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DOI: 10.4230/LIPIcs.TQC.2024.2

Stochastic Error Cancellation in Analog Quantum Simulation

Authors: Yiyi Cai, Yu Tong, and John Preskill

Published in: LIPIcs, Volume 310, 19th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2024)

Abstract

Analog quantum simulation is a promising path towards solving classically intractable problems in many-body physics on near-term quantum devices. However, the presence of noise limits the size of the system and the length of time that can be simulated. In our work, we consider an error model in which the actual Hamiltonian of the simulator differs from the target Hamiltonian we want to simulate by small local perturbations, which are assumed to be random and unbiased. We analyze the error accumulated in observables in this setting and show that, due to stochastic error cancellation, with high probability the error scales as the square root of the number of qubits instead of linearly. We explore the concentration phenomenon of this error as well as its implications for local observables in the thermodynamic limit. Moreover, we show that stochastic error cancellation also manifests in the fidelity between the target state at the end of time-evolution and the actual state we obtain in the presence of noise. This indicates that, to reach a certain fidelity, more noise can be tolerated than implied by the worst-case bound if the noise comes from many statistically independent sources.

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Yiyi Cai, Yu Tong, and John Preskill. Stochastic Error Cancellation in Analog Quantum Simulation. In 19th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 310, pp. 2:1-2:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{cai_et_al:LIPIcs.TQC.2024.2,
  author =	{Cai, Yiyi and Tong, Yu and Preskill, John},
  title =	{{Stochastic Error Cancellation in Analog Quantum Simulation}},
  booktitle =	{19th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2024)},
  pages =	{2:1--2:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-328-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{310},
  editor =	{Magniez, Fr\'{e}d\'{e}ric and Grilo, Alex Bredariol},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2024.2},
  URN =		{urn:nbn:de:0030-drops-206720},
  doi =		{10.4230/LIPIcs.TQC.2024.2},
  annote =	{Keywords: Analog quantum simulation, error cancellation, concentration of measure}
}

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Stochastic Error Cancellation in Analog Quantum Simulation

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