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.
Highlights
The simulation of quantum many-body systems is one of the main motivations for quantum computing [1]
We establish the framework of quantumcircuit Monte Carlo (QCMC) algorithm, in which quantum computing is a subroutine of Quantum Monte Carlo (QMC). We show that this algorithm has a quantum advantage in solving many-body problems, even on noisy quantum computers
We find that the error for our second-order LOR formula converges faster as O( t6) and the gate number is smaller compared with S22
Summary
The simulation of quantum many-body systems is one of the main motivations for quantum computing [1]. Based on the simulation of unitary time evolution, one can simulate open-system dynamics [35,36], solve equilibrium-state problems [37,38], and find the ground state for certain Hamiltonians [39–41] Implementation of these algorithms at a meaningful scale usually requires a fault-tolerant quantum computer [42,43], on which the logical error rate can be reduced to any level at a polynomial cost in quantum error correction [44]. The rate of increase of the variance in Green’s function Monte Carlo taking the computational basis is γc = 1 for a large class of qubit Hamiltonians Compared with this classical algorithm, QCMC reduces the variance by several orders of magnitude even on a quantum computer with significant noise, e.g., by a factor of approximately 4 × 104 when htott = 4 and = 0.1.
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