Local and nonlocal stochastic control of quantum chaos: Measurement- and control-induced criticality

Abstract

We theoretically study the topology of the phase diagram of a family of quantum models inspired by the classical Bernoulli map under stochastic control. The quantum models inherit a control-induced phase transition from the classical model and also manifest an entanglement phase transition intrinsic to the quantum setting. This measurement-induced phase transition has been shown in various settings to either coincide or split off from the control transition, but a systematic understanding of the necessary and sufficient conditions for the two transitions to coincide in this case has so far been lacking. In this work, we generalize the control map to allow for either local or global control action. While this does not affect the classical aspects of the control transition that is described by a random walk, it significantly influences the quantum dynamics, leading to the universality class of the measurement-induced transition being dependent on the locality of the control operation. In the presence of a global control map, the two transitions coincide and the control-induced phase transition dominates the measurement-induced phase transition. Contrarily, the two transitions split in the presence of the local control map or additional projective measurements and generically take on distinct universality classes. For local control, the measurement-induced phase transition recovers the Haar logarithmic conformal field theory universality class found in feedback-free models. However, for global control, a novel universality class with correlation length exponent $\nu \approx 0.7$ emerges from the interplay of control and projective measurements. This work provides a more refined understanding of the relationship between the control- and measurement-induced phase transitions.

16 pages, 10 figures

References in corpus (17)

• Random Quantum Circuits
• Critical properties of the measurement-induced transition in random quantum circuits
• Observation of measurement-induced quantum phases in a trapped-ion quantum computer
• Measurement-induced entanglement and teleportation on a noisy quantum processor
• Experimental Realization of a Measurement-Induced Entanglement Phase Transition on a Superconducting Quantum Processor
• Entanglement and charge-sharpening transitions in U(1) symmetric monitored quantum circuits
• Operator scaling dimensions and multifractality at measurement-induced transitions
• Measurements conspire nonlocally to restructure critical quantum states
• Cross Entropy Benchmark for Measurement-Induced Phase Transitions
• Controlling entanglement at absorbing state phase transitions in random circuits
• Entanglement Steering in Adaptive Circuits with Feedback
• Probing post-measurement entanglement without post-selection
• Triviality of quantum trajectories close to a directed percolation transition
• Entanglement and Absorbing-State Transitions in Interactive Quantum Dynamics
• Neural-Network Decoders for Measurement Induced Phase Transitions
• Statistical mechanics model for Clifford random tensor networks and monitored quantum circuits
• Learnability transitions in monitored quantum dynamics via eavesdropper's classical shadows

Cited by in corpus (5)

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• Monitored Fluctuating Hydrodynamics
• Random Quantum Circuits with Time-Reversal Symmetry
• Concomitant Entanglement and Control Criticality Driven by Collective Measurements
• Control-driven critical fluctuations across quantum trajectories