US 12,282,827 B2
Virtual distillation for quantum error mitigation
William Huggins, Oakland, CA (US); and Jarrod Ryan McClean, Marina Del Rey, CA (US)
Assigned to Google LLC, Mountain View, CA (US)
Appl. No. 18/036,252
Filed by Google LLC, Mountain View, CA (US)
PCT Filed Nov. 11, 2021, PCT No. PCT/US2021/058958
§ 371(c)(1), (2) Date May 10, 2023,
PCT Pub. No. WO2022/103945, PCT Pub. Date May 19, 2022.
Claims priority of provisional application 63/112,593, filed on Nov. 11, 2020.
Prior Publication US 2024/0013087 A1, Jan. 11, 2024
Int. Cl. G06N 10/70 (2022.01); G06N 10/20 (2022.01)
CPC G06N 10/70 (2022.01) [G06N 10/20 (2022.01)] 18 Claims
OG exemplary drawing
 
1. A method for determining an error-mitigated expectation value of a target observable with respect to a noisy quantum state, the method performed by a system comprising a classical processor and a quantum computer, the method comprising:
obtaining, by the quantum computer, multiple copies of the noisy quantum state, wherein the noisy quantum state comprises stochastic errors resulting from noise on the quantum computer;
performing, by the quantum computer, measurements on tensor products of M copies of the noisy quantum state to compute an expectation value of the target observable with respect to an entangled quantum state, wherein the entangled quantum state is given by ρM/Tr(ρM) where ρ represents the noisy quantum state, M≥1, and eigenvalues corresponding to non-dominant eigenvectors of the noisy quantum state in the spectral decomposition of the entangled quantum state are suppressed exponentially in M;
performing, by the quantum computer, measurements on tensor products of M copies of the noisy quantum state to compute an expectation value of an identity operator with respect to the entangled quantum state; and
dividing, by the classical processor, the computed expectation value of the target observable with respect to the entangled quantum state by the expectation value of the identity operator with respect to the entangled quantum state to determine the error-mitigated expectation value of the target observable with respect to the noisy quantum state, wherein the error-mitigated expectation value of the target observable with respect to the noisy quantum state comprises a reconstructed expectation value of the target observable with respect to a purified version of the noisy quantum state and approximates an expectation value of the target observable computed by the quantum computer in an absence of the stochastic errors and noise on the quantum computer.