Statistical Mechanics of Stochastic Quantum Control: $d$-adic Rényi Circuits
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866913915183562752 |
|---|---|
| author | Allocca, Andrew A. LeMaire, Conner Iadecola, Thomas Wilson, Justin H. |
| author_facet | Allocca, Andrew A. LeMaire, Conner Iadecola, Thomas Wilson, Justin H. |
| contents | The dynamics of quantum information in many-body systems with large onsite Hilbert space dimension admits an enlightening description in terms of effective statistical mechanics models. Motivated by this fact, we reveal a connection between three separate models: the classically chaotic $d$-adic Rényi map with stochastic control, a quantum analog of this map for qudits, and a Potts model on a random graph. The classical model and its quantum analog share a transition between chaotic and controlled phases, driven by a randomly applied control map that attempts to order the system. In the quantum model, the control map necessitates measurements that concurrently drive a phase transition in the entanglement content of the late-time steady state. To explore the interplay of the control and entanglement transitions, we derive an effective Potts model from the quantum model and use it to probe information-theoretic quantities that witness both transitions. The entanglement transition is found to be in the bond-percolation universality class, consistent with other measurement-induced phase transitions, while the control transition is governed by a classical random walk. These two phase transitions merge as a function of model parameters, consistent with behavior observed in previous small-size numerical studies of the quantum model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_16087 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Statistical Mechanics of Stochastic Quantum Control: $d$-adic Rényi Circuits Allocca, Andrew A. LeMaire, Conner Iadecola, Thomas Wilson, Justin H. Quantum Physics Disordered Systems and Neural Networks Statistical Mechanics Chaotic Dynamics The dynamics of quantum information in many-body systems with large onsite Hilbert space dimension admits an enlightening description in terms of effective statistical mechanics models. Motivated by this fact, we reveal a connection between three separate models: the classically chaotic $d$-adic Rényi map with stochastic control, a quantum analog of this map for qudits, and a Potts model on a random graph. The classical model and its quantum analog share a transition between chaotic and controlled phases, driven by a randomly applied control map that attempts to order the system. In the quantum model, the control map necessitates measurements that concurrently drive a phase transition in the entanglement content of the late-time steady state. To explore the interplay of the control and entanglement transitions, we derive an effective Potts model from the quantum model and use it to probe information-theoretic quantities that witness both transitions. The entanglement transition is found to be in the bond-percolation universality class, consistent with other measurement-induced phase transitions, while the control transition is governed by a classical random walk. These two phase transitions merge as a function of model parameters, consistent with behavior observed in previous small-size numerical studies of the quantum model. |
| title | Statistical Mechanics of Stochastic Quantum Control: $d$-adic Rényi Circuits |
| topic | Quantum Physics Disordered Systems and Neural Networks Statistical Mechanics Chaotic Dynamics |
| url | https://arxiv.org/abs/2404.16087 |