Opportunities for Nuclear Physics & Quantum Information Science

arX

iv:1

903.

0545

3v2

[nu

cl-t

h] 3

0 Ju

l 201

9

Disclaimer This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

Group photo from the workshop Intersections Between Nuclear Physics and Quantum Information held at Argonne National Laboratory on 28–30 March 2018. Names of participants can be found in Appendix A.

Opportunities for Nuclear Physics & Quan-tum Information ScienceEditorsIan C. Cloët1 and Matthew R. Dietrich1

ContributorsIan C. Cloët 1, Matthew R. Dietrich 1, John Arrington 1, Alexei Bazavov2,3, Michael Bishof 1, Adam Freese 1, AlexeyV. Gorshkov4,5, Anna Grassellino6,7, Kawtar Hafidi 1, Zubin Jacob 8, Michael McGuigan 9, Yannick Meurice10,Zein-Eddine Meziani 1, Peter Mueller 1, Christine Muschik11, James Osborn12, Matthew Otten13, Peter Petreczky14,Tomas Polakovic15, Alan Poon16, Raphael Pooser17, Alessandro Roggero18, Mark Saffman19, Brent VanDevender20,Jiehang Zhang 4, and Erez Zohar21

1Physics Division, Argonne National Laboratory, Argonne, IL 60439 USA2Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, MI 48824,USA3Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA4Joint Quantum Institute, NIST/University of Maryland, College Park, MD 20742, USA5Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, MD 20742, USA6Fermi National Accelerator Laboratory, Batavia IL, 60510, USA7Northwestern University, Evanston, IL, 60208, USA8Birck Nanotechnology Center and Purdue Quantum Center, School of Electrical and Computer Engineering, Purdue University,West Lafayette, IN 47906, USA9Computational Science Initiative, Brookhaven National Laboratory, Upton, NY 11973, USA10Department of Physics and Astronomy, The University of Iowa, Iowa City, IA 52242, USA11Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, West Waterloo, Ontario,Canada13ALCF, Argonne National Laboratory, Argonne, IL 60439 USA13Nanoscience and Technology Division, Argonne National Laboratory, Argonne, IL 60439 USA14Physics Department, Brookhaven National Laboratory, Upton, NY 11973, USA15Physics and Material Science Divisions, Argonne National Laboratory, Argonne, IL 60439 USA16Institute for Nuclear and Particle Astrophysics and Nuclear Science Division, Lawrence Berkeley National Laboratory,Berkeley, CA 94720, USA17Quantum Information Science Group, Computational Sciences and Engineering Division, Oak Ridge National Laboratory,Oak Ridge, TN 37831, USA18Institute for Nuclear Theory, University of Washington, Seattle, WA 98195, USA19Department of Physics, University of Wisconsin, Madison, WI 53706, USA20Pacific Northwest National Laboratory, Richland, WA 99354, USA21Max Planck Institute of Quantum Optics, Hans-Kopfermann-Straß e 1, 85748 Garching, Germany

T his whitepaper is an outcome of the workshop Intersections between Nuclear Physics and QuantumInformation held at Argonne National Laboratory on 28–30March 2018 [www.phy.anl.gov/npqi2018/].

The workshop brought together 116 national and international experts in nuclear physics and quantum informationscience to explore opportunities for the two fields to collaborate on topics of interest to the U.S. Department ofEnergy (DOE) Office of Science, Office of Nuclear Physics, and more broadly to U.S. society and industry. Theworkshop consisted of 22 invited and 10 contributed talks, as well as three panel discussion sessions. Topicsdiscussed included quantum computation, quantum simulation, quantum sensing, nuclear physics detectors,nuclear many-body problem, entanglement at collider energies, and lattice gauge theories.

Executive Summary . . . . . . . . . . . . . . . . 41. Introduction . . . . . . . . . . . . . . . . . . 5

1.1. Noisy Intermediate-Scale QuantumComputing . . . . . . . . . . . . . . . 5

1.2. Nuclear Many-Body Problem . . . . . . 61.3. Field Theories and Quantum Computing 71.4. Entanglement at collider energies . . . . 71.5. Document Outline . . . . . . . . . . . . 8

2. Quantum Computing . . . . . . . . . . . . . 82.1. Background . . . . . . . . . . . . . . . 82.2. Types of Quantum Computers . . . . . 92.3. Quantum Simulators . . . . . . . . . . 92.4. Qubit Technologies . . . . . . . . . . . 10

3. Quantum Sensors & Other Opportunities . . . 113.1. Electric Dipole Moments . . . . . . . . 123.2. Superconducting Technologies . . . . . 133.3. Field Detection . . . . . . . . . . . . . 133.4. Isotopes . . . . . . . . . . . . . . . . . 143.5. Ghost Imaging . . . . . . . . . . . . . 143.6. Data Analysis . . . . . . . . . . . . . . 15

4. Conclusion . . . . . . . . . . . . . . . . . . . 15References . . . . . . . . . . . . . . . . . . . . . 15A. NPQI Workshop Participants and Agenda . . 20

Executive SummaryQuantum information science (QIS) is poised to havea transformational impact on science and technology.Given the significant remaining technical and theoreticalchallenges the realization of this potential will requirethe cooperative efforts of academia, national laborato-ries, and industry so that a full spectrum of quantumtechnologies can be made ready for production use onreal-world problems.Such a program can support the core mission of the

Office of Nuclear Physics (ONP) by, e.g., the simulationof gauge field theories using quantum computers and en-abling new nuclear physics experiments using quantumsensors. There is significant overlap in the theoreticaland technical expertise between the NP and QIS commu-nities, and many currently intractable problems in NPcan potentially be tackled using technologies from QIS(e.g. quantum computing). By developing strategies thatlead to better communication and collaboration betweenthese two communities, ONP can play a leadership rolein developing quantum technologies and advancing QIStheory. This whitepaper identifies five broad researchopportunities that will help facilitate QIS research in thecontext of NP.

Research Opportunity I: To best leverage the re-

spective strengths of universities, national laboratories,and industry, funding opportunities that encourage col-laborative projects between the NP and QIS communitiesshould be emphasized. The field of QIS is highly com-petitive, with many well-established research groups.Therefore, NP faces a challenge to invest strategically sothat it can most effectively contribute to and benefit fromQIS. Some relevant NP strengths include: supercon-ducting technologies, microfabrication, supercomputingexpertise, engineering expertise, isotope programs, andnuclear theory. Collaborations within national labora-tories should also be encouraged, since the interdisci-plinary nature of these institutions has a lot to offer QIS,which itself is highly interdisciplinary.

Research Opportunity II: A broad theory programshould be supported, which can, e.g., develop methods toaddress problems inNP using digital quantum computersand quantum simulators, utilize QIS concepts to betterunderstand nuclear phenomena (such as the nuclearmany-body problem and hadronization), and developnew QIS applications of importance to nuclear physics.Technological development is often driven by the need toaddress important problems. Many facets of the nuclearmany-body problem and quantum chromodynamics cannot (currently) be addressed with conventional com-puting methods – despite decades of effort. Stronginteraction nuclear physics therefore provides an idealapplication for QIS. However, significant advances inboth NP and QIS theory (e.g. quantum algorithms) arestill needed, which will require the dedicated effort oftheorists from both communities.Research Opportunity III: Support should be given

to research that seeks to develop or capitalize on QIStechnology with nuclear physics applications. Devel-opment of technology originally intended for QIS hasfrequently generated detectors that can be used to ad-vance basic research. Support for research intendedto implement quantum sensors for nuclear physics ap-plications would further the interests of both the NPand QIS communities, while helping to generate crucialcollaborations.Research Opportunity IV: Support should be given

to develop a QIS workforce in the context of NP byfunding graduate students and postdocs that conductresearch at the intersection of these fields. NP problemsthat seem intractable today can potentially be addressedby a new NP workforce skilled in quantum computingand other aspects of QIS. To develop a robust QIS pro-gram within NP, a workforce skilled in both fields istherefore critical. Funding graduate students and post-

Page 4 of 22

1. INTRODUCTION

docs should be a priority, where collaboration with theDOEOffice of Advanced Scientific Computing Research(ASCR) should be encouraged, and support for an in-dustry internship program may be considered to betterrespond to the demands of industry.

Research Opportunity V: Meetings such as work-shops, schools, and seminars should be supported sothat the NP and QIS communities can better understandthe challenges and capabilities of their counterparts.The full extent of cross-pollination between NP and QISis not yet fully understood. It is crucial to address this byimproving general comprehension between these fields.A combination of workshops, pedagogical schools, andhigh-level seminars (all of which should be broadcast on-line) would promote the formation of new relationshipsand collaborations between interested parties in the NPand QIS communities. In addition a NP-QIS alliancecould be formed to help disseminate pertinent informa-tion (e.g. job openings, seminars, workshops, etc) andthereby help form a more cohesive NP-QIS community.These are important elements for the success of a QISprogram within ONP.

