Revision 1

Accepted · first revision · record

Title: Universality class of the measurement-induced transition in Haar circuits
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.
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).
Settled by: An analytic theory (e.g. the replica limit of the associated statistical model) giving exponents confirmed by large-scale numerics.
Kind: well-posed
Answer type: value
References: (empty)
Literature status: open
Status note: (empty)
Posed since: 2019