{"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 circuits","topic_ref":"da5948613fb7c747a01db9b5effa765ea41c69dc5d5e33ffbeb4df2a77c0fb36"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"961e30c9268c7c05b8eb74432e67c7527b8bffeeeab88b139073e95a2e1a7678","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"eab434a12432152f4be6dcc70d11fa7703a054527cd5154829fd082bcfbbcdff","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"SEYrTqG6n8OKXj2w56TBcBlnwFKbFDTVAod68ACRA2798DXktbfEt_FNVKbjIlIZlk8I2Bq-H-wCBBzR4Q2nBA"},"schema":"pubphys.envelope/1"},"record_hash":"961e30c9268c7c05b8eb74432e67c7527b8bffeeeab88b139073e95a2e1a7678","leaf_index":2020}