1. IntroductionQuantum information science (QIS) encompasses

fields such as quantum computing and simulation, quan-tum sensors, quantum information theory, and quan-tum communication. By studying and harnessing thequantum nature of matter QIS has the potential for atransformational impact on science and technology.1 Inthe context of the U.S Department of Energy’s (DOEs)Office of Nuclear Physics (ONP) program, which has thegoal to “discover, explore, and understand all forms ofnuclear matter”[1], the significant intersections betweenQIS and NP are evident, e.g., in computation, detectors,and quantum theory.NP presents science with numerous important chal-

lenges, foremost amongst these is understanding thefull implications of quantum chromodynamics (QCD),which is coupled to problems such as the nuclear many-body problem, stellar nucleosynthesis, and neutron stars.QCD is the asymptotically free gauge field theory thatforms the strong interaction piece of the Standard Modelof particle physics, and therefore provides the basis forunderstanding of all forms of nuclear matter. WhileQCD is easy to formulate in terms of quark and gluon

1This situation is not unlike the development of the transistorin the first half of the 20th century, which was also an outcome ofquantum mechanics, and led to inter alia modern computing.

fields [2], it is notoriously difficult to solve [3]. How-ever, QIS provides new methods with which to studyand understand aspects of NP, e.g., in principle quantumcomputing and quantum simulation provide the means tostudy aspects of QCD that are inaccessible with currentcomputational techniques [4, 5]; quantum sensors mayenable new and more precise measurements of nuclearphenomena [6]; and quantum information theory pro-vides a new lens with which to view and study entanglednuclear systems [7] such as nuclei and the quark-gluonstructure of QCD bound states and reactions.

Solving QCD will have profound implications for ourunderstanding of the natural world, most notably it willexplain how 99% of the mass in the visible universe iscreated [8]. The infrared domain of QCD – where therunning coupling becomes large – is also characterized byseveral interesting emergent phenomena, such as, quark-gluon confinement [3, 9], dynamical chiral symmetrybreaking [10, 11], and hadron formation [12, 13], whichcannot be addressed using the perturbative methodsthat have proven so successful with other fundamentalquantum field theories such as quantum electrodynamics.

The only known method to solve QCD over all energy-scales is lattice QCD, where QCD path integrals areevaluated on a 4-dimensional Euclidean space-time lat-tice by brute-force numerics. With the continual increasein conventional computing power lattice QCD is nowhaving a dramatic impact on strong interaction physics.For example, calculations are now done at physical quarkmasses with large lattice volumes [14], gluonic com-ponents of matter are being investigated [15], and thequark-gluon structure of light-nuclei is beginning to beexplored [16]. With the arrival of the exascale era inconventional computing over the next few years [17]lattice QCD will continue to increase its impact on QCDand hadron physics. However, there remain key prob-lems in QCD that cannot be addressed with any knownab initio methods, foremost amongst these are arguablyQCD at finite density [18] and quark-gluon hadroniza-tion [19]. Quantum computing can potentially addressthese phenomena by overcoming signal-to-noise prob-lems and providing a means to study real-time dynamicsin quantum field theories [20, 21].

1.1. Noisy Intermediate-Scale Quantum Com-puting

Quantum computing has caught the imagination of manysince Richard Feynman famously stated “Nature is quan-tum . . . So if we want to simulate it, we need a quantum

Page 5 of 22

1. INTRODUCTION

computer” [22, 23]. The first theoretical proof that quan-tum computing is a possibility came a year or so earlierwhen Paul Benioff, from Argonne National Laboratory,developed the first quantum mechanical (Hamiltonian)model for a Turing machine, and established that a quan-tum Turing machine can be used to simulate a classicalcomputer [24–26]. This problem was also recognizedby Manin around the same time [27].

Quantum computers directly exploit quantummechan-ical concepts such as superposition and entanglement,and therefore operate in a fundamentally different man-ner than classical computers. This allows quantumalgorithms to be developed, which opens completelynew possibilities in computer science by using processesfundamentally unavailable to classical computers. Nu-merous quantum algorithms already exist, where manyhave been proven to solve certain classes of problemsexponentially faster than existing algorithms for conven-tional computers [28], and a wider range of problemswith polynomial speed increases [29]. A fundamentalreason for this exponential increase in computationalpower is because of the quantum entanglement betweenquantum bits (qubits), which allows an exponential in-crease in information density [30]. The increase in com-putation power promised by quantum computers, andthe ability to develop completely new types of quantumalgorithms, opens the possibility that QIS can addressnumerous problems in nuclear physics that are currentlycomputationally challenging or even intractable.Industry is now exploiting QIS to develop quantum

computers and other technologies such as quantum sen-sors. Technology companies like Google [31], IBM [32],Intel [33], and Microsoft [34] have unveiled quantumcomputers with order 50 qubits (without error correc-tion). In 2016 IBM began offering cloud access to itsprototype quantum computers, and now provides accessto two 5-qubit, one 16-qubit, and two 20-qubit processorsthrough the IBM Q Experience [32]. Rigetti [35] alsooffers cloud based quantum computing services, andrecently announced a 128-qubit processor with plans tomake it available by August 2019 [36]. Companies suchas IonQ [37] are building quantum computers based ontrapped ions, which currently offer much lower errorrates than their superconducting counterparts, and D-wave [38] has built a quantum annealer consisting of2000 qubits which is suited to tackling certain types ofcomplex optimization problems.Quantum computing is now a reality, with machines

of 50–100 (non-error corrected) qubits expected to be-come standard within the next few years, although these

machines will still be limited by low circuit depth. Thisrepresents a significant technical milestone, althoughquantum computers of this size are still a long way fromwhat is needed for many applications, such as to breakRSA encryption using Shor’s algorithm [28].2 Thecurrent era in quantum computing has therefore beenlabeled Noisy Intermediate-Scale Quantum (NISQ) [40]because of the relatively small number of qubits and thelack of error correction.

While quantumcomputers in theNISQeramay bewellshort of what is needed to reach quantum supremacy [41,42] over a broad range of applications, a quantum com-puter with around 50–100 qubits cannot be simulatedwith contemporary supercomputers [43]. This sug-gests that quantum computers in the NISQ era maybe approaching the sophistication needed to performcomputational tasks that would be impossible on anyclassical computer for specific applications. Contempo-rary quantum computers are already finding importantapplications in fields such as quantum chemistry, andit remains an important challenge to determine whatproblems NISQ computers can have a strong impact onfor nuclear physics.

1.2. Nuclear Many-Body Problem

The nuclear many-body problem [44] is a key challengefor NP theory. Numerical solutions to this problemwith current approaches, such as Green function andvariational Monte Carlo methods [45], are hindered byan exponential growth in quantum states with increasingnumber of nucleons [46], together with a fermion signproblem [47, 48]. However, with quantum computers thecomputational cost of simulating quantum many-bodysystems can potentially be reduced from exponential topolynomial [49]. Such approaches are already findingapplication in quantum chemistry [50, 51].The development of new quantum algorithms that

have application for the nuclear many-body problem isalready underway within NP. For example, Ref. [52]presents a spectral combing algorithm for finding theground-state wave function of a quantum many-bodysystem that does not require an initial trial wave functionwith good ground-state overlap; a quantum algorithmto calculate the dynamic linear response function ofa quantum system is presented in Ref. [53]; and ahybrid quantum-classical algorithm for studying the

2A realistic implementation of Shor’s algorithm – that includeserror correction – would currently require millions of physicalqubits [39].

Page 6 of 22

1. INTRODUCTION

time evolution of out-of-equilibrium thermal states isgiven in Ref. [54].

A first step toward a realistic nuclear physics calcula-tion was taken in Ref. [55], which used the IBM QX5and Rigetti 19Q cloud quantum computing resources todetermine the binding energy of the deuteron to within afew percent. A tailored leading-order pionless effectivefield theory Hamiltonian provided the theoretical frame-work for the calculation. The deuteron ground-statewas obtained using the variational quantum eigensolveralgorithm (VQE) [56] with a low-depth version of theunitary coupled-cluster ansatz (UCC) [57]. The VQEalgorithm is a hybrid method where a quantum com-puter determines the energy expectation value for a wavefunction ansatz, then a classical optimizer supplies newparameter guesses for the wave function ansatz, andthat continues until convergence. The UCC ansatz forthe wave function has been shown to be exponentiallyfaster on a quantum computer than on a classical com-puter [56]. Using these techniques and only a few qubitson a quantum computer the deuteron’s ground-state bind-ing energy was found to be within a few percent of theempirical value.

1.3. Field Theories and Quantum Computing

The best currently available method to calculate staticproperties of hadrons – starting from the QCD La-grangian – is Wilson’s lattice QCD. However, such aformulation does not provide access to real-time dynam-ics and systems at finite density [21, 58]. Quantumcomputing can potentially overcome this restriction andsignificant progress has already been made in this di-rection. For example, simple bosonic [59, 60] andfermionic [61, 62] field theories have been formulatedsuch that they could be studied using a quantum com-puter, and quantum link models provide an alternativenon-perturbative formulation of non-abelian gauge the-ories that may allow QCD to be studied on a quantumcomputer [4, 5].An important first step in the simulation of lattice

gauge theories using a quantum computer was reportedin Ref. [63]. Using a few-qubit analog quantum simula-tor3 the real-time dynamics of spontaneous particle-antiparticle creation in the vacuum was studied in1+1 quantum electrodynamics (QED), the so calledSchwinger model [64, 65]. An analog quantum simu-lator – as opposed to a universal quantum computer –

3See Sect. 2. for a discussion of the different types of quantumcomputers.

is specifically designed to simulate a certain class ofphysical theories by, e.g., tuning the potential betweenatoms or ions in an optical lattice to mimic the physicsof a particular Hamiltonian. The real-time evolution ofthe theory can then be studied by measuring the state ofthe analog quantum simulator. The Schwinger modelhas also recently been studied using IBM’s cloud quan-tum computing resources in Ref. [66], using a hybridquantum-classical algorithm where classical computa-tion is used to find symmetry sectors on which thequantum computer evaluates the dynamics of quantumfluctuations. The ground state of this model has alsobeen studied with a variational quantum simulator [67].Analog quantum simulators with up to 50 trapped

ions or atoms (qubits) have already been built [68, 69],and with their low error rates there exists significant op-portunities for the further study of lattice gauge theoriesusing these devices [4, 5]. In particular, with relevantexpertise in atom trapping the development of an analogquantum simulator program to study lattice field theorieswithin NP would be a real possibility.

