{"paper":{"title":"Complex Quantum Dynamics Versus Classical Simulability of Noisy Random Circuits","arxiv_id":"2609.39734","primary_cat":"quant-ph","submitted_at":"2026-09-30T13:40:55+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":"Claims of quantum advantage rest on the classical hardness of simulating quantum circuits.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.03,"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":1,"p":1.0,"id":"s1","own":false,"role":"background","text":"Magic, operator scrambling, anticoncentration, and non-Gaussianity for fermionic circuits are standard diagnostics of complex quantum dynamics.","hedge":{"p":1.0,"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":0.98,"id":"s2","own":false,"role":"background","text":"For pure states, some of these have been rigorously connected to classical simulability.","hedge":{"p":0.93,"label":"asserted"},"own_p":0.05,"main_claim_p":0.02,"quantitative":false,"quantitative_p":0.08,"role_probabilities":{"gap":0.02,"method":0.0,"result":0.0,"background":0.98,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":3,"p":1.0,"id":"s3","own":false,"role":"gap","text":"Whether these diagnostics reliably track the limits of efficient classical simulation under noise remains unclear.","hedge":{"p":0.43,"label":"asserted"},"own_p":0.04,"main_claim_p":0.04,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":1.0,"method":0.0,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":4,"p":0.7,"id":"s4","own":true,"role":"result","text":"Here, we show that in noisy Clifford+$T$ and nearest-neighbour matchgate+SWAP circuits, dynamical diagnostics and classical simulability can separate in both directions.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.69,"quantitative":false,"quantitative_p":0.42,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.7,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.3,"interpretation":0.0}},{"i":5,"p":0.99,"id":"s5","own":true,"role":"result","text":"In particular, the diagnostics can remain nontrivial after classical simulation becomes efficient, or become trivial before known efficient classical algorithms apply.","hedge":{"p":0.89,"label":"asserted"},"own_p":0.87,"main_claim_p":0.26,"quantitative":false,"quantitative_p":0.34,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.99,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.01,"interpretation":0.0}},{"i":6,"p":0.98,"id":"s6","own":true,"role":"interpretation","text":"We trace this mismatch to the different statistical properties they probe: magic and scrambling depend on fourth-order statistics of the Pauli spectrum, whereas the simulation algorithms depend primarily on second-order moments, which local noise suppresses at different rates.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.82,"main_claim_p":0.13,"quantitative":true,"quantitative_p":0.64,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.02,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.98}},{"i":7,"p":0.99,"id":"s7","own":true,"role":"interpretation","text":"Thus, dynamical diagnostics measured on a noisy quantum device do not by themselves constitute evidence for classical hardness.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.66,"main_claim_p":0.86,"quantitative":false,"quantitative_p":0.06,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.01,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.99}}]},"compiled":{"main_claim":{"p":0.92,"text":"Thus, dynamical diagnostics measured on a noisy quantum device do not by themselves constitute evidence for classical hardness.","location":"abstract s7","hedge_strength":{"p":1.0,"label":"asserted"}},"provenance":{"route":{"via":"TypeSafe API","model":"classifier-1.13.0","endpoint":"https://api.typesafe.ai/v1/systemone","provider":"TypeSafe"},"packing":"one request per 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