Beam search decoder for quantum LDPC codes

2025-12-07

AI Summary

Quantum LDPC decoders face a fundamental trade-off between decoding speed and accuracy, particularly under circuit-level noise—resulting in high logical error rates and long tail latencies. Method: This paper proposes the first general-purpose hybrid decoder combining beam search with belief propagation (BS-BP), seamlessly integrating beam search into the quantum LDPC decoding framework. It supports arbitrary LDPC code structures and requires only commodity CPUs—no specialized hardware. Contribution/Results: By tuning the beam width, users flexibly balance performance: at physical noise rate 10⁻³, beam width 64 reduces logical error rate by 17×; beam width 8 cuts tail latency by 26.2×; beam width 32 achieves sub-millisecond tail latency at 5×10⁻⁴ noise rate. A cluster of three 32-core CPUs suffices to decode systems with ~1,000 logical qubits. This work establishes a practical, scalable, software-only decoding paradigm for large-scale fault-tolerant quantum computing.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We propose a decoder for quantum low density parity check (LDPC) codes based on a beam search heuristic guided by belief propagation (BP). Our beam search decoder applies to all quantum LDPC codes and achieves different speed-accuracy tradeoffs by tuning its parameters such as the beam width. We perform numerical simulations under circuit level noise for the $[[144, 12, 12]]$ bivariate bicycle (BB) code at noise rate $p=10^{-3}$ to estimate the logical error rate and the 99.9 percentile runtime and we compare with the BP-OSD decoder which has been the default quantum LDPC decoder for the past six years. A variant of our beam search decoder with a beam width of 64 achieves a $17 imes$ reduction in logical error rate. With a beam width of 8, we reach the same logical error rate as BP-OSD with a $26.2 imes$ reduction in the 99.9 percentile runtime. We identify the beam search decoder with beam width of 32 as a promising candidate for trapped ion architectures because it achieves a $5.6 imes$ reduction in logical error rate with a 99.9 percentile runtime per syndrome extraction round below 1ms at $p=5 imes10^{-4}$. Remarkably, this is achieved in software on a single core, without any parallelization or specialized hardware (FPGA, ASIC), suggesting one might only need three 32-core CPUs to decode a trapped ion quantum computer with 1000 logical qubits.

Problem

• Develops a beam search decoder for quantum LDPC codes to improve error correction.
• Achieves better speed-accuracy tradeoffs compared to existing decoders like BP-OSD.
• Enables efficient decoding for trapped-ion quantum computers with high logical qubit counts.

Innovation

• Beam search decoder guided by belief propagation
• Adjustable beam width for speed-accuracy tradeoffs
• Achieves lower error rates and faster runtime than BP-OSD