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Stochastic Error Cancellation in Analog Quantum Simulation

Authors Yiyi Cai , Yu Tong , John Preskill

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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Ordinary differential equations
  • Hardware → Quantum computation
  • Mathematics of computing → Probability and statistics
Keywords
  • Analog quantum simulation
  • error cancellation
  • concentration of measure

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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.

Cite As Get BibTex

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) https://doi.org/10.4230/LIPIcs.TQC.2024.2

Author Details

Yiyi Cai
  • Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA, USA
  • Department of Electrical Engineering, California Institute of Technology, Pasadena, CA, USA
Yu Tong
  • Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA, USA
John Preskill
  • Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA, USA
  • AWS Center for Quantum Computing, Pasadena, CA, USA

Funding

  • Cai, Yiyi: Y.C. acknowledges funding from Arthur R. Adams Summer Undergraduate Research Fellowship.
  • Tong, Yu: Y.T. acknowledges funding from U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research (DE-SC0020290), and from U.S. Department of Energy, Office of Science, Basic Energy Sciences, under Award Number DE-SC0019374.
  • Preskill, John: J.P. acknowledges support from the U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research (DE-NA0003525, DE-SC0020290), the U.S. Department of Energy, Office of Science, National Quantum Information Science Research Centers, Quantum Systems Accelerator, and the National Science Foundation (PHY-1733907).The Institute for Quantum Information and Matter is an NSF Physics Frontiers Center.

Acknowledgements

We thank Minh Tran, Matthias Caro, Mehdi Soleimanifar, Hsin-Yuan Huang, Andreas Elben, ChunJun Cao, and Christopher Pattison for helpful discussions. We thank Manuel Endres for pointing us to Ref. [Shaw et al., 2023].

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