Phase Transitions of Quantum Control

A particularly useful application of out-of-equilibrium quantum dynamics is the control of quantum matter.

High-precision quantum control defines a cutting edge frontier in developing quantum technology: high-fidelity preparation of target states with prescribed properties, experimental studies of novel phases of matter, and reliable quantum computing depend upon our ability to manipulate quantum systems.

Recently, it was discovered that optimal quantum control exhibits continuous and discontinuous phase transitions familiar from macroscopic systems: correlated/glassy phases and spontaneous symmetry breaking appear also in the optimization landscape. Despite this progress, much of the physics of this new phenomenon remains unknown.

The objectives of this project are to: (1) develop theoretical understanding for phase transitions in the optimization landscapes of nonequilibrium quantum control problems, such as quantum state preparation and entanglement reduction;(2) create a new perspective on quantum many-body control and longstanding optimization problems in many-body physics by investigating the correlations between local minima of the control landscape;(3) reveal limitations of reinforcement learning and optimal control algorithms in correlated optimization landscapes.

This unconventional approach to quantum control will allow us to quantify the complexity of nonequilibrium control tasks in terms of properties of the underlying phases of control.

We will identify common traits in the space of almost-optimal solutions, and use them to investigate features of the controlled physical systems.

The proposed research opens up a new frontier which can point to a mutually beneficial synergy between reinforcement learning, optimal control, condensed matter physics and statistical mechanics.

It combines hitherto unrelated concepts to advance our understanding of nonequilibrium quantum many-body dynamics, with applications in ultracold atoms and trapped ions.