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Overcoming scale and time: efficient simulations of collective open quantum systems


Supervisors: Katarzyna Macieszczak and David Quigley

Emergent quantum phenomena such as nonclassical phase transitions arise from interplay between many components in large systems. Computer simulation of these phenomena is however restricted to small sizes. If distinct timescales [1] also arise, the required length of simulations is equally problematic. We will circumvent the former by exploiting symmetries in collective open quantum dynamics [2,3] for experimentally relevant simulations of quantum optics [4]. We will avoid the latter by adapting rare-event simulation techniques [5] to uncover dynamical aspects of dissipative quantum phase transitions. Results will guide the adaptation of a neural network ansatz [6] to study more complex models.

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The aims of this project place it at the very overlap of quantum information science with non-equilibrium quantum physics. The models to be studied encompass a plethora of currently used quantum platforms.

The research will exploit parallel computing for efficient generation of typical as well as rare quantum trajectories, while utilising symmetries. Statistical error in those stochastic simulations will be limited by sample and population sizes. Those results could be further used for comparison and verification of machine-learning tools designed for average stationary states of open quantum systems when their performance may be affected by the presence of metastability.

While several open-source libraries have been developed for the average dynamics of permutationally invariant open quantum systems, this project could pave a way for development of open-source code for a quantum jump Monte Carlo method directly tailored to such systems.


[1] K. Macieszczak, D. C. Rose, I. Lesanovsky, J. P. Garrahan, "Theory of classical metastability in open quantum systems", Phys. Rev. Research 3, 033047 (2021)Link opens in a new window, K. Macieszczak, M. Guţă, I. Lesanovsky, J. P. Garrahan, "Towards a Theory of Metastability in Open Quantum Dynamics", Phys. Rev. Lett. 116, 240404 (2016)Link opens in a new window.
[2] K. Macieszczak, D.C. Rose, "Quantum jump Monte Carlo simplified: Abelian symmetries", Phys. Rev. A 103, 042204 (2021)Link opens in a new window.
[3] Y. Zhang, Y.-X. Zhang, and K. Mølmer, "Monte-Carlo simulations of superradiant lasing", New. J. Phys., 20, 112001 (2018)Link opens in a new window.
[4] N. Shammah, S. Ahmed, N. Lambert, S. De Liberato, and F. Nori., "Open quantum systems with local and collective incoherent processes: Efficient numerical simulations using permutational invariance", Phys. Rev. A 98, 063815 (2018)Link opens in a new window.
[5] F. Carollo, C. Pérez-Espigares, "Entanglement statistics in Markovian open quantum systems: a matter of mutation and selection", Phys. Rev. E 102, 030104 (2020)Link opens in a new window.
[6] A. Nagy and V. Savona, "Variational Quantum Monte Carlo Method with a Neural-Network Ansatz for Open Quantum Systems", Phys. Rev. Lett. 122, 250501 (2019)Link opens in a new window, M. J. Hartmann, and G. Carleo, "Neural-Network Approach to Dissipative Quantum Many-Body Dynamics", Phys. Rev. Lett. 122, 250502 (2019)Link opens in a new window, F. Vicentini, A. Biella, N. Regnault, and C. Ciuti, "Variational Neural-Network Ansatz for Steady States in Open Quantum Systems", Phys. Rev. Lett. 122, 250503 (2019)Link opens in a new window, N. Yoshioka and R. Hamazaki, "Constructing neural stationary states for open quantum many-body systems", Phys. Rev. B 99, 214306 (2019)Link opens in a new window.

Are you interested in applying for this project? Head over to our Study with Us page for information on the application process, and the HetSys training programme.

For the 2023/24 academic year, UK Research and Innovation (UKRI) funding is open to both UK and International research students. Awards pay a stipend to cover maintenance as well as paying the university fees and providing a research training support grant. For further details, please visit the HetSys Funding Page

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