Toward scalable simulations of Lattice Gauge Theories on quantum computers

Abstract

The simulation of real-time dynamics in lattice gauge theories is particularly hard for classical computing due to the exponential scaling of the required resources. On the other hand, quantum algorithms can potentially perform the same calculation with a polynomial dependence on the number of degrees of freedom. A precise estimation is however particularly challenging for the simulation of lattice gauge theories in arbitrary dimensions, where, gauge fields are dynamical variables, in addition to the particle fields. Moreover, there exist several choices for discretizing particles and gauge fields on a lattice, each of them coming at different prices in terms of qubit register size and circuit depth. Here we provide a resource counting for real-time evolution of $U(1)$ gauge theories, such as Quantum Electrodynamics, on arbitrary dimension using the Wilson fermion representation for the particles, and the Quantum Link Model approach for the gauge fields. We study the phenomena of flux-string breaking up to a genuine bi-dimensional model using classical simulations of the quantum circuits, and discuss the advantages of our discretization choice in simulation of more challenging $SU(N)$ gauge theories such as Quantum Chromodynamics.

arXiv comment20 pages, 14 figures

References in corpus (62)

• Fault-tolerant quantum computation by anyons
• A variational eigenvalue solver on a quantum processor
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Quantum Spin Liquid States
• Fermionic quantum computation
• Thermodynamics of SU(3) Lattice Gauge Theory
• Exact chiral symmetry on the lattice and the Ginsparg-Wilson relation
• Real-time dynamics of lattice gauge theories with a few-qubit quantum computer
• Towards Practical Quantum Variational Algorithms
• Self-Verifying Variational Quantum Simulation of the Lattice Schwinger Model
• Quantum Algorithms for Quantum Field Theories
• Quantum-Classical Computation of Schwinger Model Dynamics using Quantum Computers
• Full nonperturbative QCD simulations with 2+1 flavors of improved staggered quarks
• U(1) Gauge Theory of the Hubbard Model : Spin Liquid States and Possible Application to k-(BEDT-TTF)_2 Cu_2 (CN)_3
• Ultracold Quantum Gases and Lattice Systems: Quantum Simulation of Lattice Gauge Theories
• Simulating chemistry using quantum computers
• A quantum information processor with trapped ions
• Quantum Link Models: A Discrete Approach to Gauge Theories
• Solving strongly correlated electron models on a quantum computer
• Lattice gauge theories simulations in the quantum information era
• Simulating Compact Quantum Electrodynamics with ultracold atoms: Probing confinement and nonperturbative effects
• Finding Exponential Product Formulas of Higher Orders
• The mass spectrum of the Schwinger model with Matrix Product States
• Automated optimization of large quantum circuits with continuous parameters
• Simulating lattice gauge theories on a quantum computer
• A Formulation of Lattice Gauge Theories for Quantum Simulations
• Tapering off qubits to simulate fermionic Hamiltonians
• QCD as a Quantum Link Model
• Atomic quantum simulator for lattice gauge theories and ring exchange models
• Review on novel methods for lattice gauge theories
• Tensor networks for Lattice Gauge Theories and Atomic Quantum Simulation
• U(1) Wilson lattice gauge theories in digital quantum simulators
• Faster quantum simulation by randomization
• Matrix product states for gauge field theories
• A Software Methodology for Compiling Quantum Programs
• Light Hadron Masses from Lattice QCD
• General Methods for Digital Quantum Simulation of Gauge Theories
• Real-time Dynamics in U(1) Lattice Gauge Theories with Tensor Networks
• Superconducting Circuits for Quantum Simulation of Dynamical Gauge Fields
• Simulations of Subatomic Many-Body Physics on a Quantum Frequency Processor
• Gluon Field Digitization for Quantum Computers
• Digital quantum simulation of ${\mathbb{Z}}_2$ lattice gauge theories with dynamical fermionic matter
• Non-Abelian $SU(2)$ Lattice Gauge Theories in Superconducting Circuits
• Quantum simulation of the Schwinger model: A study of feasibility
• Digital quantum simulation of lattice gauge theories in three spatial dimensions
• Non-Abelian string breaking phenomena with Matrix Product States
• Lattice Gauge Tensor Networks
• Quantum simulation of lattice gauge theories using Wilson fermions
• Reliability of lattice gauge theories
• Discrete Abelian Gauge Theories for Quantum Simulations of QED
• Oracles for Gauss's law on digital quantum computers
• Phase Transitions in $Z_n$ Gauge Models: Towards Quantum Simulations of the Schwinger-Weyl QED
• Precise measurement of quantum observables with neural-network estimators
• Sigma models on quantum computers
• Quantum simulation of $(1+1)$-dimensional U(1) gauge-Higgs model on a lattice by cold Bose gases
• Slow running of the Gradient Flow coupling from 200 MeV to 4 GeV in $N_{\mathrm{f}}=3$ QCD
• Digitizing Gauge Fields: Lattice Monte Carlo Results for Future Quantum Computers
• Determination of the QCD $\Lambda$-parameter and the accuracy of perturbation theory at high energies
• Lattice Model for Fermionic Toric Code
• Real-time-dynamics quantum simulation of (1+1)-D lattice QED with Rydberg atoms
• Ordering of Trotterization: Impact on Errors in Quantum Simulation of Electronic Structure
• Robustness of gauge-invariant dynamics against defects in ultracold-atom gauge theories

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• Primitive Quantum Gates for an SU(2) Discrete Subgroup: BT
• Matrix Model simulations using Quantum Computing, Deep Learning, and Lattice Monte Carlo
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• Improved Hamiltonians for Quantum Simulations
• Molecular spin qudits for quantum simulation of light-matter interactions
• Lattice Renormalization of Quantum Simulations
• Gauge invariant quantum circuits for $U(1)$ and Yang-Mills lattice gauge theories
• Real-time dynamics of Chern-Simons fluctuations near a critical point
• Simulating (2+1)D SU(2) Yang-Mills Lattice Gauge Theory at finite density with tensor networks
• Variational quantum simulation of U(1) lattice gauge theories with qudit systems
• Digital quantum simulation of a (1+1)D SU(2) lattice gauge theory with ion qudits
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• Primitive Quantum Gates for an SU(3) Discrete Subgroup: $\Sigma (36\times 3)$
• Dynamical quantum phase transitions of the Schwinger model: real-time dynamics on IBM Quantum
• Canonical Momenta in Digitized SU(2) Lattice Gauge Theory: Definition and Free Theory
• Gauge Theory Couplings on Anisotropic Lattices
• Exponential improvements in the simulation of lattice gauge theories using near-optimal techniques
• Tensor Networks for Lattice Gauge Theories beyond one dimension: a Roadmap
• Gluon Digitization via Character Expansion for Quantum Computers
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• A Quantum Computing Implementation of Nuclear-Electronic Orbital (NEO) Theory: Towards an Exact pre-Born-Oppenheimer Formulation of Molecular Quantum Systems
• Robustness of quantum correlation in quantum energy teleportation
• Estimating truncation effects of quantum bosonic systems using sampling algorithms
• Quantum mean estimation for lattice field theory
• Toward nuclear physics from lattice QCD on quantum computers
• Computing n-time correlation functions without ancilla qubits
• Quantum Information Processing with Molecular Nanomagnets: an introduction
• Quantum Simulation with Gauge Fixing: from Ising Lattice Gauge Theory to Dynamical Flux Model
• Quantum error mitigation for parametric circuits
• Matching Lagrangian and Hamiltonian Simulations in (2+1)-dimensional U(1) Gauge Theory
• Partial confinement in a quantum-link simulator