Two-dimensional ${\mathbb{Z}}_2$ lattice gauge theory on a near-term quantum simulator: variational quantum optimization, confinement, and topological order

Abstract

We propose an implementation of a two-dimensional ${\mathbb{Z}}_2$ lattice gauge theory model on a shallow quantum circuit, involving a number of single and two-qubits gates comparable to what can be achieved with present-day and near-future technologies. The ground state preparation is numerically analyzed on a small lattice with a variational quantum algorithm, which requires a small number of parameters to reach high fidelities and can be efficiently scaled up on larger systems. Despite the reduced size of the lattice we consider, a transition between confined and deconfined regimes can be detected by measuring expectation values of Wilson loop operators or the topological entropy. Moreover, if periodic boundary conditions are implemented, the same optimal solution is transferable among all four different topological sectors, without any need for further optimization on the variational parameters. Our work shows that variational quantum algorithms provide a useful technique to be added in the growing toolbox for digital simulations of lattice gauge theories.

22 pages, 19 figures

References in corpus (32)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Variational Quantum Algorithms
• Surface codes: Towards practical large-scale quantum computation
• Quantum Phases of Matter on a 256-Atom Programmable Quantum Simulator
• Programmable quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms
• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Bipartite entanglement and entropic boundary law in lattice spin systems
• A Trailhead for Quantum Simulation of SU(3) Yang-Mills Lattice Gauge Theory in the Local Multiplet Basis
• A Formulation of Lattice Gauge Theories for Quantum Simulations
• Optical Abelian Lattice Gauge Theories
• Digital lattice gauge theories
• Towards simulating 2D effects in lattice gauge theories on a quantum computer
• SU(2) hadrons on a quantum computer
• Tensor Networks for Lattice Gauge Theories with continuous groups
• A resource efficient approach for quantum and classical simulations of gauge theories in particle physics
• Digital quantum simulation of ${\mathbb{Z}}_2$ lattice gauge theories with dynamical fermionic matter
• Parameter Concentration in Quantum Approximate Optimization
• Lattice Gauge Tensor Networks
• Discrete Abelian Gauge Theories for Quantum Simulations of QED
• Reinforcement Learning assisted Quantum Optimization
• Entanglement generation in $(1+1)D$ QED scattering processes
• Qudit surface codes and gauge theory with finite cyclic groups
• Scattering of mesons in quantum simulators
• Analyzing the Performance of Variational Quantum Factoring on a Superconducting Quantum Processor
• Quantum optimization via four-body Rydberg gates
• Photon-mediated Stroboscopic Quantum Simulation of a ${\mathbb{Z}}_2$ Lattice Gauge Theory
• Simulating 2+1d ${\mathbb{Z}}_3$ lattice gauge theory with iPEPS
• Variational Monte Carlo simulation with tensor networks of a pure ${\mathbb{Z}}_3$ gauge theory in (2+1)d
• Real-time dynamics in 2+1d compact QED using complex periodic Gaussian states
• Quantifying the efficiency of state preparation via quantum variational eigensolvers
• ${\mathbb{Z}}_N$ lattice gauge theory in a ladder geometry
• Wilson Loops and Area Laws in Lattice Gauge Theory Tensor Networks

Cited by in corpus (22)

• Avoiding barren plateaus via transferability of smooth solutions in Hamiltonian Variational Ansatz
• Unified theory of local quantum many-body dynamics: Eigenoperator thermalization theorems
• Scattering wave packets of hadrons in gauge theories: Preparation on a quantum computer
• Resource-Efficient Quantum Simulation of Lattice Gauge Theories in Arbitrary Dimensions: Solving for Gauss' Law and Fermion Elimination
• Quantum Simulation of Z2 Lattice Gauge theory with minimal resources
• Visualizing Dynamics of Charges and Strings in (2+1)D Lattice Gauge Theories
• Finding the ground state of a lattice gauge theory with fermionic tensor networks: a $2+1d$ ${\mathbb{Z}}_2$ demonstration
• Quench dynamics of the Schwinger model via variational quantum algorithms
• Simulating gauge theories with variational quantum eigensolvers in superconducting microwave cavities
• Synthetic ${\mathbb{Z}}_2$ gauge theories based on parametric excitations of trapped ions
• Quantum optimization within lattice gauge theory model on a quantum simulator
• Beyond Quantum Annealing: Optimal control solutions to MaxCut problems
• Quantum Simulation of non-Abelian Lattice Gauge Theories: a variational approach to ${\mathbb{D}}_8$
• Detecting quasi-degenerate ground states in topological models via variational quantum eigensolver
• Anderson localization of emergent quasiparticles: Spinon and vison interplay at finite temperature in a ${\mathbb{Z}}_2$ gauge theory in three dimensions
• Solving lattice gauge theories using the quantum Krylov algorithm and qubitization
• Noise-aware variational eigensolvers: a dissipative route for lattice gauge theories
• Ergodic Archimedean dimers
• A Monte Carlo Tree Search approach to QAOA: finding a needle in the haystack
• Projected Entangled Pair States for Lattice Gauge Theories with Dynamical Fermions
• Z${}_2$ topological orders in kagomé dipolar systems: Feedback from Rydberg quantum simulator
• Finite-group gauge theories on lattices as Hamiltonian systems with constraints