforms need to be enhanced,
and these communications can be strengthened by a unifying voice within the
HEP community.

In summary, in the quantum-era of computing, progress in quantum simulation of
HEP problems will be fostered by close collaborations among HEP and QIS
scientists with a range of expertise, leading to a valuable co-design process
and potentially to special-purpose platforms. This should be accompanied by
direct and broad access to leading hardware and software technologies, and via
a community-approved mechanism that can unify, advocate for, and coordinate
the accessibility needs of HEP scientists.

##  Appendix XIII Quantum ecosystem: Skill sets and workforce development

Quantum simulations of processes essential to HEP research objectives require
a diverse and inclusive quantum-ready workforce with skills that extend
significantly beyond those traditionally in HEP. This workforce will be
distributed and collaboratively trained at universities, national laboratories
and even some technology companies. The pipeline for recruitment should start
earlier, extending into high school. A complementary and robust portfolio of
funding mechanisms, career development opportunities, career paths and
mentoring will be required to create and sustain this workforce.

###  XIII.0.1 Quantum workforce for HEP

Workforce development is a key component in advancing HEP’s quantum-simulation
objectives. Through the natural re-alignment of some of the existing
workforce, and the recruitment and training of junior scientists, the HEP
workforce is expected to evolve in a way to enable HEP objectives to be
accomplished using quantum simulation. The intrinsically interdisciplinary
nature of quantum simulation for HEP requires growing or collaborating with
expertise in QIS, computer science, applied mathematics, statistics, material
science, nuclear physics, and more, with scientists, engineers and developers
residing in national laboratories, universities, and technology companies. At
this time, this growth and engagement has been underway in HEP for
approximately five years, and it will need to continue and be further enhanced
to meet HEP scientific objectives during the next decade and beyond.

The growth of the quantum-ready HEP workforce is occurring in the context of
significantly-increased national quantum information science and technology
research and development to meet broad-based present and future needs of the
nation National Academies of Sciences, Engineering, and Medicine (2019). When
mature, the associated quantum economy is expected to be comparable to the
silicon economy, and with a workforce of scale to enable a robust and
efficient pipeline from basic research to commodity devices in quantum
computing, communication, sensing, and more. It is important to recognize that
the growth of the quantum-ready HEP workforce, with skill-sets necessary to
meet HEP objectives, will be of significant benefit to the national quantum
activity. Historically, HEP scientists have contributed to, or moved into,
other areas of research, such as computing, “big data”, and device
fabrication, and have shaped the development of those areas in substantial
ways. The same is anticipated in the emerging quantum era.

The present “Snowmass” process is the first in which QIS is being considered
an integral part of HEP research and development, and consequently, estimates
of the resources and training required to meet the HEP QIS needs are less
sophisticated than in the more mature areas. This next period is one of
research and development in basic science through to advanced technologies.
This includes continued calibration, development, resource estimation and
engagement, including in the development of a quantum-ready HEP workforce with
successful career opportunities.

###  XIII.0.2 Required skill-sets and the role of universities, national labs,
and private sector

The skills required for quantum simulations of processes essential to the HEP
mission are diverse Hughes  _et al._ (2021). Experiences from the last decades
of workforce development in lattice QCD, event generators, and other HPC-
intensive research areas, have provided models of engagement that are expected
to have applicability. Collaborations of scientists, engineers, and developers
will be required to coalesce the skill-sets required to accomplish quantum-
simulation objectives. These skills include HEP phenomenology, quantum field
theory and quantum mechanics, lattice field theory, high-performance
computing, statistical analysis, experimental design and optimization, machine
learning and artificial intelligence, software stack development, quantum- and
classical-computing algorithms, quantum-circuit design, implementation and
optimization, and more. Integration with quantum hardware development through
HEP co-design efforts will further broaden this skill-set. The education and
training programs for these skills are distributed within universities,
national laboratories and the private sector. Therefore, coordination between
these sectors is required, and all have an important role to play. For
instance, one expects universities to provide basic to advanced education in
physics, including quantum mechanics, quantum field theory, and particle
theory, along with basic to advanced education in statistics and applied
mathematics. National Laboratories continue to develop the talent produced by
universities and technology companies, and can assemble significant teams to
address mission-specific objectives. Technology companies, in part, perform
focused research and development to produce commodity products. For quantum
simulation, this includes developing quantum computers and quantum devices,
developing robust software stacks, and Application Programming Interfaces.

