Quantum Algorithms for Simulating the Lattice Schwinger Model

Abstract

The Schwinger model (quantum electrodynamics in 1+1 dimensions) is a testbed for the study of quantum gauge field theories. We give scalable, explicit digital quantum algorithms to simulate the lattice Schwinger model in both NISQ and fault-tolerant settings. In particular, we perform a tight analysis of low-order Trotter formula simulations of the Schwinger model, using recently derived commutator bounds, and give upper bounds on the resources needed for simulations in both scenarios. In lattice units, we find a Schwinger model on $N/2$ physical sites with coupling constant $x^{-1/2}$ and electric field cutoff $x^{-1/2}\Lambda$ can be simulated on a quantum computer for time $2xT$ using a number of $T$-gates or CNOTs in $\tilde{O}(N^{3/2}{T}^{3/2}\sqrt{x}\Lambda )$ for fixed operator error. This scaling with the truncation $\Lambda$ is better than that expected from algorithms such as qubitization or QDRIFT. Furthermore, we give scalable measurement schemes and algorithms to estimate observables which we cost in both the NISQ and fault-tolerant settings by assuming a simple target observable---the mean pair density. Finally, we bound the root-mean-square error in estimating this observable via simulation as a function of the diamond distance between the ideal and actual CNOT channels. This work provides a rigorous analysis of simulating the Schwinger model, while also providing benchmarks against which subsequent simulation algorithms can be tested.

References in corpus (63)

• Elementary gates for quantum computation
• Quantum Amplitude Amplification and Estimation
• Hamiltonian Simulation by Qubitization
• Real-time dynamics of lattice gauge theories with a few-qubit quantum computer
• Towards Quantum Chemistry on a Quantum Computer
• Simulating Hamiltonian dynamics with a truncated Taylor series
• Elucidating Reaction Mechanisms on Quantum Computers
• Efficient quantum algorithms for simulating sparse Hamiltonians
• Toward the first quantum simulation with quantum speedup
• Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics
• Quantum Algorithms for Quantum Field Theories
• Simulating Lattice Gauge Theories within Quantum Technologies
• Restrictions on Transversal Encoded Quantum Gate Sets
• Quantum-Classical Computation of Schwinger Model Dynamics using Quantum Computers
• Quantum Simulation of Electronic Structure with Linear Depth and Connectivity
• Efficient Simulation of Quantum Systems by Quantum Computers
• Ultracold Quantum Gases and Lattice Systems: Quantum Simulation of Lattice Gauge Theories
• Floquet approach to ${\mathbb{Z}}_2$ lattice gauge theories with ultracold atoms in optical lattices
• A random compiler for fast Hamiltonian simulation
• Magic state distillation with low overhead
• Gate count estimates for performing quantum chemistry on small quantum computers
• Atomic Quantum Simulation of U(N) and SU(N) Non-Abelian Lattice Gauge Theories
• Solving strongly correlated electron models on a quantum computer
• Halving the cost of quantum addition
• A cold-atom quantum simulator for SU(2) Yang-Mills lattice gauge theory
• SU(2) non-Abelian gauge field theory in one dimension on digital quantum computers
• Light Nuclei and Hypernuclei from Quantum Chromodynamics in the Limit of SU(3) Flavor Symmetry
• Simulations of non-Abelian gauge theories with optical lattices
• Fixed-point quantum search with an optimal number of queries
• Simulating lattice gauge theories on a quantum computer
• Novel constructions for the fault-tolerant Toffoli gate
• Chemical Basis of Trotter-Suzuki Errors in Quantum Chemistry Simulation
• Efficient Bayesian Phase Estimation
• Tensor networks for Lattice Gauge Theories and Atomic Quantum Simulation
• U(1) Wilson lattice gauge theories in digital quantum simulators
• Digitization of Scalar Fields for Quantum Computing
• Higher Order Decompositions of Ordered Operator Exponentials
• General Methods for Digital Quantum Simulation of Gauge Theories
• Efficient synthesis of universal Repeat-Until-Success circuits
• Loop, String, and Hadron Dynamics in SU(2) Hamiltonian Lattice Gauge Theories
• Towards analog quantum simulations of lattice gauge theories with trapped ions
• Gluon Field Digitization for Quantum Computers
• Helium nuclei, deuteron and dineutron in 2+1 flavor lattice QCD
• Towards Quantum Simulating QCD
• Electron-Phonon Systems on a Universal Quantum Computer
• Digital quantum simulation of ${\mathbb{Z}}_2$ lattice gauge theories with dynamical fermionic matter
• Non-Abelian $SU(2)$ Lattice Gauge Theories in Superconducting Circuits
• Simulating quantum mechanics on a quantum computer
• Time-dependent Hamiltonian simulation with $L^1$-norm scaling
• Ground-State Properties of ${}^4$He and ${}^{16}$O Extrapolated from Lattice QCD with Pionless EFT
• Hyperon-Nucleon Interactions and the Composition of Dense Nuclear Matter from Quantum Chromodynamics
• Proton-proton fusion and tritium $\beta$-decay from lattice quantum chromodynamics
• Ab initio calculation of the $np\to d\gamma$ radiative capture process
• Simulating sparse Hamiltonians with star decompositions
• Helium Nuclei in Quenched Lattice QCD
• Bounding the costs of quantum simulation of many-body physics in real space
• Systematics of the HAL QCD Potential at Low Energies in Lattice QCD
• Lieb-Robinson bounds and the simulation of time evolution of local observables in lattice systems
• Spectra and Scattering of Light Lattice Nuclei from Effective Field Theory
• ${\mathbb{Z}}_N$ gauge theories coupled to topological fermions: QED${}_2$ with a quantum-mechanical $\theta$ angle
• Accelerating lattice quantum field theory calculations via interpolator optimization using NISQ-era quantum computing
• A Trotter-Suzuki approximation for Lie groups with applications to Hamiltonian simulation
• Medium-heavy nuclei from nucleon-nucleon interactions in lattice QCD

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