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DY: Fachverband Dynamik und Statistische Physik

DY 60: Quantum Dynamics, Decoherence and Quantum Information (joint session DY/TT)

DY 60.7: Talk

Friday, March 22, 2024, 12:15–12:30, A 151

Control phase transitions analysis in the quantum control landscape — •Nicolò Beato, Pranay Patil, and Marin Bukov — Max Planck Institute for the Physics of Complex Systems, Noethnitzer Str. 38, 01187 Dresden, Germany

In recent years, the presence of control phase transitions emerged while numerically surveying the quantum control landscape associated with population-transfer problems in few-qubit systems [10.1103/PhysRevX.8.031086]. Despite all efforts, an analytical understanding of quantum optimal control landscapes is largely missing.

In this work, we present a set of perturbative methods that allow for the analytical characterization of various control phase transitions. These methods provide an explicit mapping between quantum control problems and classical many-body systems at thermal equilibrium (exhibiting long-range, multi-body interactions). We demonstrate the effectiveness of these approaches by explicitly considering the single- and two- qubit state-preparation problems, previously extensively studied via numerical optimization algorithms [10.1103/PhysRevA.97.052114]. Through this approach, control phase transitions are connected to dramatic changes in the topological and geometrical properties of the near-optimal part of the control landscape.

The methods developed are largely independent from the quantum systems underlying the control problem and can be easily adapted to more complicated settings. Our work shed new light on the close connection between optimal quantum control and (spin) glassy systems.

Keywords: Quantum control; Phase transition; Glassy systems