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# Next steps in Quantum Science for HEP

US/Central
One West (Fermilab - Wilson Hall)

### One West

#### Fermilab - Wilson Hall

Fermi National Accelerator Laboratory Batavia, IL
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Description

This workshop will focus on applications of quantum computing technologies, algorithms, and theoretical developments of interest to the High Energy Physics community. Fermilab’s Theory Department and Scientific Computing Division are particularly interested in developing collaborations and working groups to target problems related to:

• Quantum simulation of quantum field theories for strongly coupled relativistic systems
• Toy models of gauge theories for near-term quantum computing resources, including simulation of restricted subprocesses in non-peturburative gauge theories
• Tailored quantum computing hardware architectures for digital quantum simulation of local field theories
• Variational quantum eigensolvers for quantum field theories
• Quantum algorithms for traditional HEP computational problems, such as phase space integration, loop and amplitude programs, optimization, and machine learning in data analysis.
• Quantum teleportation experiments and quantum circuit models of quantum gravity systems.
• Applying qubit technologies to quantum sensors in HEP experiments on the sensitivity frontier.

The workshop will include comprehensive hands on tutorials from Google and demonstrations from other technology industry partners.

This workshop builds on our past November workshop, “Near-term Applications of Quantum Computing” also held at Fermilab, and we hope these two workshops will form the groundwork for a white paper on Quantum Science in HEP.

Fermilab Quantum Inititives QIS@FNAL

• Wednesday, September 12
• Session 1 One West

### One West

#### Fermilab - Wilson Hall

Fermi National Accelerator Laboratory Batavia, IL

chair: Marcela Carena

• 1
Welcome
Speaker: Dr Marcela Carena (Fermilab)
• 2
Fermilab Quantum Science Program
Speaker: Dr Joseph Lykken (Fermilab)
• 3
Formulating Gauge Theories for a Quantum Computer
I will discuss some motivations for studying gauge theories on a quantum computer, and basic features of gauge theories in a Hamiltonian formulation. In particular, I will discuss issues regarding Gauss's law and cutoffs on the Hilbert space, both of which have to be confronted for simulations on a quantum computer.
Speaker: Prof. David B. Kaplan (INT, University of Washington)
• 4
Guass's Law and Hilbert Space Constructions for U(1) Lattice Gauge Theories
Motivated by the limited capabilities of near-term quantum computers, we reconsider the Hamiltonian formulation of lattice gauge theories and the method of truncating Hilbert space to render it finite-dimensional. Conventional formulations lead to a Hilbert space largely spanned by unphysical states; given the current inability to perform fault-tolerant large scale quantum computations, we examine here how one might restrict wave function evolution entirely or mostly to the physical subspace. We consider such constructions for the simplest of these theories containing dynamical gauge bosons — $U(1)$ lattice gauge theory without matter in d = 2, 3 spatial dimensions — and find that electric-magnetic duality naturally plays an important role. We conclude that this approach is likely to significantly reduce computational overhead in d = 2 by a reduction of variables. We further investigate potential advantages of regulating magnetic fluctuations in asymptotically-free theories, instead of electric fluctuations, which have been the focus of previous truncation proposals.
Speaker: Dr Jesse Stryker (University of Washington)
• 10:05 AM
Coffee Break One West

