Correcting a noisy quantum computer using a quantum computer

TL;DR

This paper introduces a quantum-based decoding scheme that enables real-time error correction in quantum computers by training a quantum circuit to perform decoding, eliminating the need for classical decoding methods.

Contribution

The authors propose a quantum circuit-based decoding method that operates in real-time, applicable to general quantum codes, and matches the speed of quantum operations, advancing towards self-correcting quantum computers.

Findings

Numerical experiments with surface codes up to distance 7 show comparable performance to classical algorithms.

The decoding speed matches the quantum circuit execution speed, enabling real-time error correction.

The method demonstrates that classical decoding tasks can be performed entirely within quantum circuits.

Abstract

Quantum computers require error correction to achieve universal quantum computing. However, current decoding of quantum error-correcting codes relies on classical computation, which is slower than quantum operations in superconducting qubits. This discrepancy makes the practical implementation of real-time quantum error correction challenging. In this work, we propose a decoding scheme that leverages the operations of the quantum circuit itself. Given a noisy quantum circuit $A$, we train a decoding quantum circuit $B$ using syndrome measurements to identify the logical operators needed to correct errors in circuit $A$. The trained quantum circuit $B$ can be deployed on quantum devices, such as superconducting qubits, to perform real-time decoding and error correction. Our approach is applicable to general quantum codes with multiple logical qubits and operates efficiently under various noise conditions, and the decoding speed matches the speed of the quantum circuits being corrected. We have conducted numerical experiments using surface codes up to distance 7 under circuit-level noise, demonstrating performance on par with the classical minimum-weight perfect matching algorithm. Interestingly, our method reveals that the traditionally classical task of decoding error-correcting codes can be accomplished without classical devices or measurements. This insight paves the way for the development of self-correcting quantum computers.