Speaker
Description
Quantum error mitigation is a collection of techniques for reducing the effect of noise when estimating expectation values on noisy quantum computers. In particular, fully virtual purification (FVP) suppresses errors by preparing multiple copies of a noisy quantum state and cyclically permuting them, thereby amplifying the contribution of the dominant eigenstate that is least affected by noise. Although FVP achieves exponential error suppression with respect to the number of copies, it requires nonlocal operations across different copies as well as a large number of measurements, resulting in a substantial computational cost. To reduce this overhead, localized virtual purification (LVP) has recently been proposed, in which the cyclic permutation is applied only in the vicinity of the observable being measured [1]. While the expectation values obtained from FVP and LVP generally differ, it has been shown that, for systems with a unique gapped ground state, this difference decays exponentially with the distance (d(A,C)) between the support (A) of the observable and the region (C) where the cyclic permutation is not applied [1]. This result is based on a general argument using the Lieb–Robinson bound and therefore cannot be directly extended to gapless quantum critical systems.
In this work, we investigate the error of LVP relative to FVP in one-dimensional quantum many-body systems using conformal field theory (CFT). By extending the replica method originally developed for the analysis of entanglement entropy [2], we show that, for critical ground states, the error in the expectation values of subsystem Hamiltonians and two-point correlation functions exhibits a power-law decay as a function of the distance (d(A,C)). Furthermore, we demonstrate that, for finite-temperature Gibbs states of critical systems, the error decays exponentially with distance.
References
[1] H. Hakoshima, S. Endo, K. Yamamoto, Y. Matsuzaki, and N. Yoshioka, Phys. Rev. Lett. 133, 080601 (2024).
[2] P. Calabrese and J. Cardy, J. Stat. Mech. P06002 (2004).