Facilitating Practical Fault-tolerant Quantum Computing Based on Color Codes

TL;DR

This paper advances fault-tolerant quantum computing with color codes by improving decoding methods, achieving higher thresholds, and proposing a more efficient state injection protocol, bringing practical quantum computing closer to reality.

Contribution

It introduces error-rate-weighted decoding graphs, investigates circuit-level decoding for lattice surgery, and proposes a novel state injection protocol with significantly reduced error rates.

Findings

Threshold of 0.47% for 6,6,6 color code under circuit-level noise

Efficient decoding algorithm for color code lattice surgery

State injection protocol reduces error rate by two orders of magnitude

Abstract

Color code is a promising topological code for fault-tolerant quantum computing. Insufficient research on the color code has delayed its practical application. In this work, we address several key issues to facilitate practical fault-tolerant quantum computing based on color codes. First, by introducing decoding graphs with error-rate-related weights, we obtained the threshold of $0.47\%$ of the 6,6,6 triangular color code under the standard circuit-level noise model, narrowing the gap to that of the surface code. Second, our work firstly investigates the circuit-level decoding of color code lattice surgery, and gives an efficient decoding algorithm, which is crucial for performing logical operations in a quantum computer with two-dimensional architectures. Lastly, a new state injection protocol of the triangular color code is proposed, reducing the output magic state error rate in one round of 15 to 1 distillation by two orders of magnitude compared to a previous rough protocol. We have also proven that our protocol offers the lowest logical error rates for state injection among all possible CSS codes.