Abstract
Repeated projective measurements in unitary circuits can lead to an entanglement phase transition as the measurement rate is tuned. In this work, we consider a different setting in which the projective measurements are replaced by dynamically chosen unitary gates that minimize the entanglement. This can be seen as a one-dimensional unitary circuit game in which two players get to place unitary gates on randomly assigned bonds at different rates: the “entangler” applies a random local unitary gate with the aim of generating extensive (volume-law) entanglement. The “disentangler,” based on limited knowledge about the state, chooses a unitary gate to reduce the entanglement entropy on the assigned bond with the goal of limiting to only finite (area-law) entanglement. In order to elucidate the resulting entanglement dynamics, we consider three different scenarios: (i) a classical discrete height model, (ii) a Clifford circuit, and (iii) a general unitary circuit. We find that both the classical and Clifford circuit models exhibit phase transitions as a function of the rate that the disentangler places a gate, which have similar properties that can be understood through a connection to the stochastic Fredkin chain. In contrast, the entangler always wins when using Haar random unitary gates and we observe extensive, volume-law entanglement for all nonzero rates of entangling.
- Received 30 June 2023
- Accepted 14 December 2023
DOI:https://doi.org/10.1103/PRXQuantum.5.010309
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 many-body systems out of equilibrium represent a challenging frontier and have been shown to exhibit extremely rich phenomena. Recent experimental advances in building noisy intermediate-scale quantum (NISQ) devices have opened up an entirely new territory in this context: the natural evolution implemented by NISQ devices is quantum interactive dynamics generated by a combination of unitary gates and measurements. These platforms provide an opportunity to explore vastly larger parts of the Hilbert space and go beyond what can be realized in purely unitary systems. Recent pioneering works have proposed a measurement-induced entanglement phase transition to occur in such a setting, separating phases in which the entanglement entropy obeys an area-law and a volume-law phase, respectively.
We introduce and examine a novel framework in which we try to combat the formation of volume-law entanglement by employing solely local operations based on certain knowledge about the state of the system. Our approach involves a gamelike model with two competing parties: the “entangler,” which scrambles the system, and the “disentangler,” which applies local operations trying to reduce the entanglement. Depending on the specific scenario considered, we identify different universality classes and find phase transitions in certain cases.
The introduction of this framework opens up exciting avenues for future research relevant in the realization of NISQ devices. One such direction involves investigating how much information a disentangler requires to completely evade quantum thermalization in the generic case.
