Quantum Simulation of QED in Coulomb Gauge

Abstract

A recent work considered quantum simulation of Quantum Electrodynamics on a lattice in the Coulomb gauge with gauge degrees of freedom represented in the occupation basis in momentum space. Here we consider the more efficient representation of the gauge degrees of freedom in field basis in position space and develop a quantum algorithm for real-time simulation. We show that the continuum Coulomb gauge Hamiltonian is equivalent to the temporal gauge Hamiltonian when acting on physical states consisting of fermion and transverse gauge fields. The Coulomb gauge Hamiltonian is discretized by using the Green's function of the discrete Laplacian operator under the Dirichlet boundary conditions. Both the continuum Coulomb gauge Hamiltonian and the discretized one proposed here guarantee that the unphysical longitudinal gauge fields are decoupled and commute with the corresponding Hamiltonian. Thus there is no need to impose any constraint. The local gauge field basis and the canonically conjugate variable basis are swapped efficiently using the quantum Fourier transform. We prove that the qubit cost to represent physical states and the gate count for real-time simulation scale polynomially with the lattice size, energy, time, accuracy, and Hamiltonian parameters in lattice units. The gate cost here for implementing the time evolution of the gauge field is reduced at least by a factor on the order of $10^8$ for modest lattice size and accuracy level compared with the previous work.

arXiv comment32 pages; v2: published version, added a comparison of gate costs with previous work

References in corpus (51)

• Quantum Algorithms for Quantum Field Theories
• Simulating Lattice Gauge Theories within Quantum Technologies
• The hadronic light-by-light scattering contribution to the muon anomalous magnetic moment from lattice QCD
• Quantum Simulations of Lattice Gauge Theories using Ultracold Atoms in Optical Lattices
• Calculation of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment
• Quantum Simulation for High Energy Physics
• Quantum Link Models: A Discrete Approach to Gauge Theories
• SU(2) non-Abelian gauge field theory in one dimension on digital quantum computers
• A Trailhead for Quantum Simulation of SU(3) Yang-Mills Lattice Gauge Theory in the Local Multiplet Basis
• Quantum Computing for High-Energy Physics: State of the Art and Challenges. Summary of the QC4HEP Working Group
• Standard Model Physics and the Digital Quantum Revolution: Thoughts about the Interface
• Digitization of Scalar Fields for Quantum Computing
• Loop, String, and Hadron Dynamics in SU(2) Hamiltonian Lattice Gauge Theories
• Quantum Simulating Nature's Fundamental Fields
• First lattice calculation of the QED corrections to leptonic decay rates
• Light-meson leptonic decay rates in lattice QCD+QED
• Is there a Landau Pole Problem in QED?
• Isospin splittings in the light baryon octet from lattice QCD and QED
• BQP-completeness of Scattering in Scalar Quantum Field Theory
• Determination of light quark masses from the electromagnetic splitting of pseudoscalar meson masses computed with two flavors of domain wall fermions
• Preparations for Quantum Simulations of Quantum Chromodynamics in 1+1 Dimensions: (I) Axial Gauge
• Approximate Quantum Fourier Transform with $O(n\log (n))$ T gates
• SU(2) lattice gauge theory on a quantum annealer
• Renormalization flow of QED
• Practical approximation of single-qubit unitaries by single-qubit quantum Clifford and T circuits
• Isospin splittings of meson and baryon masses from three-flavor lattice QCD + QED
• Quantum and classical spin network algorithms for $q$-deformed Kogut-Susskind gauge theories
• Stabilizing lattice gauge theories through simplified local pseudo generators
• Charged multi-hadron systems in lattice QCD+QED
• Lattice computation of the electromagnetic contributions to kaon and pion masses
• Loop-string-hadron formulation of an SU(3) gauge theory with dynamical quarks
• Classical and Quantum Computing of Shear Viscosity for $2+1D$ SU(2) Gauge Theory
• Simple Hamiltonian for Quantum Simulation of Strongly Coupled 2+1D SU(2) Lattice Gauge Theory on a Honeycomb Lattice
• From square plaquettes to triamond lattices for SU(2) gauge theory
• Eigenstate Thermalization in 2+1 dimensional SU(2) Lattice Gauge Theory
• Gauged Nambu-Jona Lasinio Studies of the Triviality of Quantum Electrodynamics
• Loop-string-hadron approach to SU(3) lattice Yang-Mills theory: I. Hilbert space of a trivalent vertex
• Toward QCD on Quantum Computer: Orbifold Lattice Approach
• Quasifragmentation functions in the massive Schwinger model
• Quantum Computing Universal Thermalization Dynamics in a (2+1)D Lattice Gauge Theory
• Real-time Dynamics of the Schwinger Model as an Open Quantum System with Neural Density Operators
• Electromagnetic contribution to $\Sigma$-$\Lambda$ mixing using lattice QCD+QED
• Quantum Computing for Energy Correlators
• Emergent Hydrodynamic Mode on SU(2) Plaquette Chains and Quantum Simulation
• Large-Scale $2+1$D $\mathrm{U}(1)$ Gauge Theory with Dynamical Matter in a Cold-Atom Quantum Simulator
• Improved Honeycomb and Hyperhoneycomb Lattice Hamiltonians for Quantum Simulations of Non-Abelian Gauge Theories
• Parton Distribution Functions in the Schwinger model from Tensor Network States
• Electromagnetic Splittings and Light Quark Masses
• Fault-tolerant simulation of Lattice Gauge Theories with gauge covariant codes
• Entanglement Properties of SU(2) Gauge Theory
• Spontaneous symmetry breaking in a $SO(3)$ non-Abelian lattice gauge theory in $2+1$D with quantum algorithms

Cited by in corpus (1)

• Eigenstate Thermalization in 1+1-Dimensional SU(2) Lattice Gauge Theory Coupled with Dynamical Fermions