Reductions from weak to strong simulation of quantum systems

          @misc{ scivideos_PIRSA:23100109,
            doi = {10.48660/23100109},
            url = {https://pirsa.org/23100109},
            author = {Bravyi, Sergey},
            keywords = {Quantum Information},
            language = {en},
            title = {Reductions from weak to strong simulation of quantum systems},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2023},
            month = {oct},
            note = {PIRSA:23100109 see, \url{https://scivideos.org/index.php/pirsa/23100109}}
          }
          

Abstract

Classical simulation techniques are widely used in quantum computation and condensed matter physics. In this talk I will describe algorithms for classically simulating measurement of an n-qubit quantum state in the standard basis, that is, sampling a bit string from the probability distribution determined by the Born rule. Our algorithms reduce the sampling task (known as weak simulation) to computing poly(n) amplitudes of n-qubit states (strong simulation). Two classes of quantum states are considered: output states of polynomial-size quantum circuits and ground states of local Hamiltonians with an inverse polynomial energy gap. We show that our algorithm can significantly accelerate quantum circuit simulations based on tensor network contraction and low-rank stabilizer decompositions. To sample ground state probability distributions we employ the fixed-node Hamiltonian construction, previously used in Quantum Monte Carlo simulations to address the fermionic sign problem. We implement the proposed sampling algorithm numerically and use it to sample from the ground state of Haldane-Shastry Hamiltonian with up to 56 qubits. 

Joint work with Giuseppe Carleo, David Gosset, and Yinchen Liu

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Zoom link https://pitp.zoom.us/j/93297869296?pwd=TVpRdVJmU3lWZjVQM3NNKzBucVVRUT09