Classical simulation of noisy quantum circuits via locally entanglement-optimal unravelings

Abstract

Classical simulations of noisy quantum circuits are instrumental to our understanding of the behavior of real-world quantum systems and the identification of regimes where one expects quantum advantage. In this work, we present a highly parallelizable tensor-network-based classical algorithm -- equipped with rigorous accuracy guarantees -- for simulating $n$-qubit quantum circuits with arbitrary single-qubit noise. Our algorithm represents the state of a noisy quantum system by a particular ensemble of matrix product states from which we stochastically sample. Each pure state evolved under a single qubit noise process is then represented by the ensemble of states that achieves the minimal average entanglement (the entanglement of formation) between the noisy qubit and the remainder. This approach lets us use a more compact representation of the quantum state for a given accuracy requirement and noise level. For a given maximum bond dimension $χ$ and circuit, our algorithm comes with an upper bound on the simulation error, runs in $\mathrm{poly}(n,χ)$-time and improves upon related prior work (1) in scope: by extending analytic methods from the three commonly considered noise models to general single qubit noise (2) in performance: by deriving an exact, closed-form solution to the local entanglement minimization problem -- previously approached via variational heuristics -- thereby guaranteeing local optimality without numerical optimization overhead, and (3) in conceptual contribution: by showing that the fixed unraveling used in prior work becomes equivalent to our choice of unraveling in the special case of depolarizing, dephasing and amplitude damping noise acting on a maximally entangled state.