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.

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• Quantum computing for chemistry and physics applications from a Monte Carlo perspective
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• 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