### One West

#### Fermilab - Wilson Hall

Fermi National Accelerator Laboratory Batavia, IL
• Session 2 One West

### One West

#### Fermilab - Wilson Hall

Fermi National Accelerator Laboratory Batavia, IL

chair: Andreas Kronfeld

• 5
Simulating quantum and classical field theories with a quantum computer
In this talk I will describe quantum algorithms by which universal fault-tolerant quantum computers can simulate quantum and classical field theories. In the case of quantum field theories the number of quantum degrees of freedom is extensive in the volume of the system to be simulated and the speedup over classical algorithms is exponential. As specific applications we consider phi-fourth theory and the Gross-Neveu model. For classical field theories the number of qubits needed for the simulation scales only logarithmically with the volume. The resulting speedup is polynomial for classical field theories in any fixed number of spatial dimensions but exponential in the number of dimensions. As a specific application we consider wave equations in three spatial dimensions (such as Maxwell's equations and the Klein-Gordon equation). In this case the quantum algorithm achieves a cubic speedup while using only logarithmically many qubits, vs. standard classical methods which have memory requirements that grow linearly with volume. I will conclude with some research directions and open questions regarding quantum algorithms for scientific computing.
Speaker: Dr Stephen Jordan (NIST / University of Maryland)
• 6
Linear Response on a Quantum Computer
Dynamics in quantum systems is notoriously difficult to treat. We demonstrate an exponential speed-up for quantum linear response as measured in electron and neutrino scattering. I will discuss some very preliminary work we have done and prospects for further studies using both classical computers to simulate quantum computers and quantum computer applications.
Speaker: Joe Carlson (LANL)
• 7
I will briefly introduce the current hardware at Google and their limitations. I will give examples on how to construct quantum circuits to simulate model Hamiltonians, such as the Fermi-Hubbard model and the Sachdev-Ye-Kitaev (SYK) model. Spatially local fermionic problems can become nonlocal after being mapped to qubit Hamiltonians. I will discuss how lattice gauge field theory can be used to construct mappings that conserve locality.
• 8
Quantum Computing for Feynman Integral Reduction
At the LHC, theory uncertainties are starting to become the dominant uncertainty for certain processes. One of the limiting factors is the ability to calculate loop diagrams for high number of loops. Here I propose a quantum algorithm that can be used to work towards removing this barrier.
Speaker: Joshua Isaacson
• 12:30 PM
Lunch One West

### One West

#### Fermilab - Wilson Hall

Fermi National Accelerator Laboratory Batavia, IL
• Session 3 One West

### One West

#### Fermilab - Wilson Hall

Fermi National Accelerator Laboratory Batavia, IL

chair: Roni Harnik

• 9
What we've learned about gravity from quantum error correction
Speaker: Prof. Daniel Harlow (MIT)
• 10
Quantum Information Techniques in High Energy Physics
In this talk I will explore the possibilities of using quantum algorithms and techniques inspired by quantum algorithms to design searches for new physics. This talk will be primarily and speculatively focused on particle physics, rather than quantum gravity, in an attempt to find new potential connections between high energy physics and quantum information science.
Speaker: Dr Ning Bao (Berkeley)
• 11
Quantum Teleportation at Fermilab
The Fermilab Quantum NETwork ([FQNET][1]) aims to produce a fully functional quantum network based initially on optical fibers with the capability to distribute time-bin photonic quantum states (qubits) across various distances by employing an intrinsic property of a multi-qubit system: entanglement. The resulting quantum network system will serve fundamental reserach and future R&D quantum communication technologies and protocols. Here we present the status of the system. [1]: http://inqnet.caltech.edu/fqnet/
Speakers: Maria Spiropulu, Dr Neil Sinclair (Caltech)
• 3:30 PM
Coffee Break One West

### One West

#### Fermilab - Wilson Hall

Fermi National Accelerator Laboratory Batavia, IL
• Quantum Computing and the Entanglement Frontier One West

### One West

#### Fermilab - Wilson Hall

Fermi National Accelerator Laboratory Batavia, IL

The quantum laws governing atoms and other tiny objects seem
to defy common sense, and information encoded in quantum systems has
weird properties that baffle our feeble human minds. John Preskill will
explain why he loves quantum entanglement, the elusive feature making
quantum information fundamentally different from information in the
macroscopic world. By exploiting quantum entanglement, quantum computers
should be able to solve otherwise intractable problems, with
far-reaching applications to cryptology, materials, and fundamental
physical science. Preskill is less weird than a quantum computer, and
easier to understand.

• 12
Colloquium: Next Steps in Quantum Science for HEP
View [video][1] [1]: http://vms.fnal.gov/asset/detail?recid=1956899
Speaker: Prof. John Preskill (Caltech)
• Thursday, September 13
• Session 4 One West

