Abstract
The extension of many-body quantum dynamics to the nonunitary domain has led to a series of exciting developments, including new out-of-equilibrium entanglement phases and phase transitions. We show how a duality transformation between space and time, on one hand, and unitarity and nonunitarity, on the other, can be used to realize steady-state phases of nonunitary dynamics that exhibit a rich variety of behavior in their entanglement scaling with subsystem size—from logarithmic to extensive to fractal. We show how these outcomes in nonunitary circuits (that are “spacetime dual” to unitary circuits) relate to the growth of entanglement in time in the corresponding unitary circuits, and how they differ, through an exact mapping to a problem of unitary evolution with boundary decoherence, in which information gets “radiated away” from one edge of the system. In spacetime duals of chaotic unitary circuits, this mapping allows us to analytically derive a nonthermal volume-law entangled phase with a universal logarithmic correction to the entropy, previously observed in unitary-measurement dynamics. Notably, we also find robust steady-state phases with fractal entanglement scaling, with tunable for subsystems of size in one dimension. We present an experimental protocol for preparing these novel steady states with only a vanishing density of postselected measurements via a type of “teleportation” between spacelike and timelike slices of quantum circuits.
- Received 21 May 2021
- Revised 18 November 2021
- Accepted 18 January 2022
DOI:https://doi.org/10.1103/PhysRevX.12.011045
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Quantum entanglement, a type of correlation without a classical analog, is key to the power of quantum computers. Its generation in the dynamics of many-body quantum systems plays an important role in fundamental and practical questions. Quantum circuits (discrete arrays of quantum bits evolving through discrete time steps) are powerful models for addressing these questions. As space and time are both discrete in these models, their roles can be exchanged, at least theoretically. This idea, known as “spacetime duality,” leads to additional insights into quantum dynamics. Here, we explain how to carry out this idea in practice on modern digital quantum simulators and uncover a powerful exact connection between the behaviors of quantum entanglement on the two sides of this duality.
We show how, under spacetime duality, the generation of entanglement over time in “unitary” circuits—which describe the evolution of isolated, unobserved systems—is related to the spatial structure of entanglement in states produced by monitored circuits, which include frequent measurements by an outside observer. Equipped with this result, we derive a new class of “fractally entangled” states and shed new light on the structure of entanglement in monitored circuits.
Spacetime duality is one example of a more general strategy: using quantum computing elements, such as measurement and “teleportation,” to alter the very structure of spacetime in quantum dynamics, with potential implications for new classical algorithms and for new quantum phenomena.