These educational and training pipelines need to be both strengthened and
expanded in the area of QIS. While Physics departments at universities
specialize in education in physics, both experimental and theoretical, an
increase in the the advanced offerings in broadly-defined quantum field theory
and quantum many-body systems, for instance through courses in HEP, nuclear
physics and condensed matter physics, would directly benefit efforts in HEP
quantum simulation. It would also be beneficial for universities to integrate
quantum-circuit design between physics, engineering, and computer science.
Such moves are already underway, but the inclusion of HEP relevant offerings
would be beneficial.

Given the scope of the anticipated quantum ecosystem, the pipeline for quantum
education and training should begin before students reach university. It would
be beneficial for introductory QIS to become part of high-school level science
requirements. The QuarkNet program qua  for developing the future technical
workforce stands as an existing example of how the community could integrate
HEP-QIS at this level. Increased opportunities for high-school students to
work with scientists at universities and national laboratories are expected to
be beneficial to quantum-simulation efforts, including in HEP.

The National Quantum Initiative (NQI) centers NQI  and QuantiSED programs
effectively support the development of junior scientists, including
postdoctoral fellows and graduate students. While Covid-19 has provided a
substantial limitation to in-person meetings, workshops and collaborations,
the regular meetings and activities have proven valuable in education and
training. More QIS-training and educational opportunities at all career levels
are required. For example, there will be utility in supporting HEP-specific
summer schools in quantum simulation, like the recently-started Quantum
Computing Internship for Physics Undergraduates Program at FNAL, alongside the
more general schools in QIS that are organized by Los Alamos National
Laboratory. Programs analogous to the “lattice-QCD Hackathons” are anticipated
to have a future role in training for quantum-simulation research. Named
fellowships are used successfully at labs and universities to attract talent
at the postdoctoral and Ph.D. levels for strategic purposes, and such
fellowships for HEP quantum simulation would be of value.

###  XIII.0.3 Career development and mentoring

In order to meet the needs of the nation at all scales, including those for
HEP quantum simulation, career development and mentoring has to be available
at all stages and levels, for those so wishing. It is important to emphasize
that this area of research did not exist until recently, and further it has a
different required skill-set for the participating workforce. Until recently,
the workforce in this area has come exclusively from transitions from other
areas, and the first generation of QIS-HEP scientists is currently being
trained. Therefore, the landscape of research in HEP-QIS has been changing
quite rapidly, but is anticipated to stabilize during the next decade. There
is only anecdotal information available regarding career paths, how one is
best positioned for a career in QIS, what courses students should take and so
forth. As universities introduce new courses, there will be differences
between offerings at different institutions. This makes mentoring by members
of our community, at all levels, crucial, as is engagement with those in the
national laboratories, the business sector, the legal sector, etc. This needs
to be addressed during the upcoming period. Programs such as the National
Science Foundation’s ExpandQISE Exp  will be essential in empowering smaller
and less-involved institutions with the QIS research.

The next period will be one of experimentation to identify the types of
mentoring and career guidance that are effective. Importantly, one type of
institution will no longer be sufficient to impart all of the skills that are
required, and collaborative mentoring should be explored and assessed.
Therefore, new and creative ways of educating and training junior, mid-career,
and senior scientists, engineers, and developers are to be encouraged and
explored. Importantly, this exploration should include drawing talent from
previously under-considered groups.

In designing/exploring potentially new avenues of developing this needed HEP-
QIS workforce, flexibility should be considered so that under-represented
sectors of the population have unimpeded and equal access to QIS education and
training, unlike previous generations, and are welcomed into the HEP
community. For this inclusive and diverse community to thrive, its members
must be supportive of each other and of the broader scientific goals, and
behave respectfully, ethically, and honestly. Codes of Conduct are now an
integral part of formal collaborations in the community, and will continue to
be important in future efforts. HEP should participate in the on-going
national-level discussions on this crucially-important subject.