1.4. Entanglement at collider energies

Concepts developed or extended within the field ofquantum information theory, such as entanglement andquantum entropy, are beginning to impact the interpreta-tion and understanding of the quark-gluon structure ofQCD bound states and reactions. For example, Ref. [70]considers the von Neumann entropy of the system ofpartons (in this case gluons) resolved by deep inelasticscattering at small Bjorken x. Their analysis motivatesthe interpretation that this von Neumann entropy canbe interpreted as the entropy of entanglement betweenthe spatial region probed by deep inelastic scatteringand the rest of the target. If this interpretation is correctthen the entanglement entropy of a proton or nucleuscould be studied using deep inelastic scattering, whereevent-by-event measurement of the hadronic final stateis made. Such an experiment would be possible at theproposed electron-ion collider [8].

Another interesting application is the impact of entan-glement on thermalization in e+e− [71, 72] and heavyion [73, 74] collisons. In both these reactions it is ob-served that the final state particle spectra have thermalproperties, even though re-scatterings effects in the fi-nal state appear not to be frequent enough to explainthis. An interesting alternative explanation is that thisthermalization is because of quantum entanglement be-tween the final state particles. Interestingly, such effects

Page 7 of 22

2. QUANTUM COMPUTING

have already been observed in recent measurements ofisolated quantum many-body systems made of ultracoldatoms [75].Ideas related to quantum entanglement are also im-

pacting the interpretation of hadron tomography [76–78],parton-parton scattering [79], and condensed matter sys-tems [80, 81]. The interaction of quantum informationtheory and nuclear theory therefore provides interestingnew opportunities to understand and interpret stronginteraction phenomena.

1.5. Document Outline

This introduction attempts to provide a snapshot of QISin the context of NP. A standard texbook on QIS thatprovides background to some of the terms and conceptsdiscussed in this document is Ref. [49]. This whitepaper on “Opportunities for Nuclear Physics & QuantumInformation Science” has been prepared at the requestof the DOE Office of Science, Office of Nuclear Physics.It represents the outcome of the workshop Intersectionsbetween Nuclear Physics and Quantum information heldat Argonne National Laboratory on 28–30 March 2018[www.phy.anl.gov/npqi2018/]. This document is acomplement to the white paper “QuantumComputing forTheoretical Nuclear Physics” which was an outcome ofthe workshop Quantum Computing for Nuclear Physicsheld at the Institute for Nuclear Theory, University ofWashington, during 14–15 November 2017 [82]. Theoutline of the remainder of this document is as follows:Sec. 2. gives an overview of quantum computing, simula-tions, and qubit technologies; Sec. 3. discusses quantumsensors and other opportunities; and conclusions areprovided in Sec. 4.

2. Quantum Computing2.1. Background

Quantum computing is a new paradigm for computingwhere attributes of quantum mechanics are leveragedto make possible new quantum algorithms that can-not be implemented efficiently on a classical Turingmachine.4 The fundamental unit of information in aquantum computer is a quantum bit (qubit), which isphysically implemented by any two level quantum sys-

4A quantum computer with around 300 qubits would containmore possible states than there are atoms in the universe, it istherefore conceivable that it would not be possible to implementcertain quantum algorithms on any classical computer.

tem.5 A qubit can take on any superposition of the formα |0〉 + β |1〉, in contrast to a classical bit which must beexactly 0 or 1. This feature alone is not sufficient to makea quantum computer useful, since it resembles an analogcomputer where the fundamental unit of informationis an analog voltage. Analog computers lack the basicerror correction protocols which are integral to digitallogic. Quantum error correction is possible however,where redundant storage of quantum information is usedto protect against specific forms of noise or decoher-ence [49]. Quantum error correction makes the dream ofuniversal fault tolerant quantum computing a possibility.The key feature of quantum mechanics that cre-

ates a quantum computer is entanglement betweena set of qubits. The profound impact of entangle-ment is illustrated following Ref. [83]; the generalstate for a set of n potentially entangled qubits readsΨ =

∑s1s2...sn αs1s2...sn ψs1s2...sn where αs1s2...sn are

complex numbers, the sum is over qubit states, andΨ is subject to the usual normalization condition:∑

s1s2...sn

��αs1s2...sn

��2 = 1. A quantum computer with nentangled qubits therefore contains, and can act upon,2n − 1 independent complex numbers. In contrast, thestate of a classical memory containing n bits can berepresented by a string of n zeros and ones. Therefore,for a given number of qubits a quantum computer canoperate on an exponentially greater amount of informa-tion than a classical computer with the same number ofbits, or conversely, a classical digital computer needs anexponentially larger amount of memory to simulate aquantum computer.A priori it is unclear whether simply having entan-

glement between qubits can in practice result in anexponential speed improvement of a quantum computerover its classical counterpart. It also does not appearto reduce the complexity of NP-complete problems.Further, entanglement is a necessary but not sufficientcondition to achieve an exponential speed improvementof a quantum computer over its classical counterpart,as seen for instance in the Gottesman-Knill theorem.However, there are several quantum algorithms that havebeen proven to provide either exponential or polynomialspeed improvements over any known classical algorithm,famous examples include Shor’s factoring algorithm [28]and Grover’s database search algorithm [29].Beside the difficulty of maintaining entanglement

between a large number of qubits over an extendedperiod of time, quantum computers also have intrinsic

5Multi-level quantum systems, called qudits, are also possible.

Page 8 of 22

2. QUANTUM COMPUTING

limitations. For example, while a quantum computer canstore an exponential amount more information comparedto an analogous classical computer, this information isin general not available to be read out from the quantummemory. A likely computing model for the foreseeablefuture is therefore having a classical CPUbased computeras the computing hub, which then executes certain taskson auxiliary quantum computers. A similar scenarioalready exists between CPUs and GPUs.

2.2. Types of Quantum Computers

There exist a number of different types of physicalrealizations of a quantum computer. The ultimate goalis to build a universal quantum computer, which forthe purposes of this document can be considered adevice that can execute any quantum algorithm. Thiscan be defined as a quantum computer that can executea complete set of universal quantum gates an arbitarynumber of times, where a set of gates is considereduniversal if any function in a given computational modelcan be computed to arbitary precision by a circuit thatuses only these gates.A universal gate set can usually be subdivided into

gates that operate on a single qubit and those that op-erate on two or more qubits. The former class is usedfor the generation of superpositions, while the latterclass is necessary for the generation of entanglement.The single qubit gates are usually σx(θ) and σz(θ) ro-tations about the x and z axes of the Bloch sphere.Because θ can take on any value, this class of gates istechnically infinite, although it is usually consideredsufficient to demonstrate a small number of such ro-tations. The rotation σx(θ) corresponds to a rotationbetween qubit levels, e.g. |0〉 → cos(θ) |0〉 + sin(θ) |1〉.Then σz(θ) rotations corresponds to a phase shift, e.g.(|0〉 + |1〉)/

√2→ [|0〉 + exp(iθ) |1〉]/

√2.

There is a growing number of known multiple qubitgates that constitute full sets, where an important ex-ample is the controlled-not or CNOT gate. In a CNOTgate, the second qubit has a NOT operation, or σx(π),performed on it if the first qubit is 1. Nothing is doneif the first qubit is 0. A CNOT gate together with thetwo aforementioned single qubit rotations constitute auniversal set of quantum gates [49]. However, quantumerror correction for qubit rotations by an arbitrary angleθ remains a significant challenge, and therefore onlydiscrete rotations usually appear as part of a practicaluniversal gate set.Another important distinction is between digital and

analog quantum computers. Digital quantum computerswork by executing a discrete set of quantum opera-tions (gates), which need not be a universal set of gates.Analog quantum computers or analog quantum simula-tors [20, 84] are purpose built quantum devices that aredesigned to simulate a specific class of quantum systems.Analog quantum computers are generally not universal,however in the NISQ era, they may be the most efficientway to model aspects of quantum systems of interest –such as lattice gauge theories [5] – in part because theydo not rely on quantum error correction.

2.3. Quantum Simulators

A major motivation for quantum computing has alwaysbeen the simulation of strongly coupled many-bodyquantum systems, with the reasoning that a quantumcomputer would already have built in the essential el-ements that make these calculations difficult on anyclassical computer. A quantum simulator is a collectionof qubits (or other multi-level quantum system) used toemulate the effects of a Hamiltonian that is preciselycontrolled by the experimenter. In order for a quantumsimulator to be more useful than the physical systemit seeks to simulate, it must have some degree of con-trol not available in the original system. For example,one could possess the ability to prepare a system ina particular state, tune the Hamiltonian that governsdynamics, or measure the quantum state of the system.The ultimate in controllability would be a full universalquantum computer, but these systems are limited in fi-delity and qubit number. So we might ask if it is possibleto achieve the desired simulation with less sensitivity tonoise, even if that comes at the expense of operationalcontrol. For example, the interactions between qubitscould simply be tuned to have the same properties asthe system under study, and allowed to evolve naturally.In this case, the effect of decoherence will just appearas noise in the final result, and in fact may be usefulfor studying decoherence in the physical system beingsimulated. This is closer to what is meant by an analogquantum simulator.

