### Conveners

#### Quantum Computing and Quantum Information

- Henry Lamm (Fermilab)

#### Quantum Computing and Quantum Information

- Raghav Jha (Jefferson Lab)

#### Quantum Computing and Quantum Information

- Giuseppe Clemente (DESY)

#### Quantum Computing and Quantum Information

- Yannick Meurice (U. of Iowa)

#### Quantum Computing and Quantum Information

- Takuya Okuda (University of Tokyo)

#### Quantum Computing and Quantum Information

- David Schaich (Liverpool)

We discuss implementations of lattice gauge theories on digital quantum computers. In particular, we investigate the number of gates required to simulate the time time evolution. Using state-of-the art methods with our own augmentation, we find that the cost of simulating a single time step evolution of an elementary plaquette is prohibitive in the current era of quantum hardware. Moreover, we...

In this study, we investigate the real-time dynamics in the $(1+1)$d U(1) gauge theory called the Schwinger model via variational quantum algorithms. Specifically, we simulate the quench dynamics in the presence of the external electric field.

We first prepare the ground state in the absence of the external field using variational quantum eigensolver (VQE) and then perform the real-time...

State preparation is a crucial aspect of quantum simulation of quantum field theories. When aiming to simulate Standard Model physics, it is likely that fault-tolerant quantum computers will be required. In this regime, it is beneficial to consider algorithms that exhibit nearly optimal scaling with the problem parameters. Many of these algorithms rely on repeated calls to a block encoding of...

The digital quantum simulation of lattice gauge theories is expected to become a major application of quantum computers. Measurement-based quantum computation is a widely studied competitor of the standard circuit-based approach. We formulate a measurement-based scheme to perform the quantum simulation of Abelian lattice gauge theories in general dimensions. The scheme uses an entangled...

One possible approach to the quantum simulation of gauge theories involves replacing the gauge group, a compact Lie group, with one of its discrete finite subgroups. We show how the electric Hamiltonian may be interpreted as a Laplacian operator on the finite group and how this is related to the degeneracy of the electric ground state. Moreover, we discuss the dimension of the physical,...

Hamiltonian simulations of quantum systems require a finite-dimensional representation of the operators acting on the Hilbert space. Here we present a discretization scheme for gauge links and canonical momenta of an SU(2) gauge theory which offers the possibility to freely refine the discretisation. This is achieved by discretising SU(2) and constructing the canonical momentum using the...

Numerical simulations of quantum Hamiltonians can be done representing the degrees of freedom as matrices acting on a truncated Hilbert space. Here we present a formulation for the lattice $SU(2)$ gauge theory in the so called "magnetic basis", where the gauge links are unitary and diagonal. The latter are obtained from a direct discretization of the group manifold, while the canonical momenta...

Simulations of bosonic field theories on quantum computers demand a truncation in field space to “fit” the theory onto limited quantum registers. We examine two different truncations preserving the same symmetries as the 1+1-dimensional $O(3)$ non-linear $\sigma$-model - one truncating the Hilbert space of functions on the unit sphere by setting an angular momentum cutoff and a fuzzy sphere...

Formulating bosonic field theories for quantum simulation is a subtle task. Ideally, one wants the smallest truncation of the bosonic Hilbert space that simultaneously exhibits a high degree of universality. But many of the most straight-forward truncations probably do not exhibit much universality. Meanwhile, recent work on the so-called "fuzzy" sigma model has shown promise as a very...

Quadratic Unconstrained Binary Optimization (QUBO) problems can be addressed on quantum annealing systems. We reformulate the strong coupling lattice QCD dual representation as a QUBO matrix. We confirm that importance sampling is feasible on the D-Wave Advantage quantum annealer. We describe the setup of the system and present the first results obtained on a D-wave quantum annealer for U(N)...

We propose three independent methods to compute the hadron mass spectra of gauge theories in the Hamiltonian formalism. The determination of hadron masses is one of the key issues in QCD, which has been precisely calculated by the Monte Carlo method in the Lagrangian formalism. We confirm that the mass of hadrons can be calculated by examining correlation functions, the one-point function, or...

We compute the low-lying spectrum of 4D SU(2) Yang-Mills in a finite volume using quantum simulations. In contrast to small-volume lattice truncations of the Hilbert space, we employ toroidal dimensional reduction to the ``femtouniverse" matrix quantum mechanics model. In this limit the theory is equivalent to the quantum mechanics of three interacting particles moving inside a 3-ball with...

We express non-linear sigma O(3) model in a form suited to continuous variable (CV) approach to quantum computing by rewriting the model in terms of boson operators in an infinite-dimensional Hilbert space. We show that it is possible to reach the scaling regime with truncation of the Fock space by considering $\mathcal{O}(10)$ photons at each site. This is an indication that it might be...

We review recent suggestions to quantum simulate scalar electrodynamics (the lattice Abelian Higgs model) in 1+1 dimensions with rectangular arrays of Rydberg atoms. We show that platforms made publicly available recently allow empirical explorations of the critical behavior of quantum simulators. We discuss recent progress regarding the phase diagram of two-leg ladders, effective Hamiltonian...

