{"paper":{"title":"Designing Quantum Solutions to the Closest String Problem with the Non-Variational QWOA","arxiv_id":"2610.33532","primary_cat":"quant-ph","submitted_at":"2026-10-24T08:19:59+00:00","version_compiled":"v1"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13.0 on the question bank abstract-p1-20260923, exactly as returned. No sentence in this record was written by a language model.","schema":"pith.compiled-record/v0","status":"compiled","abstract":{"source":"arXiv listing abstract v1","sentences":[{"i":0,"p":1.0,"id":"s0","own":false,"role":"background","text":"Quantum computing offers promising approaches to combinatorial optimization problems whose search spaces grow exponentially with problem size.","hedge":{"p":0.67,"label":"hedged_possibility"},"own_p":0.05,"main_claim_p":0.03,"quantitative":false,"quantitative_p":0.08,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":1.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":1,"p":1.0,"id":"s1","own":false,"role":"background","text":"The Closest String problem belongs to this category, which seeks a string that minimizes the maximum Hamming distance to any string in a given collection of reference strings.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.04,"main_claim_p":0.03,"quantitative":false,"quantitative_p":0.06,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":1.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":2,"p":1.0,"id":"s2","own":true,"role":"contribution","text":"In this work, we present an end-to-end quantum implementation of the Closest String problem using the Non-Variational Quantum Walk Optimization Algorithm (NV-QWOA), evaluating its resource requirements and solution amplification capabilities.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.96,"main_claim_p":0.18,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":1.0,"interpretation":0.0}},{"i":3,"p":0.98,"id":"s3","own":true,"role":"method","text":"Our automated workflow converts arbitrary problem instances into quantum circuits expressed in one- or two-qubit gates that encode candidate solutions, evaluate the objective function, and apply NV-QWOA optimisation to increase the measurement probabilities of high-quality solutions.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.1,"quantitative":false,"quantitative_p":0.14,"role_probabilities":{"gap":0.0,"method":0.98,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.02,"interpretation":0.0}},{"i":4,"p":0.75,"id":"s4","own":true,"role":"result","text":"Analytical resource estimates yield a qubit complexity of $\\mathcal{O}(nm\\log k)$ and a circuit depth of $\\mathcal{O}(pm\\log^2 n + pn\\log n)$, where $n$ is the string length, $m$ is the number of reference strings, $k$ is the alphabet size, and $p$ is the number of NV-QWOA iterations.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.93,"main_claim_p":0.08,"quantitative":true,"quantitative_p":0.97,"role_probabilities":{"gap":0.0,"method":0.06,"result":0.75,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.19,"interpretation":0.0}},{"i":5,"p":0.82,"id":"s5","own":true,"role":"contribution","text":"We introduce a revised prescription for the phase-separation parameter, $\\gamma$, that depends on problem size but requires no instance-specific optimization.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.08,"quantitative":false,"quantitative_p":0.09,"role_probabilities":{"gap":0.0,"method":0.18,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.82,"interpretation":0.0}},{"i":6,"p":0.48,"id":"s6","own":true,"role":"interpretation","text":"This prescription mitigates excessive phase wrapping modulo $2\\pi$, which can weaken the relationship between objective values and the phases guiding the optimization dynamics.","hedge":{"p":0.88,"label":"asserted"},"own_p":0.72,"main_claim_p":0.06,"quantitative":false,"quantitative_p":0.26,"role_probabilities":{"gap":0.0,"method":0.38,"result":0.01,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.13,"interpretation":0.48}},{"i":7,"p":1.0,"id":"s7","own":true,"role":"result","text":"Across all simulated problem sizes, the algorithm consistently amplifies optimal and near-optimal candidates.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.94,"main_claim_p":0.43,"quantitative":false,"quantitative_p":0.12,"role_probabilities":{"gap":0.0,"method":0.0,"result":1.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":8,"p":0.93,"id":"s8","own":true,"role":"contribution","text":"This work provides an explicit gate-level implementation, an improved phase-scaling method, and a foundation for hardware experiments and benchmarking against classical 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