Date of Award

5-19-2025

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Computer Science

First Advisor

Lin Zhong

Abstract

Quantum error correction (QEC) enables scalable quantum computation by detecting and correcting physical errors. However, decoding remains a key bottleneck—particularly for quantum low-density parity-check (qLDPC) codes, whose hypergraph structures demand complex reasoning. Most existing decoders are either too slow for real-time use or lack formal guarantees, and often struggle to generalize across diverse quantum hardware.

This thesis introduces the Minimum-Weight Parity Factor (MWPF) algorithm, a unified and certifiable decoding formulation that extends minimum-weight perfect matching to general hypergraph-based stabilizer codes. We focus on making MWPF practical and performant through a two-phase decoding architecture, consisting of a fast search phase and a refinement-based tune phase, along with a suite of algorithmic and system-level optimizations.

Our decoder, Hyperion, implements MWPF with support for floating-point and rational solvers, modular Relaxers for local LP solving, incremental dual updates, and efficient data structures for real-time performance. Benchmarks across surface and qLDPC codes show that Hyperion achieves sub-millisecond decoding latency, surpasses MWPM in accuracy,and offers flexible modularity for future integration.

Together, these contributions demonstrate that principled optimization techniques can meet the performance demands of real-time quantum decoding and pave the way for scalable, hardware-aware quantum error correction.

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