This talk will discuss a method for computing the energy spectra of quantum field theory utilizing digital quantum simulation. A quantum algorithm called coherent imaging spectroscopy quenches the vacuum with a time-oscillating perturbation and reads off the excited energy levels from the loss in the vacuum-to-vacuum probability following the quench. As a demonstration, we apply this algorithm...

Quantum simulations of lattice gauge theories are currently limited by the noisiness of the physical

hardware. Various error mitigation strategies exist to extend the use of quantum computers. We perform quantum simulations to compute two-point correlation functions of the 1 + 1d Z2 gauge theory with matter to determine the mass gap for this theory. These simulations are used as a laboratory...

We have studied the chiral and confinement-screening phase transitions in the Schwinger model at finite temperature and density using the quantum algorithm.

The theoretical exploration of the phase diagram for strongly interacting systems at finite temperature and density remains incomplete mainly due to the sign problem in the conventional Lattice Monte Carlo method.

However, quantum...

An effective way to design quantum algorithms is by heuristics. One of the representatives is Farhi et al.’s quantum approximate optimization algorithm (QAOA), which provides a powerful variational ansatz for ground state preparation. QAOA is inspired by the adiabatic evolution of a quantum system, and the ansatz can encode the real time evolution of the system Hamiltonian. In this work, we...

Lattice studies of spontaneous supersymmetry breaking suffer from a sign problem that in principle can be evaded through novel methods enabled by quantum computing. I will present ongoing work exploring ways quantum computing could be used to study spontaneous supersymmetry breaking in lower-dimensional lattice systems including the (1+1)d N=1 Wess--Zumino model. A particularly promising...

In this talk we introduce a novel quantum algorithm for the estimation of thermal averages

in the NISQ-era through an iterative combination of Variational Quantum Eigensolver techniques and reweighting.

We discuss the details of the algorithm and the scaling of resources and systematical errors,

showing some results of the application to compelling test cases.

Quantum computation often suffers from artificial symmetry breaking. We should strive to suppress the artifact both by theoretical and technical improvements. As for chiral symmetry, there is a celebrated theoretical formalism, i.e., the overlap fermion. In this presentation, I will talk about how the overlap fermion guarantees chiral symmetry in quantum computation. I will also show that,...

Constructing improved Hamiltonians for gauge theories coupled to fermionic matter will be important for improving continuum limit extrapolations of quantum computations. In this talk we will present a formulation for simulating ASQTAD fermions for lattice computation and provide fault tolerant resource costs in terms of primitive operations. We additionally show tha tthe scaling of energies...

Quantum hardware in the NISQ era suffers from noise, which affects the reliability and accuracy of quantum computation. Here we present a comparison of quantum error mitigation strategies for Hamiltonian simulation and variational quantum algorithms, using as test bench some simple quantum fermionic systems and discrete gauge theories.

In the quantum simulation of lattice gauge theories, gauge symmetry can be either fixed or encoded as a redundancy of the digitized Hilbert space. While fixing the gauge saves the number of qubits to digitize the Hilbert space, keeping the gauge redundancy can provide space to mitigate and correct certain quantum errors by checking and restoring Gauss's law. In this talk, we treat the gauge...

We explore relations between quantum error correction and gauge theory. They have a conceptual similarity that quantum error correction provides a redundant description of logical qubits in terms of encoded qubits while gauge theory has a redundancy to describe physical states. Motivated by the conceptual similarity and recent demand for efficient ways to put gauge theories on quantum...

The possibility to use fault-tolerant Quantum Computers in the "Beyond the NISQ era" is a promising perspective: it could bring the implementation of Markov Chain Monte Carlo (MCMC) quantum algorithms on real machines. Then, it would be possible to exploit the quantum properties of such devices to study the thermodynamic properties of the system. This also allows us to avoid the infamous sign...

Motivated by attempts to quantum simulate lattice models with continuous Abelian symmetries using discrete approximations, we study an extended-O(2) model that differs from the ordinary O(2) model by the addition of an explicit symmetry breaking term. Its coupling allows to smoothly interpolate between the O(2) model (zero coupling) and a $q$-state clock model (infinite coupling). In the...

The entanglement entropy is a quantity encoding important features of strongly interacting quantum many-body systems and gauge theories, but its analytical study is still limited to systems with high level of symmetry. This motivates the search for efficient techniques to investigate this quantity numerically, by means of Monte Carlo calculations on the lattice. In this talk, we present a...

We present our study of real-time dynamics and dynamical quantum phase transition (DQPT) in the (1+1)-dimensional massive Thirring mode using matrix product states (MPSs). Lattice regularisation of this model with Kogut-Susskind fermions corresponds to the XXZ spin chain with the presence of a constant and a staggered magnetic fields. In this work, we implement methods of variational uniform...

In this talk we study the Ising model living on a discretization of two dimensional anti-de Sitter space. Our numerical work uses tensor network methods based on matrix product states (MPS) and matrix product operator (MPO) constructions. We use DMRG techniques to obtain the ground state and investigate its properties. For the time evolution of the model , we use the TEBD algorithm and show...

In this talk, we investigate the Trotter evolution of an initial state in the Gross-Neveu model and hyperbolic Ising model in two spacetime dimensions, leveraging quantum computers. We identify different sources of errors prevalent in various quantum processing units and discuss challenges to scale up the size of the computation. We present benchmark results obtained from some platforms and...