{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"b9ed87658c0f5ba0b4d343f3a06a94ee89bf0854bec4124a41c47f3569500b4d","created":"2026-10-03T07:18:10Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"ff49af49b2e3a818cab2d5e00d571e502f6cc4cdb19808bb086fa362c0653cd6","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"qi.monitored-circuits.haar-mipt-universality","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"At the transition, quantities like entanglement follow power laws with universal exponents, as at a boiling point. These exponents and the theory that produces them are not known for ordinary random circuits of qubits.","posed_since":"2019","precise":"For $1+1D$ brickwork circuits of Haar-random two-qudit gates (local dimension q) with projective measurements at rate p, determine the critical exponents at $p_c$ (correlation-length exponent nu, entanglement scaling and surface exponents) and identify the field theory, for finite q and as q goes to $\\infty$ where the transition maps to classical percolation. Qubit numerics give $\\nu \\sim 1.2-1.3$ (approximate) with other exponents distinct from percolation (Zabalo et al. 2020).","problem_ref":null,"references":"","settled_by":"An analytic theory (e.g. the replica limit of the associated statistical model) giving exponents confirmed by large-scale numerics.","status_note":"","title":"Universality class of the measurement-induced transition in Haar 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