Neural network decoder for topological color codes with circuit level noise

TL;DR

This paper demonstrates that a recurrent neural network decoder can significantly improve error correction in topological color codes under circuit-level noise, extending logical qubit lifetime beyond physical qubits in simulated superconducting quantum computers.

Contribution

It introduces a neural network-based decoder tailored for topological color codes that effectively incorporates flag qubit information to mitigate circuit-level noise effects.

Findings

Neural network decoder reduces logical error rate below physical qubit error rate.

The decoder achieves power law scaling of error rates with code distance.

Simulations show extended logical qubit lifetime in superconducting quantum computer models.

Abstract

A quantum computer needs the assistance of a classical algorithm to detect and identify errors that affect encoded quantum information. At this interface of classical and quantum computing the technique of machine learning has appeared as a way to tailor such an algorithm to the specific error processes of an experiment --- without the need for a priori knowledge of the error model. Here, we apply this technique to topological color codes. We demonstrate that a recurrent neural network with long short-term memory cells can be trained to reduce the error rate $\epsilon_{\rm L}$ of the encoded logical qubit to values much below the error rate $\epsilon_{\rm phys}$ of the physical qubits --- fitting the expected power law scaling $\epsilon_{\rm L} \propto \epsilon_{\rm phys}^{(d+1)/2}$, with $d$ the code distance. The neural network incorporates the information from "flag qubits" to avoid reduction in the effective code distance caused by the circuit. As a test, we apply the neural network decoder to a density-matrix based simulation of a superconducting quantum computer, demonstrating that the logical qubit has a longer life-time than the constituting physical qubits with near-term experimental parameters.