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Title: Matchgate Shadows for Fermionic Quantum Simulation
Abstract

“Classical shadows” are estimators of an unknown quantum state, constructed from suitably distributed random measurements on copies of that state (Huang et al. in Nat Phys 16:1050, 2020,https://doi.org/10.1038/s41567-020-0932-7). In this paper, we analyze classical shadows obtained using random matchgate circuits, which correspond to fermionic Gaussian unitaries. We prove that the first three moments of the Haar distribution over thecontinuousgroup of matchgate circuits are equal to those of thediscreteuniform distribution over only the matchgate circuits that are also Clifford unitaries; thus, the latter forms a “matchgate 3-design.” This implies that the classical shadows resulting from the two ensembles are functionally equivalent. We show how one can use these matchgate shadows to efficiently estimate inner products between an arbitrary quantum state and fermionic Gaussian states, as well as the expectation values of local fermionic operators and various other quantities, thus surpassing the capabilities of prior work. As a concrete application, this enables us to apply wavefunction constraints that control the fermion sign problem in the quantum-classical auxiliary-field quantum Monte Carlo algorithm (QC-AFQMC) (Huggins et al. in Nature 603:416, 2022,https://doi.org/10.1038/s41586-021-04351-z), without the exponential post-processing cost incurred by the original approach.

 
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NSF-PAR ID:
10471987
Author(s) / Creator(s):
; ; ;
Publisher / Repository:
Springer Science + Business Media
Date Published:
Journal Name:
Communications in Mathematical Physics
ISSN:
0010-3616
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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