Analog quantum simulators are typically easier to im-plement in the lab than their digital counterparts: usingthe trapped ion platform as an example, the physicalsystem can be engineered to behave like interactingquantum spins, with long-range interactions due to theunderlying Coulomb interactions [68]. For quantumcomputing experiments, great effort is devoted to tai-loring them (e.g. through temporal pulse shaping) into

Page 9 of 22

2. QUANTUM COMPUTING

arbitrary two-qubit gate operations [85]. However, inan analog setting, the quantum simulation will exhibitthe long-range behavior naturally [68], and hence couldpotentially be engineered to yield nuclear potentials withintrinsic long-range components, such as pion-exchangemediated forces between nucleons in effective field theo-ries. Another example is the quantum simulation of theSchwinger model [63], which leveraged the naturally im-plemented long-range gates to produce the gauge degreeof freedom within an ion chain. The primary advantageof a quantum simulation for nuclear many-body or gaugetheory problems, therefore, is in reducing the qubit re-quirement of a fully digital computation, avoiding thecostly discretization of some of the dynamical degrees offreedom by mapping them onto continuous interactionspresent in the simulator.

The simulations of an analog quantum simulator nec-essarily inherit some features of the physical qubit. Thiscan be advantageous - for instance, the N-fold spin sym-metry (N > 1) of cold atom systems is an essentialfeature used in proposals to simulate SU(N) and U(N)non-abelian gauge theories. In other ways it can be dis-advantageous, since the physical qubit must be chosen tomatch the system we wish to simulate. Some examplesof relevant systems include neutral atoms [86], trappedions [87], and artificial atoms such as superconductingqubits [88]. A universal quantum computer on the otherhand will be much more flexible as the computationwill be agnostic of the underlying implementation. Thepractical issue is whether the “gate compiling” can bedone efficiently, so as to render a circuit that could runon near-term quantum machines, before the computationis spoiled by decoherence time and systematic errors.From this perspective, analog systems could do better inthe near to intermediate term due to the simultaneousnature of the interactions as well as larger system sizes.It is possible that gate compiling challenges could beaddressed with further investment in algorithms devel-opment. Therefore, the co-existence of the two typesof experimental approaches is crucial, and the develop-ment of analog-digital mixed approaches would assistin solving interesting problems in the NISQ era [40].

2.4. Qubit Technologies

The road to a full, universal, digital quantum computerthat is consistently faster than its classical counterpartis probably decades long. Moreover, we should notforget that quantum computers scale better than classicalalgorithms only for specific problems, so it may be

that even a fully mature technology will not improveperformance for most computational problems. Forthese reasons, we should strategically seek out problemsfor which quantum algorithms and technologies have astrong advantage, so as to have the largest impact in thenear to intermediate term, with an eye towards long-termsuccess. As we have seen, nuclear physics holds severalsuch problems that, if solved, can have a real impact onour understanding of nature.

No one today is able to foresee what type of qubit willbe most important to a future quantum computer, whichmay actually rely on a combination of qubit types, orindeed the key technologies may not yet even be invented.Qualities such as gate fidelity and coherence time needto be improved for all existing qubit technologies, but itis not clear where the breakthroughs may occur. Or forinstance, hybrid qubits combine the strengths of differenttechnologies to make a system capable of overcomingtheir individual weaknesses. We should not thereforerestrict research to any one qubit technology, becausefuture progress on quantum computing could be dra-matically stymied. Moreover, as seen in the workshop,a broad-based approach to QIS has enabled many newtechnologies that have positive feedback to fundamentalresearch in the form of quantum sensors. Thus, it wouldbe a disservice to the field to prematurely select a favoreddirection. However, it may be appropriate to form apanel responsible for setting time lines or benchmarksto gauge progress towards problems of interest to DOE.

2.4.1. Trapped Ions

Trapped ions are an exemplar case for the synergy be-tween academia, national labs, and industry in develop-ing quantum technologies. In fact, national labs haveplayed a central role in trapped ion quantum computingfrom the beginning; the first demonstration of any 2-qubit quantum gate was performed at NIST-Boulder, andnational labs such as Sandia continue to play a key role indeveloping the trap technology that is crucial to the hugeprogress in this field, as we heard in the presentation ofDaniel Stick. Further progress in this field will demanda level of engineering support often not available in aUniversity setting, which is where national laboratoriescan serve as a bridge, assisting in the perfection of thetechnologies that will ultimately be needed as ion trapquantum computing makes the transition into industrialproduction and application. We heard about the stateof this exciting area from Chris Monroe’s presentation,where he showed us the power of collaborative efforts

Page 10 of 22

3. QUANTUM SENSORS & OTHER OPPORTUNITIES

between academia, national labs, and startup compa-nies. Trapped ions are also a good example of qubittechnologies that can be adapted to basic physics re-search, as we heard from John Bollinger’s presentationon how entangled ensembles of ions can be used as anextremely sensitive force and electric field sensor, withimplications for tests of fundamental physics. Finally,as discussed by Christine Muschik and Chris Monroe,trapped ions have also made excellent progress recentlyin the simulation of quantum field theories, such as 1+1quantum electrodynamics.

2.4.2. Neutral Atoms

Ultracold neutral atom systems are tremendously richin their quantum interactions, which has been exploitedover years of research at many academic institutions toproduce a variety of synthetic, designer Hamiltoniansusing such phenomena as Rydberg blockade, exchangeinteractions, and Feshbach resonances. That richnessmakes neutral atom qubits ideally suited to analog quan-tum simulation, in addition to digital quantum computing.This is because once the synthetic Hamiltonian is imple-mented on the cold atom system, its ground state can befound, or a state can be prepared and evolved. One advan-tage is that we can naturally incorporate fermionic andbosonic degrees of freedom into this state, correspond-ing to fermionic and bosonic atomic species included inthe lattice, as exhibited in the talk by Erez Zohar andalso in Refs. [5, 89]. Thus, by combining various con-trollable interactions, it is possible to build simulators toemulate unique quantum systems, which may somedayinclude quantum chromodynamics. Indeed, many ofthe extant proposals for simulating new gauge theoriesutilize this approach. As has happened for trapped ions,there is an opportunity for DOE to advance neutral atomtechnology by fostering partnerships that bring togethertechnological expertise from diverse fields. In his pre-sentation, Mark Saffman discussed one specific example,suggesting a partnership bringing spatial light modula-tion (SLM) technology expertise at ANL to bear on theproblem of single qubit addressability. The richness ofcold atom interactions includes the possibility to formcold molecules, which is a young and exciting area ofresearch. Cold molecules can be used for enhancedsearches for electric dipole moments (discussed in thequantum sensors section), or, as discussed by BryceGadway, used to enable new interactions for quantumsimulators or computers.

2.4.3. Superconducting Flux Qubits

Qubits based on superconductors have made dramaticprogress in recent years, and today they are probablythe most important technology in the commercial space.The “cloud computing” machines of IBM, Rigetti, andothers are all based on this technology, and thus so isthe quantum calculation of the deuteron mass presentedby David Dean. In comparison with trapped ion orneutral atom systems, superconducting flux qubits haveextremely fast gate times, but comparatively short coher-ence times that typically limit their operational fidelity.A large improvement in their coherence times would betransformational to quantum computing, but this willrequire difficult development in materials, microfabri-cation techniques, or superconducting technologies thatmay be beyond the capabilities of the university system.These are areas of strength for national laboratoriesand DOE, so this presents a natural opportunity forcollaboration that could have huge impacts on quantumcomputing, as discussed by Alex Romanenko and DavidSchuster in their presentations.

2.4.4. Quantum Defects

Quantum defects such as nitrogen vacancies have foundmany roles in quantum information science, such assingle photon production for quantum cryptography,solid-state qubits, and tests of the foundations of quantummechanics. They are used for electric and magnetic fieldmeasurement, as well as microscopic thermometers.These myriad applications suggests utility as quantumsensors, and indeed they have proposed to enhanceprecision measurements ranging from WIMP searches[90] to chemical identification of picoliter volumes,such as proteins in a single living cell [91]. Again,these devices are limited in coherence time, which is aproblem best addressed as a materials purity concern.One way nuclear physics could contribute to this areaof research is in providing highly isotopically enrichedsamples, as outlined in the Isotopes section.

3. Quantum Sensors & Other Oppor-tunities

A qubit, being simply an isolated and controllabletwo-level quantum system, is not only the basic unit ofquantum computing, but really themost basic of quantumsystems. Thus, a variety of measurement techniques,including vapor cell magnetometry and nuclear magneticresonance have qubits at their core. However, a true qubit

Page 11 of 22

3. QUANTUM SENSORS & OTHER OPPORTUNITIES

is generally tuned to be highly insensitive to externalinteractions, whereas quantum sensors are instead tunedto be highly sensitive to specific fields or interactions.This suggests that techniques originally developed tocontrol qubits might bear fruit in measurement science.One remarkable result is squeezing, which is a specialcase of Heisenberg-limited metrology, where quantumcorrelations between particles are used to reduce theshot noise limit [6]. In this case, sensitivity can improvelinearly in the number of particles, rather than

√N , and

has been shown in specific cases to improve experimentalsensitivities by 1 or 2 orders of magnitude. Experimentsthat utilize these types of quantum sensors tend to bedominated by the demands of the sensor itself, to thepoint where often the quantum sensor is the experiment,as is the case for electric dipole moment measurements.Investment in QIS has repeatedly yielded residual

benefits across basic science. Frequently, we find tech-nologies developed for QIS which may not satisfy thenarrow definition of quantum sensors, but still haveapplication elsewhere in the form of sensitive detectors,such as superconducting nanowires, nitrogen vacancycenters, or Rydberg atoms. Through collaborative ef-forts to improve these technologies, QIS and NP canbenefit from new investments in basic science. Someopportunities are outlined below.

