A polynomial-time classical algorithm for noisy quantum circuits

July 17, 2024 Β· Declared Dead Β· πŸ› arXiv.org

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Authors Thomas Schuster, Chao Yin, Xun Gao, Norman Y. Yao arXiv ID 2407.12768 Category quant-ph: Quantum Computing Cross-listed cs.CC, cs.IT, math-ph, physics.atom-ph Citations 67 Venue arXiv.org Last Checked 5 months ago
Abstract
We provide a polynomial-time classical algorithm for noisy quantum circuits. The algorithm computes the expectation value of any observable for any circuit, with a small average error over input states drawn from an ensemble (e.g. the computational basis). Our approach is based upon the intuition that noise exponentially damps non-local correlations relative to local correlations. This enables one to classically simulate a noisy quantum circuit by only keeping track of the dynamics of local quantum information. Our algorithm also enables sampling from the output distribution of a circuit in quasi-polynomial time, so long as the distribution anti-concentrates. A number of practical implications are discussed, including a fundamental limit on the efficacy of noise mitigation strategies: for constant noise rates, any quantum circuit for which error mitigation is efficient on most input states, is also classically simulable on most input states.
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