Random Quantum Circuits

Abstract

Quantum circuits—built from local unitary gates and local measurements—are a new playground for quantum many-body physics and a tractable setting to explore universal collective phenomena far from equilibrium. These models have shed light on longstanding questions about thermalization and chaos, and on the underlying universal dynamics of quantum information and entanglement. In addition, such models generate new sets of questions and give rise to phenomena with no traditional analog, such as dynamical phase transitions in quantum systems that are monitored by an external observer. Quantum circuit dynamics is also topical in view of experimental progress in building digital quantum simulators that allow control of precisely these ingredients. Randomness in the circuit elements allows a high level of theoretical control, with a key theme being mappings between real-time quantum dynamics and effective classical lattice models or dynamical processes. Many of the universal phenomena that can be identified in this tractable setting apply to much wider classes of more structured many-body dynamics. Expected final online publication date for the Annual Review of Condensed Matter Physics, Volume 14 is March 2023. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Quantum evolution with random phase scattering

“…To mimic the effect of disorder in the evolution of a quantum state we 'scramble' a translational invariant e −iHτ /ℏ with a random phase factor e iα by using the evolution operator U = e iα e −iHτ /ℏ . This choice was inspired by the random unitary gate models that have been discussed in the context of quantum circuits [11][12][13]. The following analysis is also inspired by previous studies of the invariant measure of transport in systems with random chiral Hamiltonians [14].…”

Enhanced entanglement negativity in boundary-driven monitored fermionic chains

“…While the averaged dynamics can be described by a standard Lindblad equation, leading to diffusive average transport, distinct histories of measurement outcomes define an ensemble of quantum trajectories, displaying a much more interesting behavior. Our work is motivated by the recent literature on entanglement measurement-induced phase transitions (MIPTs) [22][23][24], providing striking examples of how individual quantum trajectories may display new phenomenology beyond the standard Lindbladian framework [25,26]. However, in contrast to most of the work in this literature which has investigated entanglement-related and quantum information aspects, we will exclusively focus on transport.…”

Quantum information phases in space-time: measurement-induced entanglement and teleportation on a noisy quantum processor

“…In particular, "monitored" circuits comprising both unitary gates and controlled projective measurements (Fig. 1a) were predicted to give rise to distinct nonequilibrium phases characterized by the structure of their entanglement 3,4,[21][22][23] -"volume-law" 24 (extensive) or "area-law" 25 (limited) depending on the rate or strength of measurement. The same underlying phenomenon has a rich variety of related manifestations, from the emergence of a dynamical quantum code 5,6 , to teleportation 18 and simulation complexity 17 phase transitions.…”