Machine learning logical gates for quantum error correction

TL;DR

This paper introduces an automated variational circuit-based method to discover and implement logical gates for quantum error correction codes, facilitating automatic gate discovery on near-term quantum devices.

Contribution

It presents a novel automated procedure using variational circuits to learn logical gates for quantum error correction, applicable to both known and newly discovered codes.

Findings

Successfully finds most known logical gates for tested codes.

Discovers new logical gates for specific quantum codes.

Demonstrates feasibility on small quantum codes via simulation.

Abstract

Quantum error correcting codes protect quantum computation from errors caused by decoherence and other noise. Here we study the problem of designing logical operations for quantum error correcting codes. We present an automated procedure which generates logical operations given known encoding and correcting procedures. Our technique is to use variational circuits for learning both the logical gates and the physical operations implementing them. This procedure can be implemented on near-term quantum computers via quantum process tomography. It enables automatic discovery of logical gates from analytically designed error correcting codes and can be extended to error correcting codes found by numerical optimizations. We test the procedure by simulation on classical computers on small quantum codes of four qubits to fifteen qubits and show that it finds most logical gates known in the current literature. Additionally, it generates logical gates not found in the current literature for the [[5,1,2]] code, the [[6,3,2]] code, and the [[8,3,2]] code.