### One West

#### Fermilab - Wilson Hall

Fermi National Accelerator Laboratory Batavia, IL

chair: Yannick Meurice

• 13
Tensor Network and Cold Atoms Methods for Lattice Gauge Theories
Quantum simulation and tensor networks are two many-body physics approaches rooted in quantum information science, which have been widely used recently, especially in condensed matter contexts, proving to be very useful. The first suggests to use controllable quantum systems as simulators of others, which might be otherwise inaccessible or hard to solve; the latter allows one to efficiently construct and study (analytically and numerically) physically relevant many body states with arbitrary symmetries. More recently, these methods have been generalized and applied to high energy physics problems as well, and in particular to gauge theories. In my talk I will discuss the application of those methods for the study of lattice gauge theories, focusing on the work carried out at the theory group at MPQ: first, quantum simulation of lattice gauge theories with ultracold atoms in optical lattices -- suggesting to observe non-perturbative elementary particle physics in atomic simulators; and finally, gauged fermionic PEPS -- a particular tensor network construction of gauge invariant states, involving dynamical gauge fields and fermionic matter, allowing one to use the efficient tensor network toolbox for the study of gauge theories, and extend it, thanks to the presence of gauge fields, to numerical studies in $(2+1)$-d and more.
Speaker: Dr Erez Zohar (Max Planck Institute of Quantum Optics)
• 14
Universal Features of the Polyakov Loop in Quantum Simulations of the Abelian Higgs Model
I will discuss our proposal to quantum simulate the Abelian Higgs model in $1+1$ dimensions. While doing this I will show how the energy gap associated with the inclusion of a static charge shows universal finite-size scaling in the discrete lattice model, and the continuous-time quantum model. This finite-size scaling is identical in both limits. I will briefly go into progress being made in $2+1$ dimensions on the $U(1)$-gauge model.
Speaker: Judah Unmuth-Yockey (Syracuse University)
• 15
Digitization of Scalar Fields for NISQ-Era Quantum Computing
With rapid developments in quantum hardware, it is increasingly important to analyze qubit, operator and gate requirements to optimally utilize available quantum resources for computation. In this talk, I present such an analysis for the digitization of interacting scalar field theories onto NISQ-era quantum devices, building upon the foundational work by Jordan, Lee and Preskill. Leveraging the Nyquist-Shannon sampling theorem (introduced in this context by Macridin, Spentzouris, Amundson and Harnik building on the work of Somma) as well as the Quantum Fourier Transform for digitization-improvement, a feasible number of qubits (< 10) can represent localized and delocalized low-energy wavefunctions with digitization errors below expected NISQ-era noise levels---naturally leading to the development of small-scale benchmarks for hardware implementations of scalar lattice field theory.
Speaker: Ms Natalie Klco (University of Washington)
• 16
An Operator Algebra Approach to Entropy Spread and Quantum Chaos
In an interacting quantum system far from equilibrium, initially local information spreads into and melds with its environment. This has many manifestations, from entanglement spread in quantum quenches to environmental coupling induced by quantum channels. The rate of entropy spread is often difficult to calculate outside of free, perturbative or holographic regimes. We propose an operator algebra approach to the problem. The close connection between Rényi entropies and non-commutative measures has yielded strong results in the channel setting. We apply similar ideas to the setting of many-body quantum quenches, including in the SYK model. We discuss connections to chaos and rates of scrambling. For practical applications, we consider how our methods apply to decoherence in quantum computation and memory.
Speaker: Mr Nicholas LaRacuente (University of Illinois at Urbana-Champaign)
• 10:40 AM
Coffee Break One West