3.1. Electric Dipole Moments

Searches for electric dipole moments (EDMs) are per-haps the cleanest example of a quantum sensor appliedto fundamental symmetries research. We know that theobserved baryon asymmetry of the universe demandsthat there be undiscovered sources of CP-violation hid-den somewhere in nature, since the currently knownsources of CP-violation are insufficient to create theabundance of normal matter in the universe. EDMsare sensitive to CP-violation, and so non-zero EDMsare a generic feature of physics theories that extend theStandard Model. Indeed, nature’s bizarre preference forEDMs that are almost exactly zero has placed some of thestrongest constraints on new physics theories ever sinceRamsey performed the first neutron EDM experimentin the 1950s. Today, a collection of EDM experimentstogether constrain the complicated phase space of CP-violating theories beyond the Standard Model, includingthe electron and neutron, and EDMs from the nuclei ofmercury, xenon, radium, and thallium fluoride. Theseexperiments generally work by measuring the Larmorprecession frequency of some atom or nucleon in the

presence of an electric field. In this case, the electricfield will cause a shift to the precession frequency ifand only if the subject possesses an EDM. Because itinvolves the conversion of a signal into a frequency, thistechnique enables experiments of exquisite precision andsensitivity. That same aspect make these experimentsstrong candidates to benefit from quantum sensing tech-niques, such as spin squeezing and electron shelving,which can dramatically improve the detection of phase[92, 93]. The demonstrated gains with spin squeezingin recent years are impressive, giving signal to noiseimprovements of one to two orders of magnitude overthe standard quantum limit [92], with a commensurateimprovement to EDM sensitivity to be expected. Fewexperiments today can take immediate advantage ofsuch improvements, however as the next generation ofcold-atom and cold-molecule EDM experiments comeon line, they will have the ability to take advantage ofthese techniques, vastly improving our understandingof CP-violation within the nucleus. Another excitingdirection with connections to QIS is the search for EDMswith cold molecules. The effective electric field withina molecule is roughly 1000 times stronger than whatcan be achieved in the lab, with a similar improvementin the sensitivity reach of molecule-based EDM experi-ments. Such improvements have already been realizedfor electron EDM searches, but are still in their infancyfor nuclear-based experiments.An alternative explanation for the CP problem is the

axion. Axions are a highly parsimonious theory, andcould simultaneously explain the lack of CP-violationin the nucleus as well as the observed abundance ofdark matter throughout the universe. In this theory, thephysical parameter describing CP-violation underwentspontaneous symmetry breaking in the early universe,thereby destroying the evidence of CP-violation whileleaving behind a pseudo-Goldstone boson called theaxion. This new massive particle would then permeatethe universe while interacting very weakly with ordinarymatter, thus becoming the source of the dark matterwe now observe. The axion could cause a non-zerobut oscillating EDM in nuclei if several requirementsare satisfied: it must exist, it must be the constituentparticle of dark matter, it must be ultralight, and theEarth must reside in a sizable patch of dark matter[94]. Since the average EDM is still zero, all previousexperiments would have been ignorant of the non-zeroEDM. A new generation of experiments are now beingdesigned that will be sensitive to this interesting physicalmodel, such as CASPER and ARIADNE (presented

Page 12 of 22

3. QUANTUM SENSORS & OTHER OPPORTUNITIES

by Andrew Geraci). In fact limits have already beenplaced on this kind of dark matter using neutron EDM.These experiments explore a very different region ofphase space frommore traditional WIMP searches, sincethe dark matter particles considered here have massesless than an electron volt, which would be completelyundetectable in a nuclear recoil experiment due to thelow momentum transfer.

3.2. Superconducting Technologies

The Department of Energy has a long history of sup-porting development in superconducting devices, whichhave taken a central stage in quantum computing andnow present a strong opportunity for cross-pollinationbetween NP and QIS. Transition edge sensors (TESs)and superconducting nanowire single-photon detectors(SNSPDs) are two such technologies, presented byAaronMiller and Clarence Chang. These devices are madefrom thin films of superconducting material and exploitthe fact that the superconducting phase transition is verynarrow in order to detect single photons that have ener-gies as high as MeV or as low as the microwave regime.Because they entail a phase transition and the interactionis thermal, these devices have extremely high quantumefficiencies, 50% for TESs and over 90% for SNSPDs,and SNSPDs are also extremely fast, with timing reso-lutions of order 10 picoseconds. TESs have even beenshown to have excellent energy resolution, a rarity fordetectors of photons with this energy. These instrumentshave previously been used for quantum cryptography,where the high detection efficiencies are critical, but arenow being leveraged by researchers at Argonne for usein fundamental symmetry studies and cosmology. Forexample, TES’s are used at the South Pole telescopeto measure the cosmic microwave background. Theyare also being built with energy resolution sufficientfor use in the CUPID neutrinoless-double beta decayexperiment, where they will help in the identificationof decay events. Superconducting detectors could alsohave promising applications in detectors for colliders,possibly addressing challenges in timing resolution, asoutlined in Jose Repond’s presentation. Several tech-nological challenges must first be overcome. However,progress is being made to produce versions that areradiologically hard and resistant to high magnetic fields,which could open the door to possible SNSPD-basedcalorimeters suitable for detectors at locations such asthe future electron ion collider.Due to their structure, superconducting flux qubits

tend to have coherence times of order 100 µs. This isa major disadvantage of superconducting qubits whencompared to atom or ion trap-based quantum comput-ers which routinely have coherence times measured inseconds. However, the DOE has world-class experiencein building superconducting cavities with coherencetimes of many seconds. If these technologies couldbe successfully interfaced, the combination could betransformative for superconducting qubit technology andquantum computing as a whole. This is precisely theobjective behind the University of Chicago-Fermi Labqubit collaboration, discussed by David Schuster andAlex Romanenko, which seeks to create a quantummem-ory for long-term storage of qubits during computation,using transmons. One challenge they seek to addressis to produce superconducting cavities that retain theirhigh quality factor when they contain only a few photons.Feedback to basic physics research is very strong in thiscase, since similar cavity technology is used to searchfor Primakov decay of axion-like dark matter. If anaxion-like particle passes into a high-Q superconductingcavity that is resonant with the axion mass, a decaymode will be hugely enhanced, where the axion decaysinto two photons which can then be detected. A num-ber of experiments have been designed to exploit thistechnique, such as the ADMX and HAYSTAC collabora-tions, which complement the Oscillating-EDM methoddiscussed earlier for detection of low mass dark matter.National labs have considerable expertise in these areas,including design and manufacturing, that could provebeneficial to progress in quantum computing in industryas well as fundamental physics research.National labs have considerable expertise in these

areas, including design and manufacturing, that can ac-celerate development of these techniques. Indeed, otherquantum critical transitions, besides the superconductingone, may provide a general avenue for designing newquantum-limited detectors suitable for nuclear physicsapplications [95]. Such detectors could prove beneficialto progress in quantum computing in industry as well asfundamental physics research.

3.3. Field Detection

The oldest examples of quantum sensors, such as vaporcell magnetometers, are sensitive to magnetic or electricfields. Some more recent examples include trappedions (John Bollinger), Rydberg atoms (Georg Raithel),and quantum defects, such as nitrogen vacancy centers.As Georg Raithel showed us, Rydberg atoms are being

Page 13 of 22

3. QUANTUM SENSORS & OTHER OPPORTUNITIES

developed as a source of absolute calibration for RF fieldintensities, which has potential applications to measure-ments for DOE facilities. Precision measurements onRydberg atoms can also be used to improve constraintson the Rydberg constant, with direct relevance to theproton radius puzzle. Andrew Geraci presented on opti-cally levitated nanospheres, which when cooled to theirquantum ground state, have fantastic potential for testsof modified gravity at short distances. John Bollingershowed us how highly entangled systems of trappedions can be used not only for quantum simulation, butalso how squeezing can perform extraordinarily precisemeasurements of force, with implications for searchesof ultralight dark matter. Measurement of forces andfields is a basic operation of precision measurementand tests of fundamental symmetries, and some of themost exciting developments today take advantage of QIStechniques.

3.4. Isotopes

There are several applications for isotopes in quantuminformation. One is closely related to elimination ofmagnetic noise in so-called quantum defects, such asSi:P or nitrogen vacancy (NV) centers. Quantum de-fects are optically active spin sites embedded in somesubstrate; carbon diamond for NV centers and siliconfor phosphorus. These devices have many applicationsin QIS, such as single photon generation, magneticand electric field detection, or in quantum computingas qubits. Like superconducting qubits, these devicesgenerally have extremely limited coherence times. Forthese examples, however, it is known that the coherencetime is limited by the presence of nearby isotopic im-purities that possess a magnetic dipole, carbon-13 orsilicon-29 to be specific. By using a highly enrichedsubstrate, the coherence times of these systems can beenhanced by orders of magnitude, a key requirement forseveral applications [96, 97]. It should be noted thatin the past magnetic noise from these impurities havebeen controlled using techniques very familiar to nuclearphysicists, including hyperpolarization and dynamic nu-clear polarization [98]. There are some substrates wherethis will remain true because no spin-0 nucleus existsfor the constituant atoms, such as for GaAs substrates.Isotopic impurities may be responsible for noise in otherquantum systems as well - its been suggested that noisein superconducting flux qubits is caused by environmen-tal radioactivity, which suggests qubit coherence timecould be improved using the same approaches developed

by nuclear physics for precision measurement, such asneutrinoless double beta decay. Identification of needsand capabilities for isotopically pure samples may callfor a roundtable discussion to coordinate efforts betweenQIS and NP experts.

