Quantum technologies have been recognized to have the potential to revolutionize our society. They aim at harnessing the power of quantum processes in order to exploit quantum systems for communication, encryption, simulations, and computation. Once harnessed, they will enable humanity to solve problems that would be intractable on classical computers; this will change our lives in fundamental ways, much like classical computers did.
A singularly important aspect of quantum technologies is the control of quantum matter. The ability to manipulate quantum systems with high precision defines the cutting-edge frontier of present-day quantum technology, and determines the pace at which progress is made to:
(i) improve current understanding of quantum materials where quantum laws govern the behavior on macroscopic lengthscales (e.g. superconductors, topological insulators, quantum solids);
(ii) build new devices which operate intrinsically using quantum phenomena (e.g. transistors, NMR machines);
(iii) it presents an enabling technology in the quest for reliable large-scale quantum computation.
Quantum control is important both from a practical and a fundamental perspective. Practically, it allows for the preparation of target states with prescribed properties, and ordered low-energy phases of matter. It represents an essential part of virtually any modern quantum experiment. At the same time, many theoretical studies proposing to engineer novel quantum effects, often delegate the means to prepare the system in the desired state to quantum control. Fundamentally, optimal control goes beyond (quasi-)equilibrium processes which obey the adiabatic theorem: it investigates fast processes that can excite the system far away from equilibrium, providing one of a handful of controlled approaches to study nonequilibrium dynamics.
PHASEQUANTROL adopts a distinct, unconventional approach to advance our understanding of optimal control: it aims to study phase transitions [in the sense of, e.g. water to gas transitions] in the process of finding optimal controls. This approach allows to quantify the complexity of control tasks in terms of properties of the underlying phases of control. In conventional optimal control studies, the goal is to find optimal protocols; yet in many interesting cases no guarantees can be given that the best solution has been found, nor can its functional form be explained. Unlike conventional approaches, in PHASEQUANTROL we tried to identify common hallmarks in the space of almost-optimal solutions, in order to use them to study the properties of the controlled physical system.
The objectives of the project are to:
1) Develop a theoretical understanding of phase transitions in the optimization landscapes of quantum control problems;
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 protocols;
3) Reveal limitations of Reinforcement Learning and Optimal Control algorithms in correlated landscapes.
