Matchgate Shadows for Fermionic Quantum Simulation

          @misc{ pirsa_PIRSA:22110086,
            doi = {10.48660/22110086},
            url = {https://pirsa.org/22110086},
            author = {Wan, Kianna},
            keywords = {Condensed Matter},
            language = {en},
            title = {Matchgate Shadows for Fermionic Quantum Simulation},
            publisher = {Perimeter Institute},
            year = {2022},
            month = {nov},
            note = {PIRSA:22110086 see, \url{https://pirsa.org}}
          }
          

Abstract

In this talk, I'll describe new tomographic protocols for efficiently estimating various fermionic quantities, including both local observables (i.e., expectation values of local fermionic operators) and certain global properties (e.g., inner products between an unknown quantum state and arbitrary fermionic Gaussian states). Our protocols are based on classical shadows arising from random matchgate circuits. As a concrete application, they enable us to implement the recently introduced quantum-classical hybrid quantum Monte Carlo algorithm, without the exponential post-processing cost incurred by the original approach.