One of the lessons learned from the recent decades of SciDAC sci  and HPC-
oriented projects in HEP is in regard to the career path of senior researchers
who start as domain scientists and evolve into specialist algorithm designers
and coders for HEP. This set of talented and essential scientists and
developers will typically leave the community to assume positions in the
private sector. This impacts the workforce, while building connections with
the private sector. Without identifying more desirable career paths within
HEP, this situation may repeat itself in the HEP quantum-simulation era.

Joint positions between laboratories and universities have been successful in
sustaining the HEP workforce. In contrast, the use of strategic bridge
positions to strengthen the HEP workforce has been under-utilized. As there is
a strategic need to increase the workforce in quantum simulation for HEP,
consideration should be given to using joint and bridge positions at
universities at the Assistant Professor level (or higher) to attract talent
into the program, and also to address the expected in-balance between Ph.D.
graduates and postdocs leaving HEP research for a career in the private
sector. The HEP experts in universities are sure to be attracted to technology
companies, and efforts should be undertaken to future-proof the HEP program
for the long-term health of the community.

In summary, the HEP community is starting to develop a quantum-simulation
workforce in order to address important objectives of the HEP scientific
mission. For a diverse and inclusive quantum-ready HEP workforce of
scientists, engineers, and developers to be at the forefront of quantum
simulation, close collaborations between universities, national laboratories,
and technology companies are critical, see also Supp. XIV. The types of
resources and the nature of engagements that are anticipated to be required
for this to be successfully accomplished were outlined in this Suuplemental
Section.

##  Appendix XIV Quantum ecosystem: Academia, government, industry partnership

Quantum simulation in HEP is a unique research discipline that cannot grow in
isolation. When algorithm, software, and hardware developments are concerned,
there are multiple players in the field, from universities to national
laboratories to private companies, each contributing to the advancements
according to the organizations’ strategic agendas. It is important for HEP
scientists to acknowledge this entangled web of contributors, and to form
partnerships that are long-lasting and mutually beneficial.

###  XIV.0.1 The role of national laboratories in advancing quantum simulation

HEP has a long-standing history of driving developments in classical high-
performance computing (HPC), an example of which is the emergence of IBM’s
BG/L,P,Q supercomputers starting from the collaborative efforts of Columbia
University, RIKEN, and and Brookhaven National Laboratory (BNL). An important
outcome of this co-design effort and HPC testbed(s) were the technical skills
acquired through “hands-on” experience(s). Similar collaborative efforts are
emerging in HEP in the areas of machine learning and artificial intelligence,
as well as quantum computing, the results of which will benefit many
scientific and technology communities.

The QuantiSED program(s) through DOE HEP that successfully supports QIS in HEP
includes integrated collaborative efforts including FNAL, LANL, BNL, LBNL with
universities and technology companies, and brings together experts from HEP
and other areas, such as computer science, atomic-molecular-optical physics,
machine learning, nuclear physics, condensed matter, and QIS, with a
significant effort related to quantum simulation. Research groups at the
laboratories have skills related to, and are focused on, accomplishing the
objectives of the laboratory. The QuantiSED programs provide a strategic
supplement to these skills through a closer coupling to outside experts. It is
expected that such activities will be essential for further developing the
HEP-QIS workforce going forward. It is also expected that the QIS expertise at
the national laboratories with a HEP footprint to continue to increase
significantly during the next period to meet HEP objectives. A similar
evolution is anticipated in university-based HEP groups, but in a way that
complements the growth at the laboratories. This is, in part, to provide an
education beneficial to the laboratories.

For HPC-centric HEP objectives, such as those advancing lattice QCD and event
generators, the SciDAC program has played a critical role, bringing together
domain scientists and experts in applied mathematics, computer science,
statistics and more through the SciDAC Institutes. These valuable projects are
typically jointly supported by DOE HEP and ASCR. Analogous opportunities for
advancing quantum simulation to meet HEP scientific objectives would provide a
valuable resource.

