Virtual Distillation for Quantum Error Mitigation

Physical Review X, vol. 11

Abstract

Contemporary quantum computers have relatively high levels of noise, making it difficult to use them to perform useful calculations, even with a large number of qubits.Quantum error correction is expected to eventually enable fault-tolerant quantum computation at large scales, but until then, it will be necessary to use alternative strategies to mitigate the impact of errors.We propose a near-term friendly strategy to mitigate errors by entangling and measuring M copies of a noisy state ρ.This enables us to estimate expectation values with respect to a state with dramatically reduced error ρ M =Trðρ M Þ without explicitly preparing it, hence the name "virtual distillation."As M increases, this state approaches the closest pure state to ρ exponentially quickly.We analyze the effectiveness of virtual distillation and find that it is governed in many regimes by the behavior of this pure state (corresponding to the dominant eigenvector of ρ).We numerically demonstrate that virtual distillation is capable of suppressing errors by multiple orders of magnitude and explain how this effect is enhanced as the system size grows.Finally, we show that this technique can improve the convergence of randomized quantum algorithms, even in the absence of device noise.

Authors 9

1. William J. Huggins

   Google (United States) · University of California, Berkeley

   Affiliation as printed

   Berkeley Quantum Information and Computation Center, Challenge Institute for Quantum Computation, and Department of Chemistry, University of California, Berkeley, California 94720, USA

   Google Quantum AI, Venice, California 90291, USA

2. Sam McArdle

   Google (United States) · University of Oxford

   Affiliation as printed

   Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, United Kingdom

   Google Quantum AI, Venice, California 90291, USA

3. Thomas E. O’Brien Aachen Instituut-Lorentz

   Leiden University · Google (United States)

   Affiliation as printed

   Google Quantum AI, Venice, California 90291, USA

   Instituut-Lorentz, Universiteit Leiden, 2300 RA Leiden, Netherlands

4. Joonho Lee

   Columbia University

   Affiliation as printed

   Department of Chemistry, Columbia University, New York, New York 10027, USA

   Department of Chemistry, Columbia University, New York, New York 10027., USA

5. Nicholas C. Rubin

   Google (United States)

   Affiliation as printed

   Google Quantum AI, Venice, California 90291, USA

6. Sergio Boixo

   Google (United States)

   Affiliation as printed

   Google Quantum AI, Venice, California 90291, USA

7. K. Birgitta Whaley

   University of California, Berkeley

   Affiliation as printed

   Berkeley Quantum Information and Computation Center, Challenge Institute for Quantum Computation, and Department of Chemistry, University of California, Berkeley, California 94720, USA

8. Ryan Babbush

   Google (United States)

   Affiliation as printed

   Google Quantum AI, Venice, California 90291, USA

9. Jarrod R. McClean

   Google (United States)

   Affiliation as printed

   Google Quantum AI, Venice, California 90291, USA