Unbiasing fermionic quantum Monte Carlo algorithm assisted with quantum computer

Quantum Monte Carlo (QMC) method is a powerful tool to deal with interacting many-body systems. However, there exists notorious sign problems that may cause exponentially large variance. One approach to avoid sign problem is to impose constraints on the importance sampling at the expense of introducing bias into the results, e.g. the constrained path approximation in auxiliary field quantum Monte Carlo (AFQMC)[1]. In this talk, I will introduce a recent experiment that claims to succeed in removing the bias with the use of quantum computer [2]. In this experiment, they prepared trial wave functions for AFQMC via quantum circuits involving up to 16 qubits, which are usually intractable on classical computers, and calculated the wavefunction overlaps via the shadow tomography technique [3]. The overall quantum-classical hybrid strategy may serve as a promising approach to achieving quantum advantage in fermionic simulation.

[1] Zhang, S., Carlson, J. and Gubernatis, J. E., Phys. Rev. B 55, 7464 (1997).

[2] W. J. Huggins, B. A. O’Gorman, N. C. Rubin, D. R. Reichman, R. Babbush, and J. Lee, Nature 603, 416 (2022).

[3] H.-Y. Huang, R. Kueng, and J. Preskill, Nature Physics 16, 1050 (2020).