Noise-adapted recovery circuits for quantum error correction

TL;DR

This paper introduces noise-adapted quantum recovery circuits, including Petz map implementations, that improve resource efficiency and fidelity estimation for quantum error correction on noisy quantum devices.

Contribution

The authors develop three novel circuit constructions for the Petz recovery map, reducing resource requirements and enabling direct fidelity estimation in quantum error correction.

Findings

Improved resource efficiency over existing methods

Successful implementation of Petz recovery circuits for a 4-qubit code

Effective noise-adapted recovery demonstrated through simulations

Abstract

Implementing quantum error correction (QEC) protocols is a challenging task in today's era of noisy intermediate-scale quantum devices. We present quantum circuits for a universal, noise-adapted recovery map, often referred to as the Petz map, which is known to achieve close-to-optimal fidelity for arbitrary codes and noise channels. While two of our circuit constructions draw upon algebraic techniques such as isometric extension and block encoding, the third approach breaks down the recovery map into a sequence of two-outcome POVMs. In each of the three cases we improve upon the resource requirements that currently exist in the literature. Apart from Petz recovery circuits, we also present circuits that can directly estimate the fidelity between the encoded state and the recovered state. As a concrete example of our circuit constructions, we implement Petz recovery circuits corresponding to the $4$-qubit QEC code tailored to protect against amplitude-damping noise. The efficacy of our noise-adapted recovery circuits is then demonstrated through ideal and noisy simulations.