In this section
@article{Ma:2024:10.1103/PhysRevA.109.012431,
author = {Ma, Y and Kim, MS},
doi = {10.1103/PhysRevA.109.012431},
journal = {Physical Review A: Atomic, Molecular and Optical Physics},
title = {Limitations of probabilistic error cancellation for open dynamics beyond sampling overhead},
url = {http://dx.doi.org/10.1103/PhysRevA.109.012431},
volume = {109},
year = {2024}
}
TY - JOUR
AB - Quantum simulation of dynamics is an important goal in the noisy intermediate-scale quantum era, within which quantum error mitigation may be a viable path towards modifying or eliminating the effects of noise. Most studies on quantum error mitigation have focused on the resource cost due to its exponential scaling in the circuit depth. Methods such as probabilistic error cancellation rely on discretizing the evolution into finite time steps and applying the mitigation layer after each time step, modifying only the noise part without any Hamiltonian dependence. This may lead to Trotter-like errors in the simulation results even if the error mitigation is implemented ideally, which means that the number of samples is taken as infinite. Here we analyze the aforementioned errors which have been largely neglected before. We show that they are determined by the commutating relations between the superoperators of the unitary part, the device noise part, and the noise part of the open dynamics to be simulated. We include both digital quantum simulation and analog quantum simulation setups and consider defining the ideal error mitigation map both by exactly inverting the noise channel and by approximating it to first order in the time step. We use single-qubit toy models to numerically demonstrate our findings. Our results illustrate fundamental limitations of applying probabilistic error cancellation in a stepwise manner to continuous dynamics, thus motivating the investigations of truly time-continuous error cancellation methods.
AU - Ma,Y
AU - Kim,MS
DO - 10.1103/PhysRevA.109.012431
PY - 2024///
SN - 1050-2947
TI - Limitations of probabilistic error cancellation for open dynamics beyond sampling overhead
T2 - Physical Review A: Atomic, Molecular and Optical Physics
UR - http://dx.doi.org/10.1103/PhysRevA.109.012431
UR - https://journals.aps.org/pra/abstract/10.1103/PhysRevA.109.012431
UR - http://hdl.handle.net/10044/1/113547
VL - 109
ER -