Micro Blossom: Accelerated Minimum-Weight Perfect Matching Decoding for Quantum Error Correction

2025-02-20

AI Summary

Minimum-Weight Perfect Matching (MWPM) decoding for surface-code quantum error correction fails to meet the microsecond-scale real-time requirements of superconducting qubits. Method: We propose the first hardware-accelerated, sub-microsecond, exact MWPM decoder, co-designing a heterogeneous soft–hard architecture that maps vertex- and edge-level parallel computation units onto an FPGA. Leveraging circuit-level noise modeling and graph-partitioning–optimized blossom algorithms, the design achieves O(d³) parallel processing. Results: On a d=13 surface code with physical error rate 0.1%, the FPGA prototype achieves a measured average latency of only 0.8 μs at 62 MHz—eight times faster than the best prior result in the literature—and marks the first demonstration breaking the 1-μs latency barrier, thereby significantly enhancing real-time surface-code error correction capability.

Technology Category

Machine Learning: Hardware-aware MLCognitive Modeling & Cognitive Systems: Neural Spike CodingPlanning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterizationEconomics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystemsGraph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Minimum-Weight Perfect Matching (MWPM) decoding is important to quantum error correction decoding because of its accuracy. However, many believe that it is difficult, if possible at all, to achieve the microsecond latency requirement posed by superconducting qubits. This work presents the first publicly known MWPM decoder, called Micro Blossom, that achieves sub-microsecond decoding latency. Micro Blossom employs a heterogeneous architecture that carefully partitions a state-of-the-art MWPM decoder between software and a programmable accelerator with parallel processing units, one of each vertex/edge of the decoding graph. On a surface code with code distance $d$ and a circuit-level noise model with physical error rate $p$, Micro Blossom's accelerator employs $O(d^3)$ parallel processing units to reduce the worst-case latency from $O(d^{12})$ to $O(d^9)$ and reduce the average latency from $O(p d^3+1)$ to $O(p^2 d^2+1)$ when $p ll 1$. We report a prototype implementation of Micro Blossom using FPGA. Measured at $d=13$ and $p=0.1%$, the prototype achieves an average decoding latency of $0.8 mu s$ at a moderate clock frequency of $62 MHz$. Micro Blossom is the first publicly known hardware-accelerated exact MWPM decoder, and the decoding latency of $0.8 mu s$ is 8 times shorter than the best latency of MWPM decoder implementations reported in the literature.

Problem

• Achieves sub-microsecond decoding latency
• Reduces worst-case latency significantly
• First hardware-accelerated exact MWPM decoder

Innovation

• Heterogeneous architecture accelerates MWPM decoding
• Parallel processing reduces latency significantly
• FPGA implementation achieves sub-microsecond decoding