Session K24: Dynamical Entanglement Transitions in Monitored Random Quantum Circuits

Quantum Dynamics in Noisy and Monitored Random Circuits

The sustained storage, transmission, or processing of quantum information will likely be a non-equilibrium process that requires monitoring the system and applying some form of feedback to produce fault-tolerance. In this talk, I will discuss a class of models based on random quantum circuits with intermediate measurements that display a similar phenomenology to standard models for fault-tolerance, including the existence of a threshold, but with several helpful simplifications. I will discuss recent progress on understanding this novel class quantum phases and quantum critical phenomena. The emphasis will be on describing efficient protocols we have developed that allow experimental access in noisy-intermediate scale quantum processors.   

Cross Entropy Benchmark for Measurement-Induced Phase Transitions

Open quantum dynamics can host a rich phenomenology, including a family of measurement-induced phase transitions (MIPT) in the scaling of entanglement along quantum trajectories in monitored systems. While the MIPT occurs generically in a number of different models, its verification can be challenging even on an error-corrected quantum computer, due to the so-called ``postselection problem". I will describe the prospects of employing the linear cross-entropy to experimentally access measurement-induced phase transitions (MIPT) without requiring any postselection of quantum trajectories. By running two random circuits that are identical in the bulk but with different initial states - one on a quantum and the other on a classical computer - the linear cross entropy between the bulk measurement outcome distributions in the two circuits can be used to distinguish the volume law from area law phases. Besides the volume-law to area law MIPT, the linear cross-entropy can be employed to access other dynamical phase transitions in monitored systems, as I will describe.   

Topological transitions in weakly monitored free fermions

We study a free fermion  model where two sets of non-commuting non-projective measurements stabilize area-law entanglement scaling phases of distinct topological order. We show the presence of a topological phase transition that is of a different universality class than that observed in stroboscopic projective circuits. In the presence of  unitary dynamics, the two topologically distinct phases are separated by a region with sub-volume scaling of the entanglement entropy. We find that this entanglement transition is well identified by a emph{combination} of the bipartite entanglement entropy and the topological entanglement entropy.

We further show that the phase diagram is qualitatively captured by an analytically tractable non-Hermitian model obtained via post-selecting the measurement outcome. Finally we introduce a partial-post-selection continuous mapping, that  uniquely associates  topological indices of the non-Hermitian Hamiltonian to  the  distinct phases of the stochastic measurement-induced dynamics.   

An entanglement transition on a quantum tree and its relation to the measurement transition in all-to-all circuits

The measurement phase transition is a dynamical transition resulting from the competition between entangling gates and non-unitary operations. Its universal properties are known exactly in a type of classical limit obtained by considering the Hartley function or by taking the local Hilbert space dimension to infinity. It can also be understood using numerics on large systems for specific fine tuned models, such as Clifford or automaton circuits. In all these cases the universality of the transition is some version of percolation (or close to it). However, we do not have such a comprehensive understanding of its nature for generic quantum evolution, beyond small system numerics. I will describe our work on all-to-all circuits, where we argue that the transition is controlled by an entanglement transition on a tree tensor network. In this case rigorous results can be obtained for generic entangling gates. We show that this transition occurs at a finite distance from the classical percolation transition and also has a different universality class.   

Measurement and feedback driven entanglement transition in the probabilistic control of chaos

We uncover a dynamical entanglement transition in a monitored quantum system that is heralded

by a local order parameter. Classically, chaotic systems can be stochastically controlled onto unstable

periodic orbits and exhibit controlled and uncontrolled phases as a function of the rate at which

the control is applied. We show that such control transitions persist in open quantum systems

where control is implemented with local measurements and unitary feedback. Starting from a

simple classical model with a known control transition, we define a quantum model that exhibits

a diffusive transition between a chaotic volume-law entangled phase and a disentangled controlled

phase. Unlike other entanglement transitions in monitored quantum circuits, this transition can

also be probed by correlation functions without resolving individual quantum trajectories.