Towards practical classical processing for the surface code

TL;DR

This paper presents efficient classical processing algorithms for the surface code in quantum error correction, achieving optimal time complexity and parallelization with minimal resources, enabling practical fault-tolerant quantum computing.

Contribution

It introduces algorithms that perform surface code error correction in O(n^2) time and O(1) parallel time, using constant resources, improving practicality.

Findings

Classical processing for surface code can be optimized to O(n^2) time.

Parallel processing achieves O(1) time per round with constant resources.

Algorithms are optimal in complexity.

Abstract

The surface code is unarguably the leading quantum error correction code for 2-D nearest neighbor architectures, featuring a high threshold error rate of approximately 1%, low overhead implementations of the entire Clifford group, and flexible, arbitrarily long-range logical gates. These highly desirable features come at the cost of significant classical processing complexity. We show how to perform the processing associated with an nxn lattice of qubits, each being manipulated in a realistic, fault-tolerant manner, in O(n^2) average time per round of error correction. We also describe how to parallelize the algorithm to achieve O(1) average processing per round, using only constant computing resources per unit area and local communication. Both of these complexities are optimal.