Unconditionally decoherence-free quantum error mitigation by density matrix vectorization

TL;DR

This paper introduces a novel quantum error mitigation method that encodes noisy density matrices into noiseless pure states without requiring noise model knowledge, enhancing the performance of NISQ devices in variational algorithms.

Contribution

The work presents a new density matrix vectorization approach for error mitigation that is noise-model independent and NISQ-friendly, with practical measurement and post-processing procedures.

Findings

Protocol effectively maps noisy states to pure states

Compatible with variational quantum algorithms

Numerical experiments confirm improved error mitigation

Abstract

Fighting against noise is crucial for NISQ devices to demonstrate practical quantum applications. In this work, we give a new paradigm of quantum error mitigation based on the vectorization of density matrices. Different from the ideas of existing quantum error mitigation methods that try to distill noiseless information from noisy quantum states, our proposal directly changes the way of encoding information and maps the density matrices of noisy quantum states to noiseless pure states, which is realized by a novel and NISQ-friendly measurement protocol and a classical post-processing procedure. Our protocol requires no knowledge of the noise model, no ability to tune the noise strength, and no ancilla qubits for complicated controlled unitaries. Under our encoding, NISQ devices are always preparing pure quantum states which are highly desired resources for variational quantum algorithms to have good performance in many tasks. We show how this protocol can be well-fitted into variational quantum algorithms. We give several concrete ansatz constructions that are suitable for our proposal and do theoretical analysis on the sampling complexity, the expressibility, and the trainability. We also give a discussion on how this protocol is influenced by large noise and how it can be well combined with other quantum error mitigation protocols. The effectiveness of our proposal is demonstrated by various numerical experiments.