There are some examples in ion trap quantum comput-ing where a specific isotope is desirable due to its nuclearspin. For example, there is only one naturally occurringisotope of calcium with nuclear spin, Ca-43, which hasan abundance of only .135%. Thus, qubits based oncalcium generally do not take advantage of long-livednuclear coherence, because Ca-43’s scarcity makes itdifficult to trap. A robust source of isotopically enrichedCa-43 would enable new qubits that are rarely used today.Barium-133 is another interesting opportunity. Spin 1/2nuclei are especially desirable in ion trap QC due tothe simplicity of state preparation and readout, whilebarium ions are desirable due to the long wavelengthof its optical transitions, which facilitates long distancecommunication between ions. Unfortunately, the stableisotopes of barium have either spin 0 or spin 3/2. Theonly exception is the radioisotope barium-133 (halflife10.551 years, spin 1/2), which has recently been demon-strated for use as a qubit [99], and has the potential toovercome several long-standing limitations. Universi-ties and national labs can work closely in the creation,preparation and handling of such isotope samples.

3.5. Ghost Imaging

Ghost imaging is a technique that exploits particle corre-lations to produce an image of an object without havingspatial resolution on the particles that scatter from the ob-ject itself [100]. This in principle can enable researchersto image an object using an entangled particle of dif-ferent wavelength or even type than what the object isexposed to. For instance, although an object might onlybe opaque in the infrared, it can be imaged with entan-gled visible photons, where cameras are much cheaper.This has been demonstrated with photons for many years,but more recently it and related techniques have beenemployed to exciting effect with electrons, having keVor MeV energies. The ‘quantum electron microscope’is a variant of this technique used to perform electronmicroscopy without damaging the surface imaged [101].More recently, MeV energy electrons were used to imagean aperture without any spatial resolution on the highenergy electron [102]. What if this technology could beextended in to the GeV energy range relevant to mediumand high energy physics? Ghost imaging could enable

Page 14 of 22

REFERENCES

entirely new detector or source schemes, where the rele-vant degrees of freedom of the electron wave functionare mapped onto initial or entangled final states that aremore easily accessed.

3.6. Data Analysis

The ultimate purpose of quantum computing is to builddevices that are capable of executing algorithms fasterthan any classical algorithm achieving the same task.These algorithms are necessarily quantum in nature,and cannot always be understood using the traditionalparadigms of classical computing, which inherently lackthe basic operations that enable the quantum speedup.The types of problems that are known to have an effi-cient quantum analog are relatively small in number,although some of them potentially have very generaluse, such as the quantum Fourier transform, Grover’salgorithm for database search, and matrix inversion [49,103]. If these known algorithms could be used in concertwith modern computers, like a quantum co-processor, itcould present an opportunity for an early application ofquantum computing. With the right choice of algorithm,nuclear physics could benefit substantially in the form ofimproved data analysis capabilities. Clearly, technicalchallenges remain, not only in terms of demonstratingquantum supremacy for a specific problem, but also interms of transferring data onto the co-processor effi-ciently, and managing the small number of noisy qubitswhich are likely to be available in the near to interme-diate time frame. Even if a processor with quantumsupremacy is demonstrated, this input/output problemmust be solved in order to not obviate the advantage theco-processor enables in the first place. That sort of chal-lenge is one where collaborations of the kind describedhere could excel, with engineering and computing exper-tise provided in conjunction with universities and privateindustry capabilities. Due to the enormous significanceof such technology, including to nuclear physics, a com-pelling data analysis application could mobilize manyresearchers within DOE to work on this topic.

4. ConclusionThe road to universal quantum computing is just be-

ginning but is likely paved with numerous opportunitieswhich will further basic science and nuclear physics.These opportunities include potentially transformativenew approaches to the calculation and simulation ofnuclear systems, and new detectors for nuclear physics

experiments. As we have discussed, QIS can addressseveral challenges faced by nuclear physics, and QIS inturn will benefit from development through real-worldproblems. Incubation of these technologies for applica-tions in physics will have broad consequences not onlyfor our understanding of nature but also for computationgenerally. To strategically identify relevant problemsand technologies a new community working at the in-tersection of nuclear physics and quantum informationshould be fostered, who can carefully identify and ex-ploit these opportunities. The myriad and significanttechnical challenges will demand the combined capa-bilities of academia, national laboratories, and industry,but their solution can bear rewarding fruit for both QISand nuclear physics. Herein, we have outlined a startingpoint for how such a collaboration may begin and someof the promising directions it could pursue.

AcknowledgementsICC andMRDwould like to thank all of the organizers

and participants of the workshop Intersections betweenNuclear Physics and Quantum Information which leadto this whitepaper. This work was supported by theU.S. Department of Energy, Office of Science, Office ofNuclear Physics, contract no. DEAC02-06CH11357.

References[1] https : / / science . energy . gov / np /

about/.[2] G. Altarelli, Partons in Quantum Chromodynam-

ics, Phys. Rept. 81, 1 (1982).[3] K. G. Wilson, Confinement of Quarks, Phys. Rev.

D10, 2445 (1974).[4] U.-J. Wiese, Ultracold Quantum Gases and Lat-

tice Systems: Quantum Simulation of LatticeGauge Theories, Annalen Phys. 525, 777 (2013).

[5] E. Zohar, J. I. Cirac, and B. Reznik, QuantumSimulations of Lattice Gauge Theories usingUltracold Atoms in Optical Lattices, Rept. Prog.Phys. 79, 014401 (2016).

[6] C. L. Degen, F. Reinhard, and P. Cappellaro,Quantum sensing, Rev. Mod. Phys. 89, 035002(2017).

[7] T. Pichler, M. Dalmonte, E. Rico, P. Zoller, andS. Montangero, Real-time Dynamics in U(1)Lattice Gauge Theories with Tensor Networks,Phys. Rev. X6, 011023 (2016).

Page 15 of 22

REFERENCES

[8] E. National Academies of Sciences andMedicine, An Assessment of U.S.-BasedElectron-Ion Collider Science, (2018) 10 .17226/25171.

[9] R. L. Jaffe and K. Johnson, UnconventionalStates of Confined Quarks and Gluons, Phys.Lett. 60B, 201 (1976).

[10] H. Pagels,Dynamical Chiral Symmetry Breakingin Quantum Chromodynamics, Phys. Rev. D19,3080 (1979).

[11] S. Weinberg, Phenomenological Lagrangians,Physica A96, 327 (1979).

[12] Z. Fodor and C. Hoelbling, Light HadronMassesfrom Lattice QCD, Rev. Mod. Phys. 84, 449(2012).

[13] A. Metz and A. Vossen, Parton Fragmenta-tion Functions, Prog. Part. Nucl. Phys. 91, 136(2016).

[14] C. C. Chang et al.,Aper-cent-level determinationof the nucleon axial coupling from quantumchromodynamics, Nature 558, 91 (2018).

[15] C. Alexandrou, M. Constantinou, K. Hadjiyian-nakou, K. Jansen, C. Kallidonis, et al., NucleonSpin and Momentum Decomposition Using Lat-tice QCD Simulations, Phys. Rev. Lett. 119,142002 (2017).

[16] F. Winter, W. Detmold, A. S. Gambhir, K.Orginos, M. J. Savage, et al., First lattice QCDstudy of the gluonic structure of light nuclei,Phys. Rev. D96, 094512 (2017).

[17] S. Habib et al., ASCR/HEP Exascale Require-ments Review Report, [arXiv:1603.09303[physics.comp-ph]] (2016).

[18] P. de Forcrand, Simulating QCD at finite density,PoS LAT2009, 010 (2009).

[19] M. Panero, K. Rummukainen, and A. Schäfer,Investigating jet quenching on the lattice, Nucl.Phys. A932, 122 (2014).

[20] S. Lloyd,Universal quantum simulators, Science(1996).

[21] U.-J. Wiese, Towards Quantum Simulating QCD,Nucl. Phys. A931, 246 (2014).

[22] W. Knight, MIT Technology Review (2018).[23] R. P. Feynman, Simulating physics with comput-

ers, Int. J. Theor. Phys. 21, [,923(1981)], 467(1982).

[24] P. Benioff, The computer as a physical system: Amicroscopic quantum mechanical Hamiltonianmodel of computers as represented by Turingmachines, Journal of Statistical Physics 22 (5),563 (1980).

[25] P. Benioff, Quantum mechanical Hamiltonianmodels of discrete processes that erase theirown histories: application to Turing machines,International Journal of Theoretical Physics 21(3/4), 177 (1982).

[26] P. Benioff, Quantum mechanical Hamiltonianmodels of Turing machines, Journal of StatisticalPhysics 29 (3), 515 (1982).

[27] Y.Manin,Computable and uncomputable (sovet-skoye radio press, moscow) (in russian), (1980).