###  XIV.0.2 Engagement with Technology Companies

A robust engagement between universities, national laboratories, and
technology companies is essential. There is significant and growing expertise
already in the private sector in all areas of quantum. To minimize the time
from development of an idea, prototyping and subsequent integration into a
commodity device, close ties with technology companies are vital. In order for
HEP to be at the forefront of quantum simulation, engagement with technology
companies is critical, and will be mutually beneficial. This engagement spans
areas such as quantum hardware, operating systems, and application programming
interfaces.

A somewhat novel aspect of HEP-QIS is the need to address IP rights within
collaborations, which will involve legally-binding agreements. This represents
somewhat of a “different culture” for many in the HEP community, and perhaps
this may be a conceptual hurdle that has to be overcome as it does collide
with the basic concepts of open science. It has to be the case that all
developments of importance to HEP research from engagements with technology
companies are future-proofed. That is to say that any advance that enables
accomplishing one or more objectives of the HEP mission must be able to reside
in the community and not be lost behind an IP barrier if a company decides
that this line of research is no longer a priority.

###  XIV.0.3 Engagement with other domain sciences, engineering, and computing

The types of problems that require quantum simulation in HEP are similar in
form to those in the other domain sciences. For example, non-equilibrium
dynamics in quantum many-body systems is of interest in QIS, condensed matter,
nuclear physics, fluid dynamics, fusion, biology, as well as HEP. It is also
the case that the techniques that are being developed for the simulation of
QFTs may also be of relevance for quantum sensing and communications.
Workshops, meetings and collaborations, as are being enabled by the NQI
centers, are crucial to optimal exchange of ideas and translations between
languages and notations of these different communities. In order for the
communities to not have to reinvent the wheel, it is important that areas of
overlap are identified and developments are being transported across
seemingly-disjoint disciplines. For example, lessons can be learned from how
quantum information impacted and advanced studies of condensed-matter systems
over the past decade, since it is likely that the HEP research can be
similarly invigorated by the QIS concepts and tools. Finally, HEP will likely
be instrumental in motivating and advancing QIS research, thus an integrated
HEP-QIS effort will be mutually beneficial in quantum simulation.

##  Appendix XV Community endorsement

  1. 1.

M. Sohaib Alam
_Quantum Artificial Intelligence Laboratory (QuAIL), NASA Ames Research
Center, Moffett Field, CA, 94035, USA_

_USRA Research Institute for Advanced Computer Science (RIACS), Mountain View,
CA, 94043, USA_

  2. 2.

Mohsen Bagherimehra
_Chemical Physics Theory Group, Department of Chemistry, University of
Toronto, Ontario, Canada_

_Institute for Quantum Science and Technology, University of Calgary, Alberta,
Canada_

  3. 3.

Aniruddha Bapat
_Physics Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720,
USA_

  4. 4.

Douglas H. Beck
_Department of Physics and Illinois Quantum Information Science and Technology
(IQUIST) Center, University of Illinois, 1110 W. Green Street, Urbana, IL
61801, USA_

  5. 5.

Paulo F. Bedaque
_Department of Physics and Maryland Center for Fundamental Physics, University
of Maryland, College Park, MD 20742, USA_

  6. 6.

David Berenstein
_Department of Physics, University of California, Santa Barbara, CA 93106,
USA_

  7. 7.

Joseph Carlson
_Theoretical Division, Los Alamos National Lab, NM 87545, USA_

  8. 8.

Alessio Celi
_Departament de Física, Universitat Autònoma de Barcelona, E-08193 Bellaterra,
Spain_

  9. 9.

Shailesh Chandrasekharan
_Department of Physics, Duke University, Durham NC, USA_ 27708-0305

  10. 10.

Anthony N. Ciavarella
_InQubator for Quantum Simulation (IQuS), Department of Physics, University of
Washington, Seattle, WA 98195_

  11. 11.

