{"paper":{"title":"Quantum approximate stochastic combinatorial optimisation","arxiv_id":"2610.22876","primary_cat":"quant-ph","submitted_at":"2026-10-16T03:26:22+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":"Two-stage stochastic combinatorial optimisation concerns discrete decisions made before all relevant information is known.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.04,"main_claim_p":0.02,"quantitative":false,"quantitative_p":0.05,"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":"An initial decision is made; once uncertainty is resolved, it can be adapted to the realised scenario, at a cost.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.04,"main_claim_p":0.02,"quantitative":false,"quantitative_p":0.04,"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":false,"role":"background","text":"The aim is to find the initial decision that minimises the upfront cost plus the expected cost of optimal adaptation.","hedge":{"p":1.0,"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":3,"p":0.93,"id":"s3","own":false,"role":"background","text":"The first-stage decision problem is often NP-hard, and computing the expected minimum recourse cost can be $\\#\\mathrm{P}$-hard for a single first-stage candidate.","hedge":{"p":0.92,"label":"asserted"},"own_p":0.05,"main_claim_p":0.02,"quantitative":false,"quantitative_p":0.32,"role_probabilities":{"gap":0.07,"method":0.0,"result":0.0,"background":0.93,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":4,"p":0.73,"id":"s4","own":true,"role":"contribution","text":"We introduce Quantum Approximate Stochastic Combinatorial Optimisation (QASCO), a variational quantum-walk ansatz that coherently incorporates scenario-dependent recourse into its dynamics to search over first-stage decisions without explicitly evaluating expected minimum recourse costs.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.94,"main_claim_p":0.2,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.27,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.73,"interpretation":0.0}},{"i":5,"p":0.6,"id":"s5","own":true,"role":"contribution","text":"We demonstrate QASCO for MaxCut with stochastic edge weights, obtain a circuit with polynomial per-layer gate complexity, and study the ansatz via exact state-vector simulation.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.97,"main_claim_p":0.08,"quantitative":false,"quantitative_p":0.45,"role_probabilities":{"gap":0.0,"method":0.26,"result":0.14,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.6,"interpretation":0.0}},{"i":6,"p":1.0,"id":"s6","own":true,"role":"result","text":"Across the instances considered, QASCO concentrates amplitude more effectively on stochastic-optimal first-stage decisions than a previously proposed two-stage QAOA construction.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.2,"quantitative":true,"quantitative_p":0.92,"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":7,"p":0.84,"id":"s7","own":true,"role":"result","text":"We further show that the ansatz can be calibrated using a depth-independent number of parameters and applied to unseen instances without further circuit-parameter optimisation, including joint decision--scenario--recourse spaces spanning more than $2^{32}$ configurations.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.96,"main_claim_p":0.15,"quantitative":true,"quantitative_p":0.95,"role_probabilities":{"gap":0.0,"method":0.02,"result":0.84,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.14,"interpretation":0.0}},{"i":8,"p":1.0,"id":"s8","own":true,"role":"result","text":"Under a query-cost model, comparison with the tested classical heuristics using sample-average approximations of the expected minimum recourse cost shows that QASCO more reliably reaches globally optimal first-stage solutions while requiring fewer cut evaluations.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.26,"quantitative":true,"quantitative_p":0.94,"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":9,"p":0.98,"id":"s9","own":true,"role":"interpretation","text":"These results show how to incorporate scenario-dependent recourse into the ansatz dynamics, providing a general framework for variational quantum walks in two-stage stochastic combinatorial optimisation.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.84,"main_claim_p":0.77,"quantitative":false,"quantitative_p":0.03,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.02,"interpretation":0.98}}]},"compiled":{"main_claim":{"p":0.78,"text":"These results show how to incorporate scenario-dependent recourse into the ansatz dynamics, providing a general framework for 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