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Statistical mechanics of stochastic quantum control: d-adic Rényi circuits
Andrew A Allocca1,2, Conner LeMaire1, Thomas Iadecola3,4
1Department of Physics and Astronomy, <a href="https://ror.org/05ect4e57">Louisiana State University</a>, Baton Rouge, Louisiana 70803, USA.
Physical Review. E
|September 19, 2024
Summary
This study connects quantum information dynamics to statistical mechanics, revealing how control and entanglement transitions in quantum systems can be tuned. These transitions, linked to a Potts model, offer insights into quantum chaos and measurement effects.
Area of Science:
- Quantum Information Science
- Statistical Mechanics
- Quantum Chaos
Background:
- Quantum information dynamics in many-body systems can be described by statistical mechanics.
- Connections between classical chaotic maps, quantum analogs, and statistical models are explored.
Purpose of the Study:
- To reveal a connection between a chaotic d-adic Rényi map, its quantum analog for qudits, and a Potts model.
- To investigate the interplay between control and entanglement phase transitions in a quantum system.
Main Methods:
- Developed a quantum analog of a classically chaotic map with stochastic control.
- Derived an effective Potts model from the quantum model to analyze information-theoretic quantities.
- Studied phase transitions related to system ordering and entanglement content.
Main Results:
- Identified a shared transition between chaotic and controlled phases in classical and quantum models.
- Observed that measurements in the quantum model drive an entanglement phase transition.
- Found the entanglement transition belongs to the bond-percolation universality class.
Conclusions:
- The entanglement transition is governed by measurement-induced phase transitions, while the control transition follows a classical random walk.
- Coinciding the two phase transitions is possible by parameter variation, aligning with previous numerical studies.
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