Eleanor Crane
_Cambridge Quantum Deutschland GmbH, Leopoldstrasse 180, 80804 Munich,
Germany_

  12. 12.

Marcello Dalmonte
_The Abdus Salam International Centre for Theoretical Physics (ICTP), strada
Costiera 11, 34151 Trieste, Italy_

  13. 13.

Andrea Delgado
_Oak Ridge National Laboratory, Oak Ridge, TN, USA_

  14. 14.

Xi Dong
_Department of Physics, University of California, Santa Barbara, CA 93106,
USA_

  15. 15.

Lena Funcke
_Center for Theoretical Physics, Co-Design Center for Quantum Advantage, and
NSF AI Institute for Artificial Intelligence and Fundamental Interactions,
Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA
02139, USA_

  16. 16.

Bryce Gadway
_Department of Physics, University of Illinois, 1110 W. Green Street, Urbana,
IL 61801, USA_

  17. 17.

Daniel González-Cuadra
_Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck,
Austria_
_Institute for Quantum Optics and Quantum Information of the Austrian Academy
of Sciences, 6020 Innsbruck, Austria_

  18. 18.

Alexey V. Gorshkov
_Joint Quantum Institute and Joint Center for Quantum, Information and
Computer Science, NIST/University of Maryland, College Park, Maryland 20742,
USA_

  19. 19.

Erik Gustafson
Fermi National Accelerator Laboratory, Batavia, IL 60510, USA

  20. 20.

Mohmmad Hafezi
_Joint Quantum Institute, University of Maryland, College Park, MD 20742, USA_

  21. 21.

Jad C. Halimeh
_Department of Physics and Arnold Sommerfeld Center for Theoretical Physics
(ASC), Ludwig-Maximilians-Universität München, Theresienstraße 37, D-80333
München, Germany_
_Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4,
D-80799 München, Germany_

  22. 22.

Aram Harrow
_Center for Theoretical Physics, Massachusetts Institute of Technology,
Cambridge, MA 02139, USA_

  23. 23.

Philipp Hauke
_INO-CNR BEC Center and Department of Physics, University of Trento, Via
Sommarive 14, I-38123 Trento, Italy_

  24. 24.

Florian Herren
_Fermi National Accelerator Laboratory, Batavia, IL 60510, USA_

  25. 25.

Ciaran Hughes
_Theoretical Physics Department, CERN, 1211 Geneva 23, Switzerland_

  26. 26.

Travis S. Humble
_Oak Ridge National Laboratory, Oak Ridge, TN, USA_

  27. 27.

Joshua Isaacson
_Fermi National Accelerator Laboratory, Batavia, IL 60510, USA_

  28. 28.

Karl Jansen
_Deutsches Elektronen-Synchrotron DESY, Platanenallee 6, 15738 Zeuthen,
Germany_

  29. 29.

Natalie Klco
_Institute for Quantum Information and Matter and Walter Burke Institute for
Theoretical Physics, California Institute of Technology, Pasadena CA 91125,
USA_

  30. 30.

Michael Kreshchuk
_Physics Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720,
USA_

  31. 31.

Andreas Kronfeld
_Fermi National Accelerator Laboratory, Batavia, IL 60510, USA_

  32. 32.

Doga Murat Kurkcuoglu
_Superconducting Quantum Materials and Systems Center (SQMS), Fermi National
Accelerator Laboratory, Batavia, IL 60510, USA_

  33. 33.

Nima Lashkari
_Department of Physics and Astronomy, Purdue University, West Lafayette, IN
47907, USA_

  34. 34.

Randy Lewis
_Department of Physics and Astronomy, York University, Toronto, ON, M3J 1P3,
Canada_

  35. 35.

Andy C. Y. Li
_Fermi National Accelerator Laboratory, Batavia, IL 60510, USA_

  36. 36.

Norbert M. Linke
_Joint Quantum Institute and Department of Physics, University of Maryland,
College Park, Maryland 20742, USA_

  37. 37.

