Fusion Blossom: Fast MWPM Decoders for QEC

TL;DR

This paper introduces Fusion Blossom, a fast and scalable MWPM decoder for quantum error correction that can handle millions of measurements per second with low latency, enabling real-time quantum computing.

Contribution

The paper presents Parity Blossom and Fusion Blossom, novel MWPM decoders with near-linear time complexity and parallelization, significantly improving decoding speed for quantum error correction.

Findings

Fusion Blossom decodes a million rounds per second at code distance 33.

Supports stream decoding with 0.7 ms latency at code distance 21.

Achieves near-linear time complexity proportional to the number of defect measurements.

Abstract

The Minimum-Weight Perfect Matching (MWPM) decoder is widely used in Quantum Error Correction (QEC) decoding. Despite its high accuracy, existing implementations of the MWPM decoder cannot catch up with quantum hardware, e.g., 1 million measurements per second for superconducting qubits. They suffer from a backlog of measurements that grows exponentially and as a result, cannot realize the power of quantum computation. We design and implement a fast MWPM decoder, called Parity Blossom, which reaches a time complexity almost proportional to the number of defect measurements. We further design and implement a parallel version of Parity Blossom called Fusion Blossom. Given a practical circuit-level noise of 0.1%, Fusion Blossom can decode a million measurement rounds per second up to a code distance of 33. Fusion Blossom also supports stream decoding mode that reaches a 0.7 ms decoding latency at code distance 21 regardless of the measurement rounds.