[28] P.W. Shor,Polynomial time algorithms for primefactorization and discrete logarithms on a quan-tum computer, SIAM J. Sci. Statist. Comput. 26,1484 (1997).

[29] L. K. Grover, A Fast quantum mechanical al-gorithm for database search, Proceedings ofthe Twenty-eighth Annual ACM Symposium onTheory of Computing, 212 (1996).

[30] D. Rotta, F. Sebastiano, E. Charbon, and E. Prati,Quantum information density scaling and qubitoperation time constraints of cmos silicon-basedquantum computer architectures, npj QuantumInformation 3, 26 (2017).

[31] https://ai.google/research/teams/applied-science/quantum-ai/.

[32] https://www.research.ibm.com/ibm-q/.[33] https : / / newsroom . intel . com / press -

kits/quantum-computing/.[34] https : / / www . microsoft . com / en - us /

quantum/.[35] https://www.rigetti.com/.[36] https : / / www . forbes . com / sites /

alexknapp / 2018 / 09 / 07 / rigetti -computing- takes- small- step- toward-cloud - services - in - big - leap - for -quantum-computing/.

[37] https://ionq.co/.[38] https://www.dwavesys.com/home.[39] J. O’Gorman and E. T. Campbell, Quantum

computation with realistic magic-state factories,Phys. Rev. A 95, 032338 (2017).

Page 16 of 22

REFERENCES

[40] J. Preskill, Quantum Computing in theNISQ era and beyond, [arXiv:1801.00862[quant-ph]] (2018).

[41] B. M. Terhal, Quantum supremacy, here wecome, Nature Physics 14, 530 (2018).

[42] M.-H. Yung, Quantum supremacy: some fun-damental concepts, National Science Review,nwy072 (2018).

[43] E. Pednault, J. A. Gunnels, G. Nannicini, L.Horesh, T. Magerlein, et al., Breaking the 49-Qubit Barrier in the Simulation of QuantumCircuits, ArXiv e-prints (2017).

[44] P. Ring and P. Schuck, The Nuclear Many-Body Problem, Springer-Verlag Berlin Heidel-berg (1980).

[45] J. Carlson, S. Gandolfi, F. Pederiva, S. C. Pieper,R. Schiavilla, et al.,QuantumMonte Carlo meth-ods for nuclear physics, Rev. Mod. Phys. 87,1067 (2015).

[46] S. C. Pieper and R. B. Wiringa, Quantum MonteCarlo calculations of light nuclei, Ann. Rev.Nucl. Part. Sci. 51, 53 (2001).

[47] M. Troyer and U.-J. Wiese, Computational com-plexity and fundamental limitations to fermionicquantum Monte Carlo simulations, Phys. Rev.Lett. 94, 170201 (2005).

[48] Z.-X. Li and H. Yao, Sign-Problem-FreeFermionic Quantum Monte Carlo: Develop-ments and Applications, [arXiv:1805.08219[cond-mat.str-el]] (2018).

[49] Nielsen, M. A. and Chuang, Isaac L., QuantumComputation and Quantum Information, Cam-bridge University Press.

[50] B. P. Lanyon, J. D. Whitfield, G. G. Gillett, M. E.Goggin, M. P. Almeida, et al., Towards quan-tum chemistry on a quantum computer, NatureChemistry 2, Article, 106 EP (2010).

[51] J. I. Colless, V. V. Ramasesh, D. Dahlen, M. S.Blok, M. E. Kimchi-Schwartz, et al., Computa-tion of molecular spectra on a quantum proces-sor with an error-resilient algorithm, Phys. Rev.X 8, 011021 (2018).

[52] D. B. Kaplan, N. Klco, and A. Roggero, GroundStates via Spectral Combing on a Quantum Com-puter, [arXiv:1709 . 08250 [quant-ph]](2017).

[53] A. Roggero and J. Carlson, Linear Response ona Quantum Computer, [arXiv:1804.01505[quant-ph]] (2018).

[54] H. Lamm and S. Lawrence, Simulation ofNonequilibrium Dynamics on a Quantum Com-puter, [arXiv:1806 . 06649 [quant-ph]](2018).

[55] E. F. Dumitrescu, A. J. McCaskey, G. Hagen,G. R. Jansen, T. D.Morris, et al.,CloudQuantumComputing of an Atomic Nucleus, Phys. Rev. Lett.120, 210501 (2018).

[56] A. Peruzzo, J. McClean, P. Shadbolt, M.-H.Yung, X.-Q. Zhou, et al., A variational eigen-value solver on a photonic quantum processor,Nature Communications 5, 4213 (2014).

[57] J. R. McClean, J. Romero, R. Babbush, and A.Aspuru-Guzik, The theory of variational hybridquantum-classical algorithms, New Journal ofPhysics 18, 023023 (2016).

[58] P. Silvi, E. Rico, M. Dalmonte, F. Tschirsich,and S. Montangero, Finite-density phase dia-gram of a (1+1)-d non-abelian lattice gauge the-ory with tensor networks, [arXiv:1606.05510[quant-ph]] (2016) 10.22331/q-2017-04-25-9.

[59] A. Retzker, J. I. Cirac, and B. Reznik, Detectingvacuum entanglement in a linear ion trap, Phys.Rev. Lett. 94, 050504 (2005).

[60] S. P. Jordan, K. S. M. Lee, and J. Preskill, Quan-tum Algorithms for Quantum Field Theories,Science 336, 1130 (2012).

[61] J. I. Cirac, P. Maraner, and J. K. Pachos, Coldatom simulation of interacting relativistic quan-tum field theories, Phys. Rev. Lett. 105, 190403(2010).

[62] L. Mazza, A. Bermudez, N. Goldman, M. Rizzi,M. A. Martin-Delgado, et al., An optical-lattice-based quantum simulator for relativistic fieldtheories and topological insulators, New Journalof Physics 14, 015007 (2012).

[63] E. A. Martinez et al., Real-time dynamics oflattice gauge theories with a few-qubit quantumcomputer, Nature 534, 516 (2016).

[64] J. S. Schwinger, Gauge Invariance and Mass. 2.Phys. Rev. 128, 2425 (1962).

Page 17 of 22

REFERENCES

[65] J. B. Kogut and L. Susskind, Hamiltonian For-mulation of Wilson’s Lattice Gauge Theories,Phys. Rev. D11, 395 (1975).

[66] N. Klco and M. J. Savage, Digitization ofScalar Fields for NISQ-Era Quantum Com-puting, [arXiv:1808 . 10378 [quant-ph]](2018).

[67] C. Kokail et al., Self-Verifying Variational Quan-tum Simulation of the Lattice Schwinger Model,[arXiv:1810.03421 [quant-ph]] (2018).

[68] J. Zhang, G. Pagano, P. W. Hess, A. Kyprianidis,P. Becker, et al., Observation of a many-bodydynamical phase transition with a 53-qubit quan-tum simulator, Nature 551, 601 EP (2017).

[69] H. Bernien, S. Schwartz, A. Keesling, H. Levine,A. Omran, et al., Probing many-body dynamicson a 51-atom quantum simulator, Nature 551,Article, 579 EP (2017).

[70] D. E. Kharzeev and E. M. Levin, Deep inelasticscattering as a probe of entanglement, Phys. Rev.D95, 114008 (2017).

[71] J. Berges, S. Floerchinger, and R. Venugopalan,Thermal excitation spectrum from entanglementin an expanding quantum string, Phys. Lett.B778, 442 (2018).

[72] J. Berges, S. Floerchinger, and R. Venugopalan,Dynamics of entanglement in expanding quan-tum fields, JHEP 04, 145 (2018).

[73] O. K. Baker and D. E. Kharzeev, Thermalradiation and entanglement in proton-protoncollisions at energies available at the CERNLarge Hadron Collider, Phys. Rev. D98, 054007(2018).

[74] R. Bellwied,Quantum entanglement in the initialand final state of relativistic heavy ion collisions,J. Phys. Conf. Ser. 1070, 012001 (2018).

[75] A. M. Kaufman, M. E. Tai, A. Lukin, M. Rispoli,R. Schittko, et al., Quantum thermalizationthrough entanglement in an isolated many-bodysystem, Science 353, 794 (2016).

[76] Y. Hagiwara, Y. Hatta, B.-W. Xiao, and F. Yuan,Classical and quantum entropy of parton distri-butions, Phys. Rev. D97, 094029 (2018).

[77] P. J. Mulders, The 3D entangled structure of theproton: transverse degrees of freedom in QCD,momenta, spins and more, Few Body Syst. 59,10 (2018).

[78] P. J. Mulders, Emergent symmetries of the Stan-dard Model, Phys. Lett. B787, 193 (2018).

[79] Y. Liu and I. Zahed, Entanglement in ReggeizedScattering using AdS/CFT, [arXiv:1803 .09157 [hep-ph]] (2018).

[80] A. Cervera-Lierta, J. I. Latorre, J. Rojo, and L.Rottoli, Maximal Entanglement in High EnergyPhysics, SciPost Phys. 3, 036 (2017).

[81] N. Laflorencie, Quantum entanglement in con-densed matter systems, Phys. Rept. 646, 1 (2016).

[82] http : / / www . int . washington . edu /PROGRAMS/17-66W/.

[83] S. Weinberg, Lectures on quantum mechanics,(2015) 10.1017/CBO9781316276105.

[84] I. Buluta and F. Nori, Quantum simulators, Sci-ence 326, 108 (2009).