Niklas Mueller
_Department of Physics, Maryland Center for Fundamental Physics, and Joint
Quantum INstitute, University of Maryland, College Park, MD 20742, USA_

  38. 38.

Yasser Omar
_Portuguese Quantum Institute, and Instituto Superior Técnico, Universidade de
Lisboa, P-1049-001 Lisbon, Portugal_

  39. 39.

Vincent R. Pascuzzi
_Brookhaven National Laboratory, Upton, NY 11973, USA_

  40. 40.

Indrakshi Raychowdhury
_Birla Institute of Technology and Science, Pilani, K. K. Birla Goa Campus,
Zuarinagar, Goa - 403726, India._

  41. 41.

Enrique Rico
_IKERBASQUE, Basque Foundation for Science, Plaza Euskadi 5, 48009 Bilbao,
Spain_
_Department of Physical Chemistry, University of the Basque Country UPV/EHU,
Apartado 644, 48080 Bilbao, Spain_
_EHU Quantum Center, University of the Basque Country, UPV/EHU, Barrio
Sarriena s/n, 48940 Leioa, Biscay, Spain_

  42. 42.

Ananda Roy
_Department of Physics and Astronomy, Rutgers University, Piscataway, NJ
08854-8019, USA_

  43. 43.

Alexander Schuckert
_Cambridge Quantum Deutschland GmbH, Leopoldstrasse 180, 80804 Munich,
Germany_

  44. 44.

Hersh Singh
_InQubator for Quantum Simulation (IQuS), Department of Physics, University of
Washington, Seattle, Washington 98195-1550, USA_

  45. 45.

Jesse Stryker
_Department of Physics,= and Maryland Center for Fundamental Physics,
University of Maryland, College Park, MD 20742, USA_

  46. 46.

Federica Maria Surace
_Department of Physics and Institute for Quantum Information and Matter,
California Institute of Technology, Pasadena, California 91125, USA_

  47. 47.

Shan-Wen Tsai
_Department of Physics and Astronomy, University of California, Riverside, CA
92521, USA_

  48. 48.

James P. Vary
_Department of Physics and Astronomy, Iowa State University, Ames, IA USA_

  49. 49.

Wei Xue
_Department of Physics, University of Florida, Gainesville, FL 32611, USA_

  50. 50.

Torsten V. Zache
_Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck,
Austria_
_Institute for Quantum Optics and Quantum Information of the Austrian Academy
of Sciences, 6020 Innsbruck, Austria_

  51. 51.

Erez Zohar
_Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem
91904, Givat Ram, Israel_

  52. 52.

Peter Zoller
_Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck,
Austria_
_Institute for Quantum Optics and Quantum Information of the Austrian Academy
of Sciences, 6020 Innsbruck, Austria_

##  Appendix XVI Acknowledgements and funding information

We are grateful to the members of the community who endorsed this document as
named in Suppl. XV, as well as to Mohsen Bagherimehrab, Aniruddha Bapat,
Shailesh Chandrasekharan, Lena Funcke, Jad Halimeh, Aram Harrow, Philipp
Hauke, Joshua Isaacson, Karl Jansen, Natalie Klco, Michael Kreshchuk, Andreas
Kronfeld, Norbert Linke, Vincent Pascuzzi, Indrakshi Raychowdhury, Enrique
Rico Ortega, Ananda Roy, Federica Surace, Wei Xue, Erez Zohar, and Martin
Zwierlein for valuable feedback on an earlier draft of this whitepaper.

Christian Bauer is supported by the U.S. Department of Energy’s (DOE’s) Office
of Science under contract DE-AC02-05CH11231. In particular, support comes from
Quantum Information Science Enabled Discovery (QuantISED) for High Energy
Physics (KA2401032).

Zohreh Davoudi is supported in part by the U.S. DOE’s Office of Science Early
Career Award, under award no. DE-SC0020271, the DOE’s Office of Science,
Office of Advanced Scientific Computing Research, Quantum Computing
Application Teams program, under fieldwork proposal number ERKJ347, and the
Accelerated Research in Quantum Computing program under award DE-SC0020312.
She also acknowledges support from National Science Foundation Quantum Leap
Challenge Institute for Robust Quantum Simulation under grant OMA-2120757.

