Dilution of error in digital Hamiltonian simulation

Abstract

We provide analytic, numerical and experimental evidence that the amount of noise in digital quantum simulation of local observables can be independent of system size in a number of situations. We provide a microscopic explanation of this dilution of errors based on the "relevant string length" of operators, which is the length of Pauli strings in the operator at time $s$ that belong to the exponentially small subspace of strings that can give a non-zero expectation value at time $t$. We show that this explanation can predict when dilution of errors occurs and when it does not. We propose an error mitigation method whose efficiency relies on this mechanism. Our findings imply that digital quantum simulation with noisy devices is in appropriate cases scalable in the sense that gate errors do not need to be reduced linearly to simulate larger systems.

arXiv comment17 pages + appendix

References in corpus (32)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
• Error mitigation for short-depth quantum circuits
• Hamiltonian Simulation by Qubitization
• Optimal Hamiltonian Simulation by Quantum Signal Processing
• Simulating Hamiltonian dynamics with a truncated Taylor series
• Elucidating Reaction Mechanisms on Quantum Computers
• Operator Spreading in Random Unitary Circuits
• Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
• Demonstration of the trapped-ion quantum-CCD computer architecture
• Thermalization and prethermalization in isolated quantum systems: a theoretical overview
• Operator spreading and the emergence of dissipative hydrodynamics under unitary evolution with conservation laws
• Robustness of adiabatic quantum computation
• A Theory of Trotter Error
• Floquet-Magnus Theory and Generic Transient Dynamics in Periodically Driven Many-Body Quantum Systems
• A Universal Operator Growth Hypothesis
• Quantum Quench in the Transverse Field Ising chain I: Time evolution of order parameter correlators
• Solution of a minimal model for many-body quantum chaos
• Low Depth Quantum Simulation of Electronic Structure
• Quantum Computing for High-Energy Physics: State of the Art and Challenges. Summary of the QC4HEP Working Group
• Quantum localization bounds Trotter errors in digital quantum simulation
• Noise resistance of adiabatic quantum computation using random matrix theory
• Towards near-term quantum simulation of materials
• Hamiltonian simulation with random inputs
• Effective quantum volume, fidelity and computational cost of noisy quantum processing experiments
• Destructive Error Interference in Product-Formula Lattice Simulation
• Self-healing of Trotter error in digital adiabatic state preparation
• Decoherence scaling transition in the dynamics of quantum information scrambling
• Classical algorithms for many-body quantum systems at finite energies
• Continuous Hamiltonian dynamics on digital quantum computers without discretization error
• Exploiting anticommutation in Hamiltonian simulation
• Operator Growth in Open Quantum Systems

Cited by in corpus (5)

• Experimental Demonstration of Break-Even for the Compact Fermionic Encoding
• AppQSim: Application-oriented benchmarks for Hamiltonian simulation on a quantum computer
• Lindblad engineering for quantum Gibbs state preparation under the eigenstate thermalization hypothesis
• Simulating sparse SYK model with a randomized algorithm on a trapped-ion quantum computer
• Robustness of near-thermal dynamics on digital quantum computers