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Paper 1
NLTS Hamiltonians from classical LTCs
Zhiyang He, Chinmay Nirkhe
- Year
- 2022
- Journal
- arXiv preprint
- DOI
- arXiv:2210.02999
- arXiv
- 2210.02999
We provide a completely self-contained construction of a family of NLTS Hamiltonians [Freedman and Hastings, 2014] based on ideas from [Anshu, Breuckmann, and Nirkhe, 2022], [Cross, He, Natarajan, Szegedy, and Zhu, 2022] and [Eldar and Harrow, 2017]. Crucially, it does not require optimal-parameter quantum LDPC codes and can be built from simple classical LTCs such as the repetition code on an expander graph. Furthermore, it removes the constant-rate requirement from the construction of Anshu, Breuckmann, and Nirkhe.
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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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