A. Baha Balantekin is supported in part by the U.S. DOE’s Office of Science,
Office of High Energy Physics, under award no. DE-SC0019465.

Tanmoy Bhattacharya is partly supported by the Los Alamos National Laboratory
and the U.S. DOE’, Office of Science, Office of High Energy Physics, under
Contract with Triad National Security, LLC, Contract Grant no.
89233218CNA000001 to Los Alamos National Laboratory.

Marcela Carena and Ying-Ying Li are supported by the DOE through the Fermilab
QuantiSED program in the area of “Intersections of QIS and Theoretical
Particle Physics”. Fermilab is operated by Fermi Research Alliance, LLC under
contract number DE-AC02-07CH11359 with the United States Department of Energy.

Wibe Albert de Jong was supported by the DOE’s Office of Science, Office of
Advanced Scientific Computing Research Accelerated Research for Quantum
Computing Program under contract no. DE-AC02-05CH11231.

Patrick Draper and Aida El-Khadra acknowledge support from the DOE’s Office of
Science QuantISED program under an award for the Fermilab Theory Consortium
”Intersections of QIS and Theoretical Particle Physics”.

The work of Masanori Hanada is partly supported by the Royal Society
International Exchanges award IEC/R3/213026.

The work of Dmitri Kharzeev is supported in part by the U.S. DOE’s Office of
Science grants no. DE-FG88ER40388 and DE-SC0012704, and Office of Science,
National Quantum Information Science Research Centers, Co-design Center for
Quantum Advantage under contract DE-SC0012704.

Junyu Liu is supported in part by International Business Machines (IBM)
Quantum through the Chicago Quantum Exchange, and the Pritzker School of
Molecular Engineering at the University of Chicago through AFOSR MURI
(FA9550-21-1-0209).

Yannick Meurice is supported in part by the U.S. DOE’s Office of Science,
Office of High Energy Physics QuantISED program, under award no. DE-SC0019139.

Christopher Monroe is supported by the NSF’s STAQ program, under award
PHY-1818914 and the DOE’s Office of Science, Office of High Energy Physics,
under award no. DESC0019380.

Guido Pagano acknowledges support by the DOE’s Office of Science, Office of
Nuclear Physics, under award no. DE-SC0021143. He is further supported by the
NSF CAREER Award (award no. PHY-2144910), the Army Research Office
(W911NF21P0003), and the Office of Naval Research (N00014-20-1-2695,
N00014-22-1-2282).

The work of Enrico Rinaldi is partly supported by the Royal Society
International Exchanges award IEC/R3/213026. He is further supported by Nippon
Telegraph and Telephone Corporation (NTT) Research.

Martin Savage is supported in part by the U.S. DOE’s Office of Science, Office
of Nuclear Physics, InQubator for Quantum Simulation (IQuS) under award no.
DE-SC0020970.

George Siopsis acknowledges support by the Army Research Office under award
W911NF-19-1-0397, the National Science Foundation under award DMS-2012609, and
by the Defense Advanced Research Projects Agency (DARPA) Optimization with
Noisy Intermediate-Scale Quantum devices (ONISQ) program under award no.
W911NF-20-2-0051.

Kübra Yeter-Aydeniz was supported by MITRE Corporation TechHire Program,
approved for public release with case number 21-03848-2.

##  Appendix XVII Statement of Conflict of Interest

A number of the authors of this whitepaper have a financial interest in the
field of quantum computing and quantum simulation: Nate Gemelke is the Chief
Technology Officer of QuEra Computing Inc., Junyu Liu is a scientific advisor
for qBraid Corporation, Mikhail Lukin is the co-founder of QuEra Computing
Inc., Christopher Monroe is co-founder and chief scientist at IonQ Inc., and
Kübra Yeter-Aydeniz is the Lead Quantum Algorithms Specialist at the MITRE
Corporation.

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