Accelerated quantum Monte Carlo with mitigated error on noisy quantum computer

Abstract

Quantum Monte Carlo and quantum simulation are both important tools for understanding quantum many-body systems. As a classical algorithm, quantum Monte Carlo suffers from the sign problem, preventing its application to most fermion systems and real time dynamics. In this paper, we introduce a novel non-variational algorithm using quantum simulation as a subroutine to accelerate quantum Monte Carlo by easing the sign problem. The quantum subroutine can be implemented with shallow circuits and, by incorporating error mitigation, can reduce the Monte Carlo variance by several orders of magnitude even when the circuit noise is significant. As such, the proposed quantum algorithm is applicable to near-term noisy quantum hardware.

22 pages, 7 figures

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• Quantum Error Mitigation
• Unbiasing Fermionic Quantum Monte Carlo with a Quantum Computer
• Improved Hamiltonians for Quantum Simulations
• Quantum computing for chemistry and physics applications from a Monte Carlo perspective
• Error statistics and scalability of quantum error mitigation formulas
• Virtual quantum resource distillation
• Error-resilient Monte Carlo quantum simulation of imaginary time
• Gauge Theory Couplings on Anisotropic Lattices
• Quantum computing quantum Monte Carlo with hybrid tensor network for electronic structure calculations
• Fault-tolerant quantum algorithms for quantum molecular systems: A survey
• Quantum-assisted Monte Carlo algorithms for fermions
• Simple and high-precision Hamiltonian simulation by compensating Trotter error with linear combination of unitary operations
• Measurement-efficient quantum Krylov subspace diagonalisation
• Unified multivariate trace estimation and quantum error mitigation
• Exponentially reduced circuit depths in Lindbladian simulation
• TE-PAI: Exact Time Evolution by Sampling Random Circuits
• High-precision and low-depth quantum algorithm design for eigenstate problems
• Exponential distillation of dominant eigenproperties
• Resource-efficient Quantum Algorithms for Selected Hamiltonian Subspace Diagonalization