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Paper 1

Geometry- and Topology-Informed Quantum Computing: From States to Real-Time Control with FPGA Prototypes

Gunhee Cho

Year

2026

Journal

arXiv preprint

DOI

arXiv:2601.09556

arXiv

2601.09556

This book gives a geometry-first, hardware-aware route through quantum-information workflows, with one goal: connect states, circuits, and measurement to deterministic classical pipelines that make hybrid quantum systems run. Part 1 develops the backbone (essential linear algebra, the Bloch-sphere viewpoint, differential-geometric intuition, and quantum Fisher information geometry) so evolution can be read as motion on curved spaces and measurement as statistics. Part 2 reframes circuits as dataflow graphs: measurement outcomes are parsed, aggregated, and reduced to small linear-algebra updates that schedule the next pulses, highlighting why low-latency, low-jitter streaming matters. Part 3 treats multi-qubit structure and entanglement as geometry and computation, including teleportation, superdense coding, entanglement detection, and Shor's algorithm via quantum phase estimation. Part 4 focuses on topological error correction and real-time decoding (Track A): stabilizer codes, surface-code decoding as "topology -> graph -> algorithm", and Union-Find decoders down to microarchitectural/RTL constraints, with verification, fault injection, and host/control-stack integration under product metrics (bounded latency, p99 tails, fail-closed policies, observability). Optional Track C covers quantum cryptography and streaming post-processing (BB84/E91, QBER/abort rules, privacy amplification, and zero-knowledge/post-quantum themes), emphasizing FSMs, counters, and hash pipelines. Appendices provide visualization-driven iCEstick labs (switch-to-bit conditioning, fixed-point phase arithmetic, FSM sequencing, minimal control ISAs), bridging principles to implementable systems.

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Paper 2

Toward Uncertainty-Aware and Generalizable Neural Decoding for Quantum LDPC Codes

Xiangjun Mi, Frank Mueller

Year

2025

Journal

arXiv preprint

DOI

arXiv:2510.06257

arXiv

2510.06257

Quantum error correction (QEC) is essential for scalable quantum computing, yet decoding errors via conventional algorithms result in limited accuracy (i.e., suppression of logical errors) and high overheads, both of which can be alleviated by inference-based decoders. To date, such machine-learning (ML) decoders lack two key properties crucial for practical fault tolerance: reliable uncertainty quantification and robust generalization to previously unseen codes. To address this gap, we propose \textbf{QuBA}, a Bayesian graph neural decoder that integrates attention to both dot-product and multi-head, enabling expressive error-pattern recognition alongside calibrated uncertainty estimates. Building on QuBA, we further develop \textbf{SAGU }\textbf{(Sequential Aggregate Generalization under Uncertainty)}, a multi-code training framework with enhanced cross-domain robustness enabling decoding beyond the training set. Experiments on bivariate bicycle (BB) codes and their coprime variants demonstrate that (i) both QuBA and SAGU consistently outperform the classical baseline belief propagation (BP), achieving a reduction of on average \emph{one order of magnitude} in logical error rate (LER), and up to \emph{two orders of magnitude} under confident-decision bounds on the coprime BB code $[[154, 6, 16]]$; (ii) QuBA also surpasses state-of-the-art neural decoders, providing an advantage of roughly \emph{one order of magnitude} (e.g., for the larger BB code $[[756, 16, \leq34]]$) even when considering conservative (safe) decision bounds; (iii) SAGU achieves decoding performance comparable to or even outperforming QuBA's domain-specific training approach.

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