Efficient information recovery from Pauli noise via classical shadow
Yifei Chen Zhan Yu Chenghong Zhu Xin Wang
The rapid advancement of quantum computing has led to an extensive demand for
effective techniques to extract classical information from quantum systems,
particularly in fields like quantum machine learning and quantum chemistry.
However, quantum systems are inherently susceptible to noises, which adversely
corrupt the information encoded in quantum systems. In this work, we introduce
an efficient algorithm that can recover information from quantum states under
Pauli noise. The core idea is to learn the necessary information of the unknown
Pauli channel by post-processing the classical shadows of the channel. For a
local and bounded-degree observable, only partial knowledge of the channel is
required rather than its complete classical description to recover the ideal
information, resulting in a polynomial-time algorithm. This contrasts with
conventional methods such as probabilistic error cancellation, which requires
the full information of the channel and exhibits exponential scaling with the
number of qubits. We also prove that this scalable method is optimal on the
sample complexity and generalise the algorithm to the weight contracting
channel. Furthermore, we demonstrate the validity of the algorithm on the 1D
anisotropic Heisenberg-type model via numerical simulations. As a notable
application, our method can be severed as a sample-efficient error mitigation
scheme for Clifford circuits.