Source-linked AI summary
Towards practical classical processing for the surface code
Austin G. Fowler, Adam C. Whiteside, Lloyd C. L. Hollenberg
TL;DR
The paper addresses the classical processing complexity of fault-tolerant surface-code error correction. It introduces a minimum-weight perfect-matching approach with local processing, achieving O(n^2) average time and O(1) average time when parallelized.
Problem
Fault-tolerant surface-code processing requires complex classical computation on a 2-D nearest-neighbor architecture.
Method
The paper uses minimum weight perfect matching with graph sparsification and local information for continuous fault-tolerant surface-code processing.
Results
O(n^2) average processing time is achieved for an n × n lattice, with O(1) average time on an infinite lattice using constant resources per unit area and local communication.
Takeaways & Limitations
The algorithm supports complexity-optimal classical processing of fault-tolerant surface-code operation and can simulate millions of qubits.
Takeaways & Limitations
Near the threshold, memory limitations prevented gathering statistics at higher code distances, while large blossoms dominate memory cost.
Abstract
from arXiv · showhide
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.