Measurement-induced criticality in extended and long-range unitary circuits

Abstract

We explore the dynamical phases of unitary Clifford circuits with variable-range interactions, coupled to a monitoring environment. We investigate two classes of models, distinguished by the action of the unitary gates, which either are organized in clusters of finite-range two-body gates, or are pair-wise interactions randomly distributed throughout the system with a power-law distribution. We find the range of the interactions plays a key role in characterizing both phases and their measurement-induced transitions. For the cluster unitary gates we find a transition between a phase with volume-law scaling of the entanglement entropy and a phase with area-law entanglement entropy. Our results indicate that the universality class of the phase transition is compatible to that of short range hybrid Clifford circuits. Oppositely, in the case of power-law distributed gates, we find the universality class of the phase transition changes continuously with the parameter controlling the range of interactions. In particular, for intermediate values of the control parameter, we find a non-conformal critical line which separates a phase with volume-law scaling of the entanglement entropy from one with sub-extensive scaling. Within this region, we find the entanglement entropy and the logarithmic negativity present a cross-over from a phase with algebraic growth of entanglement with system size, and an area-law phase.

Quantum information spreading in random spin chains

“…For instance, we recall that the α = 1/2 mutual information was found to be proportional to the negativity (see below for a definition) in many settings, ranging from integrable models [66][67][68][69] to conformal field thoeries [24,70,71]. We note that this relationship has been recently investigated also within quantum circuits [72], where it was found to hold at early times, and within monitored and open quantum systems [73][74][75][76][77][78], where it was shown to hold and breakdown in specific setups and regimes.…”

Topological order and entanglement dynamics in the measurement-only XZZX quantum code

“…In a quantum circuit, frequent local measurements, which do not commute with the generators of the unitary dynamics induce a phase transition in the dynamics of entanglement [1][2][3]. This phenomenon has been observed in random quantum circuits, where the unitary evolution is generated by Clifford [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] or Haar [1,3,[18][19][20][21][22][23][24][25][26] random gates and in Hamiltonian systems, where the unitary time evolution is continuous [27][28][29][30][31][32][33][34][35][36][37][38][39]. Due to the inherent randomness of the measurement process, the entanglement phase transitions do not manifest on the level of ensemble averaged, local order parameters but only in higher moments, or replicas of the state [11,20,31,<...>…”

Purification and scrambling in a chaotic Hamiltonian dynamics with measurements

“…For example in a many-body system (hybrid circuit models, etc.) coupled to environments such as dissipation and measurements, a dynamical entanglement phase transition induced by measurements has been extensively studied [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. In particular, Ref.…”