[85] S. Debnath, N.M. Linke, C. Figgatt, K. A. Lands-man, K. Wright, et al., Demonstration of a smallprogrammable quantum computer with atomicqubits, Nature 536, 63 (2016).

[86] C. Gross and I. Bloch, Quantum simulationswith ultracold atoms in optical lattices, Science357, 995 (2017).

[87] R. Blatt and C. F. Roos, Quantum simulationswith trapped ions, Nature Physics 8, 277 (2012).

[88] A. A. Houck, H. E. Türeci, and J. Koch, On-chip quantum simulation with superconductingcircuits, Nature Physics 8, 292 (2012).

[89] E. Rico, M. Dalmonte, P. Zoller, D. Banerjee,M. Bögli, et al., SO(3) "Nuclear Physics" withultracold Gases, Annals Phys. 393, 466 (2018).

[90] S. Rajendran, N. Zobrist, A. O. Sushkov, R.Walsworth, and M. Lukin, A method for di-rectional detection of dark matter using spec-troscopy of crystal defects, Physical Review D96, 035009 (2017).

[91] D.R.Glenn,D.B.Bucher, J. Lee,M.D. Lukin,H.Park, et al., High-resolution magnetic resonancespectroscopy using a solid-state spin sensor,Nature 555, 351 (2018).

[92] O. Hosten, N. J. Engelsen, R. Krishnakumar, andM. A. Kasevich,Measurement noise 100 timeslower than the quantum-projection limit usingentangled atoms, Nature 529, 505 (2016).

Page 18 of 22

REFERENCES

[93] M. R. Dietrich, N. Kurz, T. Noel, G. Shu, andB. B. Blinov, Hyperfine and optical barium ionqubits, Physical Review A 81, 052328 (2010).

[94] Y. V. Stadnik and V. V. Flambaum, Axion-induced effects in atoms, molecules, and nu-clei: parity nonconservation, anapole moments,electric dipole moments, and spin-gravity andspin-axion momentum couplings, Physical Re-view D 89, 043522 (2014).

[95] L.-P. Yang and Z. Jacob, Quantum Critical De-tector : Amplifying Weak Signals Using First-Order Dynamical Quantum Phase Transitions,[arXiv:1807.04617 [quant-ph]] (2018).

[96] G. Balasubramanian, P. Neumann, D. Twitchen,M. Markham, R. Kolesov, et al., Ultralong spincoherence time in isotopically engineered dia-mond, Nature Materials 8, 383 (2009).

[97] J. T. Muhonen, J. P. Dehollain, A. Laucht, F. E.Hudson, R. Kalra, et al., Storing quantum in-formation for 30 seconds in a nanoelectronicdevice, Nature Nanotechnology 9, 986 (2014).

[98] S. Foletti, H. Bluhm, D. Mahalu, V. Umansky,and A. Yacoby, Universal quantum control oftwo-electron spin quantum bits using dynamicnuclear polarization, Nature Physics 5, 903(2009).

[99] D. Hucul, J. E. Christensen, E. R. Hudson, andW. C. Campbell, Spectroscopy of a synthetictrapped ion qubit, Physical Review Letters 119,100501 (2017).

[100] P.-A. Moreau, E. Toninelli, T. Gregory, and M. J.Padgett, Ghost imaging using optical correla-tions, Laser and Photonics Reviews 12, 1700143(2017).

[101] P. Kruit, R. G. Hobbs, C. S. Kim, Y. Yang,V. R. Manfrinato, et al., Designs for a quantumelectron microscope, Ultramicroscopy 164, 31(2016).

[102] S. Li, F. Cropp, K. Kabra, J. Lane T., G. Wet-zstein, et al., Electron ghost imaging, Phys. Rev.Lett. 121, 114801 (2018).

[103] A. W. Harrow, A. Hassidim, and S. Lloyd,Quan-tum algorithm for linear systems of equations,Phys. Rev. Lett. 103, 150502 (2009).

Page 19 of 22

A. NPQI WORKSHOP PARTICIPANTS AND AGENDA

A. NPQI Workshop Participants andAgenda

The website for the workshop Intersections betweenNuclear Physics and Quantum Information can be foundat http://www.phy.anl.gov/npqi2018/ which, in-ter alia, contains a record of the presentations. Thefollowing gives the workshop participants and agenda:

Yuri Alexeev Argonne National Laboratory, WhitneyArmstrong Argonne National Laboratory, John Ar-rington Argonne National Laboratory, Birger Back Ar-gonne National Laboratory, Alexei BazavovMichiganState University, Silas Beane University of Washing-ton, Kyle Bednar Kent State University, Leo Bellan-toni Fermilab, Paul Benioff Argonne National Labora-tory, Alexey Bezryadin University of Illinois, MichaelBishof Argonne National Laboratory, David BlythArgonne National Laboratory, John Bollinger NIST,Richard Brower Boston University, Paul BruillardPNNL,Mary Burkey University of Chicago,MichaelCarpenter Argonne National Laboratory, ClarenceChang Argonne National Laboratory, Yong Chen Pur-due University, Ian Cloët Argonne National Labora-tory, Zachary Conway Argonne National Laboratory,David Dean Oak Ridge National Laboratory, MarcelDemarteauArgonneNational Laboratory,MatthewDi-etrich Argonne National Laboratory, Patrick DreherNC State University, Eugene Dumitrescu Oak RidgeNational Laboratory, Estia Eichten Fermilab, EdenFigueroa Stony Brook University,Mael Flament StonyBrook University, Stefan Floerchinger Heidelberg Uni-versity, Aaron Fluitt Argonne National Laboratory,Nikolaos Fotiadis Los Alamos National Laboratory,Adam Freese Argonne National Laboratory, BryceGadway University of Illinois U-C, Dave Gaskell Jef-ferson Lab, Donald Geesaman Argonne National Lab-oratory, Andrew Geraci Northwestern University,Wal-ter Giele Fermilab, Alexey Gorshkov Joint QuantumInstitute, Anna Grassellino Fermilab, Stephen GrayArgonne National Laboratory, Nathan Guisinger Ar-gonne National Laboratory, Peter Gysbers TRIUMF,Kawtar Hafidi Argonne National Laboratory,Moham-mad Hattawy Argonne National Laboratory, Eric Her-bert Lewis University, Joseph Heremans Argonne Na-tional Laboratory,KielHoweFermilab,CiaranHughesFermilab, Zubin Jacob Purdue University, Xiao-YongJin Argonne National Laboratory, Sereres JohnstonArgonne National Laboratory, Bertus Jordaan StonyBrook University, David Kaplan University of Wash-

ington, Natalie Klco University of Washington, AndyKowalski Jefferson Lab, Ushma Kriplani Argonne Na-tional Laboratory, T.-S. Harry Lee Argonne NationalLaboratory, Daniel Lopez Argonne National Labora-tory, Ivar Martin Argonne National Laboratory, JoseMartinez Argonne and IIT, Edward May Argonne Na-tional Laboratory, Anna McCoy TRIUMF, MichaelMcGuigan Brookhaven National Laboratory, RobertMcKeown Jefferson Lab, Yannick Meurice Universityof Iowa, Aaron Miller Quantum Opus LLC, MisunMin Argonne National Laboratory, Peter Mintun Uni-versity of Chicago, Christopher Monroe Universityof Maryland, Peter Mueller Argonne National Labora-tory,ChristineMuschik Institute for Quantum Comput-ing, Petr Navratil TRIUMF, Mike Norman ArgonneNational Laboratory, Blaine Norum University of Vir-ginia, Thomas O’Donnell Virginia Tech Physics De-partment, James Osborn Argonne National Laboratory,Matthew Otten NanoScience and Technology, PeterPetreczky Brookhaven National Laboratory, Tomas Po-lakovicArgonneNational Laboratory,AlanPoonBerke-ley Lab, Raphael Pooser Oak Ridge National Labora-tory, David Potterveld Argonne National Laboratory,John Preskill Caltech, Tenzin Rabga Argonne Na-tional Laboratory, Gulshan Rai U.S. Department of En-ergy, Georg Raithel University of Michigan, ThomasReid Argonne National Laboratory, Jose Repond Ar-gonne National Laboratory, Pedro Rivero Illinois Insti-tute of Technology, Alessandro Roggero Los AlamosNational Laboratory, Alexander Romanenko Fermi-lab, Mark Saffman University of Wisconsin-Madison,Daniel SantiagoArgonne National Laboratory,MartinSavage Institute for Nuclear Theory, John Schiffer Ar-gonne National Laboratory, David Schuster Universityof Chicago, James Simone Fermilab, Pete SlawniakArgonne National Laboratory, Paul Sorensen U.S. De-partment of Energy, Daniel Stick Sandia National Labs,Oleksii Strelchenko Fermilab, Brent VanDevenderPNNL, Frank Verstraete University of Ghent, MatteoVorabbi TRIUMF,Gensheng Wang Argonne NationalLaboratory, Robert Wiringa Argonne National Labo-ratory, Junqi Xie Argonne National Laboratory, LiangYang University of Illinois U-C, Yongchao Yang Ar-gonne National Laboratory, Boram Yoon Los AlamosNational Laboratory, Linda Young Argonne NationalLaboratory, Jake Zappala Argonne National Labora-tory, Jiehang Zhang University of Maryland, Zhao-hui Zhang Northeastern University, Erez Zohar MaxPlanck Institute of Quantum Optics.

Page 20 of 22

A. NPQI WORKSHOP PARTICIPANTS AND AGENDA

Page 21 of 22