### One West

#### Fermilab - Wilson Hall

Fermi National Accelerator Laboratory Batavia, IL
• Session 5 One West

### One West

#### Fermilab - Wilson Hall

Fermi National Accelerator Laboratory Batavia, IL

chair: Kiel Howe

• 17
Contracting Tensor Network on a Noisy Quantum Computer
I will argue that even a medium-scale (50 to \ensuremath{\sim}100 qubits) quantum computer can significantly speed up the existing tensor network calculations. This is because the classical tensor network contraction algorithms have hit a plateau, and because the contraction time on a quantum computer scales much favorably compared to the classical methods. What makes this proposal realistic is the fact that the method is noise-resilient. Under the standard noise model, the effect of noise on low-point correlation functions remains controlled even in the large system limit. I expect this method to primarily help understand challenging quantum many-body systems, but we will also muse on other speculative possibilities (\emph{e.g.}, machine learning) as well.
Speaker: Isaac Kim (Stanford University)
• 18
Tensor Networks for Fine-Graining Lattice Gauge Theory, and Also Path Integral Geometry
There are many tensor network approaches to studying quantum field theories. In this talk we summarize two: (1) An approach to fine-graining (UV-completing) lattice Yang-Mills theory in the Hamiltonian formalism. Central to this approach are local maps that perform curvature interpolation in the gauge-group, which together form the building blocks of a gauge-invariant MERA tensor network. (2) A way of assigning geometric content to pieces of certain well-known tensor networks for critical systems, via their mimicry of pieces of euclidean time path integral (of a conformal field theory).
Speaker: Ashley Milsted (Perimeter Institute for Theoretical Physics)
• 19
Approaching Lattice Gauge Theories with Matrix Product States and Gaussian States
In recent years variational approaches based on efficient ansatzes for the wave function of a quantum many-body system have proven their power for addressing the Hamiltonian lattice formulation of gauge theories. For one, methods based on Matrix Product States, a particular kind of one-dimensional Tensor Network, have been successfully applied to various Abelian and non-Abelian lattice gauge models in $1+1$ dimension. Lately, we developed a variational ansatz based on Gaussian States for $(1+1)$-dimensional lattice gauge theories. These techniques do not suffer from the sign problem and allow for addressing problems which cannot be tackled with conventional Monte Carlo methods, such as out-of-equilibrium dynamics or the presence of a chemical potential. In this talk I will present some results demonstrating the capabilities of these techniques using the Schwinger model and a $(1+1)$-dimensional SU(2) lattice gauge theory as a test bench. In particular, I will show that we can reliably simulate the static aspects as well as the real-time dynamics of string breaking in these models, and that these methods might be helpful for exploring questions relevant for an implementation in (analog) quantum simulators.
Speaker: Dr Stefan Kuehn (Perimeter Institute for Theoretical Physics)
• 12:20 PM
Lunch One West

### One West

#### Fermilab - Wilson Hall

Fermi National Accelerator Laboratory Batavia, IL
• Session 8 One West

### One West

#### Fermilab - Wilson Hall

Fermi National Accelerator Laboratory Batavia, IL

chair: Jim Simone

• 20
Trapped-ion systems for Quantum Simulation of Lattice Gauge Theory
Linear arrays of trapped and laser cooled atomic ions are among the foremost candidates for realizing quantum simulation and computation platforms. High fidelity coherent manipulations together with nearly perfect detection guarantee an unprecedented control over a large number of qubits, which can be used to run quantum algorithms [1] or engineer Hamiltonians to emulate physical systems of interest [2]. Recently trapped ions have been employed for proof of principle demonstrations of quantum simulation of high energy physics, including the Dirac equation [3] and the 1+1D Schwinger model [4]. In this talk I will describe the main features of the trapped-ion quantum hardware and discuss proposals [5,6] and perspectives for an analog implementation of lattice gauge theories in trapped-ion systems. References [1] S. Debnath et al. Nature 536, 63 (2016) [2] J. Zhang, GP, et al., Nature 551, 601 (2017) [3] E. Martinez, et al., Nature 534, 516 (2016) [4] R. Gerritsma, et al., Nature 463, 68 (2010) [5] P. Hauke, et. al., PRX 3, 041018 (2013) [6] D. Yang, et al., PRA 94, 052321 (2016)
Speaker: Dr Guido Pagano (University of Maryland)
• 21
A lower bound method for Hamiltonian simulation based on quantum marginals and its relation to quantum information
In this talk we introduce a lower bound simulation method based on variational determination of the quantum marginal distribution, and how the geometric constraints associated with enforcing feasibility in the variational procedure can be employed to certify physicality in a marginal tomography routine. The feasibility constraints we employ are derived from 'outer' approximations to the n-representability problem which provide a hierarchy of semidefinite programs that are relaxations of the ground state energy problem. We demonstrate that with modern semidefinite program solvers i): the lower bound method can provide tight approximations to the ground state energies for chemical and condensed matter model systems that are challenging for traditional methods and ii) provide a computationally efficient method for fermionic marginal tomography that will be paramount for finding utility with near-term quantum resources.
Speaker: Nick Rubin (Rigetti)
• Tutorial Hornet's Nest (8th Floor)

### Hornet's Nest (8th Floor)

#### Fermilab - Wilson Hall

Fermi National Accelerator Laboratory Batavia, IL
• 22
Refresher Tutorial
• 23
Cirq Intro
• 4:25 PM
Coffee Break One West

### One West

#### Fermilab - Wilson Hall

Fermi National Accelerator Laboratory Batavia, IL
• Tutorial Hornet's Nest (8th Floor)

