Quantum error correction via purification using a single auxiliary

TL;DR

This paper introduces a novel quantum error correction method using a single auxiliary system and purification, which enhances error correction capabilities for various quantum codes and noise types.

Contribution

The proposed framework employs a single auxiliary-assisted purification process for quantum error correction, expanding correctable errors and improving performance under realistic noisy conditions.

Findings

Achieves unit fidelity in error correction

Expands correctable error classes, especially amplitude damping

Effective for multiple quantum codes and noise models

Abstract

We propose a single auxiliary-assisted purification-based framework for quantum error correction, capable of correcting errors that drive a system from its ground-state subspace into excited-state sectors. The protocol consists of a joint time evolution of the system-auxiliary duo under a specially engineered interaction Hamiltonian, followed by a single measurement of the auxiliary in its energy eigenbasis and a subsequent post-selection of one of the measurement outcomes. We show that the resulting purified state always achieves unit fidelity, while the probability of obtaining any energy of the auxiliary other than its ground state energy yields the success rate of the protocol. We demonstrate the power of this proposed method for several low-distance quantum codes, including the three-, four-, and five-qubit codes, and for the one-dimensional isotropic Heisenberg model, subjected to bit-flip, phase-flip, and amplitude-damping noises acting on all qubits. Notably, the protocol expands the class of correctable errors for a given code, particularly in the presence of amplitude-damping noise. We further analyze the impact of replacing the auxiliary qudit with a single auxiliary qubit, and the changes in the performance of the protocol under the realistic scenario where noise remains active during the correction cycle.