Abstract
Simulating quantum circuits classically is an important area of research in quantum information, with applications in computational complexity and validation of quantum devices. One of the state-of-the-art simulators, that of Bravyi et al, utilizes a randomized sparsification technique to approximate the output state of a quantum circuit by a stabilizer sum with a reduced number of terms. In this paper, we describe an improved Monte Carlo algorithm for performing randomized sparsification. This algorithm reduces the runtime of computing the approximate state by the factorℓ/m, whereℓandmare respectively the total and non-Clifford gate counts. The main technique is a circuit recompilation routine based on manipulating exponentiated Pauli operators. The recompilation routine also facilitates numerical search for Clifford decompositions of products of non-Clifford gates, which can further reduce the runtime in certain cases by reducing the 1-norm of the vector of expansion,‖a‖1. It may additionally lead to a framework for optimizing circuit implementations over a gate-set, reducing the overhead for state-injection in fault-tolerant implementations. We provide a concise exposition of randomized sparsification, and describe how to use it to estimate circuit amplitudes in a way which can be generalized to a broader class of gates and states. This latter method can be used to obtain additive error estimates of circuit probabilities with a faster runtime than the full techniques of Bravyi et al. Such estimates are useful for validating near-term quantum devices provided that the target probability is not exponentially small.
Highlights
Digital simulation of quantum phenomena is a central problem in computational physics, with deep theoretical and practical significance
This is the case since the overhead associated with implementing non-Clifford gates fault-tolerantly is huge, for example accounting for nearly 90% of the number of physical
Randomized sparsification can be performed using a sum-over-Cliffords Monte Carlo method [5], which we briefly review before stating our contribution
Summary
Digital simulation of quantum phenomena is a central problem in computational physics, with deep theoretical and practical significance. Fault-tolerant implementations of quantum computing in the near-term are likely to contain a small number of non-Clifford gates. This variant removes the dependence on the total number of gates in the circuit It reduces the time cost of computing the CH description of |vi from O( n2) to O(mn2), where m is the non-Clifford gate count in U. This reduces the runtime of key subroutines in [5] by the factor /m, which can be significant for circuits in which the number of Clifford gates is very large compared to non-Clifford gates. The shorthand Mb:a, with b > a, denotes the product MbMb−1 . . . Ma
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