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<p>Noise detrimentally affects quantum computations so that they not only become less accurate but also easier to simulate classically as systems scale up. We construct a classical simulation algorithm, <span>lowesa</span> (low weight efficient simulation algorithm), for estimating expectation values of noisy parameterised quantum circuits with a fixed observable. It combines previous results on spectral analysis of parameterised circuits with Pauli back-propagation and recent ideas for simulations of noisy random circuits. We show, under some conditions on the circuits and mild assumptions on noise, that <span>lowesa</span> gives an efficient, polynomial algorithm in the number of qubits (and depth), with approximation error that vanishes exponentially in the physical error rate and a controllable cutoff parameter. This is valid for any expectation value that may be efficiently evaluated on a quantum computer. We discuss the practical limitations of the method for circuit classes with correlated parameters and its scaling with decreasing error rates.</p>

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Classical simulations of noisy variational quantum circuits

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月22日

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  • Enrico Fontana,
  • Manuel S. Rudolph,
  • Ross Duncan,
  • Ivan Rungger,
  • Cristina Cîrstoiu

摘要

Noise detrimentally affects quantum computations so that they not only become less accurate but also easier to simulate classically as systems scale up. We construct a classical simulation algorithm, lowesa (low weight efficient simulation algorithm), for estimating expectation values of noisy parameterised quantum circuits with a fixed observable. It combines previous results on spectral analysis of parameterised circuits with Pauli back-propagation and recent ideas for simulations of noisy random circuits. We show, under some conditions on the circuits and mild assumptions on noise, that lowesa gives an efficient, polynomial algorithm in the number of qubits (and depth), with approximation error that vanishes exponentially in the physical error rate and a controllable cutoff parameter. This is valid for any expectation value that may be efficiently evaluated on a quantum computer. We discuss the practical limitations of the method for circuit classes with correlated parameters and its scaling with decreasing error rates.