Quantum-assisted Monte Carlo algorithms for fermions

Abstract

Quantum computing is a promising way to systematically solve the longstanding computational problem, the ground state of a many-body fermion system. Many efforts have been made to realise certain forms of quantum advantage in this problem, for instance, the development of variational quantum algorithms. A recent work by Huggins et al. reports a novel candidate, i.e. a quantum-classical hybrid Monte Carlo algorithm with a reduced bias in comparison to its fully-classical counterpart. In this paper, we propose a family of scalable quantum-assisted Monte Carlo algorithms where the quantum computer is used at its minimal cost and still can reduce the bias. By incorporating a Bayesian inference approach, we can achieve this quantum-facilitated bias reduction with a much smaller quantum-computing cost than taking empirical mean in amplitude estimation. Besides, we show that the hybrid Monte Carlo framework is a general way to suppress errors in the ground state obtained from classical algorithms. Our work provides a Monte Carlo toolkit for achieving quantum-enhanced calculation of fermion systems on near-term quantum devices.

References in corpus (18)

• Variational Quantum Algorithms
• Noisy intermediate-scale quantum (NISQ) algorithms
• Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals
• Unbiasing Fermionic Quantum Monte Carlo with a Quantum Computer
• Variational quantum Monte Carlo simulations with tensor-network states
• Avoiding barren plateaus using classical shadows
• Quantum Krylov subspace algorithms for ground and excited state energy estimation
• Error mitigation via verified phase estimation
• A theory of quantum subspace diagonalization
• Efficient Tensor Network ansatz for high-dimensional quantum many-body problems
• Quantum Error Mitigation using Symmetry Expansion
• Condensed Matter Physics in Time Crystals
• Accelerated quantum Monte Carlo with mitigated error on noisy quantum computer
• Symmetry projected Jastrow mean field wavefunction in variational Monte Carlo
• Exponential challenges in unbiasing quantum Monte Carlo algorithms with quantum computers
• Fixed and partial-node approximations in Slater determinant space for molecules
• Improved Hardness Results for the Guided Local Hamiltonian Problem
• Response to "Exponential challenges in unbiasing quantum Monte Carlo algorithms with quantum computers"

Cited by in corpus (8)

• Quantum computing for chemistry and physics applications from a Monte Carlo perspective
• Perturbative quantum simulation
• Quantum computing quantum Monte Carlo with hybrid tensor network for electronic structure calculations
• Evaluating a quantum-classical quantum Monte Carlo algorithm with Matchgate shadows
• Maximising Quantum-Computing Expressive Power through Randomised Circuits
• Quantum computing quantum Monte Carlo algorithm
• A quantum computing approach to fixed-node Monte Carlo using classical shadows
• Exponential distillation of dominant eigenproperties