Periodic Reporting for period 1 - PHASEQUANTROL (Phase Transitions of Quantum Control)
Periodo di rendicontazione: 2021-09-01 al 2023-08-31
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.
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.
The project resulted in 2 publications and 6 preprints currently under peer review.
The first major result of PHASEQUANTROL is the development of machine-learning-aided algorithms for quantum control. We approached the outstanding challenge in quantum control to combine continuous and discrete degrees of freedom, which would bring a versatile manipulation framework for modern quantum computing devices. In collaboration with research groups at UC Berkeley and Stanford, we developed two algorithms, called RL-QAOA and MCTS-QAOA. Our results are published as two papers in the conference proceedings Mathematical and Scientific Machine Learning. In a different work, we also developed a new deep learning architecture based on tensor networks, which allows the control of quantum states in the many-body regime, which is a prerequisite for achieving quantum supremacy.
The second line of results concerns the application of quantum control techniques to a quantum simulator of nitrogen-vacancy centers. In a series of two studies jointly performed in collaboration with an experimental group at UC Berkeley, we conceived a quantum manipulation protocol to realize the first continuous-time observation of a discrete time crystal. This exotic phase of matter does not exist in equilibrium; hence, our research revealed this new way in which nature behaves. In a follow-up study, we developed a novel protocol to stabilize and manipulate long-lived spin degrees of freedom, and verified its applicability on the quantum simulator; we believe that this technique could be used for quantum computing. These studies resulted in two preprints, currently under peer review.
A third study investigated the optimization landscape of a notoriously difficult model, known to describe magnetic quantum order. We analyzed in detail the behavior of a widely-used algorithm, called variational Monte Carlo with neural quantum states. We managed to establish a connection between the behavior of the algorithm and the glassy properties of the rugged energy landscape of the physical model. We published our results in an open-access journal.
Finally, we verified the validity of the celebrated Jarzynski equality in the quantum many-body regime. To do this, we devised a novel control protocol to excite the system and showed that it is capable of counteracting dissipation on modern quantum computing devices. This allowed us to push the state of the art, and reach system sizes an order of magnitude larger than previously thought possible.
The results obtained above were disseminated in five conference talks in Germany, Poland, India, and Sweden, and one seminar talk at Oxford University.
The first major result of PHASEQUANTROL is the development of machine-learning-aided algorithms for quantum control. We approached the outstanding challenge in quantum control to combine continuous and discrete degrees of freedom, which would bring a versatile manipulation framework for modern quantum computing devices. In collaboration with research groups at UC Berkeley and Stanford, we developed two algorithms, called RL-QAOA and MCTS-QAOA. Our results are published as two papers in the conference proceedings Mathematical and Scientific Machine Learning. In a different work, we also developed a new deep learning architecture based on tensor networks, which allows the control of quantum states in the many-body regime, which is a prerequisite for achieving quantum supremacy.
The second line of results concerns the application of quantum control techniques to a quantum simulator of nitrogen-vacancy centers. In a series of two studies jointly performed in collaboration with an experimental group at UC Berkeley, we conceived a quantum manipulation protocol to realize the first continuous-time observation of a discrete time crystal. This exotic phase of matter does not exist in equilibrium; hence, our research revealed this new way in which nature behaves. In a follow-up study, we developed a novel protocol to stabilize and manipulate long-lived spin degrees of freedom, and verified its applicability on the quantum simulator; we believe that this technique could be used for quantum computing. These studies resulted in two preprints, currently under peer review.
A third study investigated the optimization landscape of a notoriously difficult model, known to describe magnetic quantum order. We analyzed in detail the behavior of a widely-used algorithm, called variational Monte Carlo with neural quantum states. We managed to establish a connection between the behavior of the algorithm and the glassy properties of the rugged energy landscape of the physical model. We published our results in an open-access journal.
Finally, we verified the validity of the celebrated Jarzynski equality in the quantum many-body regime. To do this, we devised a novel control protocol to excite the system and showed that it is capable of counteracting dissipation on modern quantum computing devices. This allowed us to push the state of the art, and reach system sizes an order of magnitude larger than previously thought possible.
The results obtained above were disseminated in five conference talks in Germany, Poland, India, and Sweden, and one seminar talk at Oxford University.
PHASEQUANTROL also contributed service to the community.
Alongside the scientific work on the project, two bachelor students, and two PhD students were supervised by the researcher and developed new skills. The researcher also participated in Sofia University's mentoring program, where master and PhD students are assigned a mentor to receive academic guidance.
The researcher also helped with the co-organization of a track as part of the Machine Learning Days 2022 conference, and took part in the UKRAPRO conference in support of Ukrainian scientists that were forced to leave their country due to the unprovoked Russian military aggression.
Alongside the scientific work on the project, two bachelor students, and two PhD students were supervised by the researcher and developed new skills. The researcher also participated in Sofia University's mentoring program, where master and PhD students are assigned a mentor to receive academic guidance.
The researcher also helped with the co-organization of a track as part of the Machine Learning Days 2022 conference, and took part in the UKRAPRO conference in support of Ukrainian scientists that were forced to leave their country due to the unprovoked Russian military aggression.