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Paper 1

Quantum Error Correction near the Coding Theoretical Bound

Daiki Komoto, Kenta Kasai

Year

2024

Journal

arXiv preprint

DOI

arXiv:2412.21171

arXiv

2412.21171

Recent progress in quantum computing has enabled systems with tens of reliable logical qubits, built from thousands of noisy physical qubits. However, many impactful applications demand quantum computations with millions of logical qubits, necessitating highly scalable quantum error correction. In classical information theory, low-density parity-check (LDPC) codes can approach channel capacity efficiently. Yet, no quantum error-correcting codes with efficient decoding have been shown to approach the hashing bound - a fundamental limit on quantum capacity - despite decades of research. Here, we present quantum LDPC codes that not only approach the hashing bound but also allow decoding with computational cost linear in the number of physical qubits. This breakthrough paves the way for large-scale, fault-tolerant quantum computation. Combined with emerging hardware that manages many qubits, our approach brings quantum solutions to important real-world problems significantly closer to reality.

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Paper 2

Fidelity-Guaranteed Entanglement Routing with Distributed Purification Planning

Anthony Gatti, Anoosha Fayyaz, Prashant Krishnamurthy, Kaushik P. Seshadreesan, Amy Babay

Year

2026

Journal

arXiv preprint

DOI

arXiv:2605.00246

arXiv

2605.00246

Many quantum-network applications require end-to-end Bell pairs whose fidelity exceeds a request-specific threshold, but existing entanglement routing algorithms either optimize only throughput without regard for fidelity or enforce fidelity guarantees using centralized controllers with global link-state knowledge. We present Q-GUARD, an online entanglement routing algorithm that enforces per-request fidelity thresholds within a distributed protocol model in which nodes exchange link-state information only with their $k$-hop neighbors. After link outcomes are realized in each slot, Q-GUARD builds per-link purification cost tables from realized Bell pairs, allocates per-hop fidelity targets using a Werner-state equal-split rule, and selects between candidate path segments using a segment-local expected-goodput (EXG) metric that jointly accounts for swap success, purification overhead, and resource availability. We also introduce Q-GUARD-WS, an extension that exploits per-link hardware quality estimates to allocate purification effort non-uniformly across hops. On synthetic 100-node topologies with heterogeneous link fidelity and stochastic BBPSSW purification, Q-GUARD raises the qualified success rate from under 20\% to over 85\% on 4-hop paths and nearly doubles the qualified service radius in Euclidean distance relative to throughput-only and naive-purification baselines, while Q-GUARD-WS provides additional throughput gains under high hardware heterogeneity.

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