### Hornet's Nest (8th Floor)

#### Fermilab - Wilson Hall

Fermi National Accelerator Laboratory Batavia, IL
• 24
OpenFermion Intro
• 5:40 PM
Break
• 25
Programming and Experiments
• Friday, September 14
• Tutorial Hornet's Nest (8th Floor)

### Hornet's Nest (8th Floor)

#### Fermilab - Wilson Hall

Fermi National Accelerator Laboratory Batavia, IL
• 26
OpenFermion-Cirq VQE Hands On Tutorial Hornets Nest (WH8)

### Hornets Nest (WH8)

• 10:30 AM
Coffee Break One West

### One West

#### Fermilab - Wilson Hall

Fermi National Accelerator Laboratory Batavia, IL
• Session 6 One West

### One West

#### Fermilab - Wilson Hall

Fermi National Accelerator Laboratory Batavia, IL

chair: Panagiotis Spentzouris

• 27
The IBM-Q Initiative as a Resource for HEP Quantum Computing
This is the first of two talks on the IBM-Q quantum computing systems. The presentation will briefly summarize the concept of an IBM-Q Hub and the preparations at NC State for implementation of the only university-based IBM-Q Hub in the Americas. There will be a brief discussion of the role that the Hub will play in forming research partnerships with industry and the preparations for building a university based educational role for quantum computing. The talk will also introduce the Hub’s capabilities and how they can potentially be focused toward high energy physics problems.
Speaker: Dr Patrick Dreher (NC State University)
• 28
Fermionic Systems and Quantum Computing
In this talk I will review methods for simulating fermionic systems on quantum computers, present ideas on how quantum resources can be optimized, and how to deal with noise rates in current quantum processors. I will then demonstrate the capability of the IBM open-access software Qiskit Aqua, a full-stack quantum computing framework.
Speaker: Dr Antonio Mezzacapo (IBM)
• 29
A Universal Training Algorithm for Quantum Deep Learning
In recent months, the field of Quantum Machine Learning (QML) has had numerous advances and a rapid growth of interest from academia and industry alike. Recent works have focused on a particular class of QML algorithms, the so-called quantum variational algorithms (often called quantum neural networks), where an optimization over a set of parametrized quantum circuit ansatze is performed in order to learn certain quantum states or quantum transformations. The explicit connection between these quantum parametric circuits and neural networks from classical deep learning had so far remained elusive. In this talk, we will establish how to port over classical neural networks as quantum parametric circuits, and we will further introduce a quantum-native backpropagation principle which can be leveraged to train any quantum parametric network. We will present two main quantum optimizers leveraging this quantum backpropagation principle: Quantum Dynamical Descent (QDD), which uses quantum-coherent dynamics to optimize network parameters, and Momentum Measurement Gradient Descent (MoMGrad), which is a quantum-classical analogue of QDD. We will briefly cover multiple applications of QDD/MoMGrad to various problems of quantum information learning, and how to use these optimizers to train classical neural networks in a quantum fashion. Furthermore, we will show how to efficiently train hybrid networks comprised of classical neural networks and quantum parametric circuits, running on classical and quantum processing units, respectively. Talk based on [\arXiv{1806.09729}].
Speaker: Mr Guillaume Verdon (Institute for Quantum Computing)
• 12:45 PM
Lunch One West

### One West

#### Fermilab - Wilson Hall

Fermi National Accelerator Laboratory Batavia, IL
• Session 7 One West

### One West

#### Fermilab - Wilson Hall

Fermi National Accelerator Laboratory Batavia, IL

chair: James Amundson

• 31
TBD: Quantum Simulation of Field Theories
Speaker: Prof. Martin Savage (Institute For Nuclear Theory)
• 32
Closing Remarks
I will review the current status of quantum computing research, and assess the prospects (both near-term and long-term) for advancing fundamental physics through simulations of quantum field theory using quantum computers and quantum simulators.
Speaker: Prof. John Preskill (Caltech)
• 3:30 PM
Wine & Cheese One West

### One West

#### Fermilab - Wilson Hall

Fermi National Accelerator Laboratory Batavia, IL
• Fermilab Joint Experimental-Theoretical Physics Seminar One West

### One West

#### Fermilab - Wilson Hall

Fermi National Accelerator Laboratory Batavia, IL
• 33
Entanglement in Gauge Theories
Speaker: Dr Sandip Trivedi (Tata Institute for Fundamental Research)