Optimal Control applied to Quantum Computing

• Grant number: 24/23566-4
• Support Opportunities: Scholarships in Brazil - Doctorate (Direct)
• Start date: January 01, 2026
• End date: February 28, 2030
• Field of knowledge: Physical Sciences and Mathematics - Physics - General Physics
• Principal Investigator: Emanuel Fernandes de Lima
• Grantee: Gustavo Fernandes da Costa
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

Quantum Computing is one of the most promising areas of Physics. Its full realization will allow solving problems that are prohibitive for classical computing. In the last decades, there has been considerable progress in quantum technologies. Several quantum devices with some level of noise and at intermediate scale (around 100 qubits) are in operation or under development, called NISQ devices. Variational quantum algorithms, together with adiabatic and quantum annealing algorithms, have been developed for these platforms with applications in chemistry, optimization and machine learning. Controlling quantum systems efficiently and in the shortest possible time to avoid deleterious effects of system-environment interaction is crucial for quantum computing and for quantum technologies in general. Optimal Control Theory has been invoked as an important tool both for optimizing quantum gates with high fidelity and for improving the performance of quantum algorithms. Another recent approach to these optimal control problems is based on machine learning, especially reinforcement learning. This project aims to investigate the optimization of protocols for quantum computing. In addition to considering the central problems of circuit-based quantum computing, which are the transfer between predetermined states and the construction of unitary operators, called quantum gates, we will also consider computation in the context of variational, adiabatic and quantum annealing algorithms, which represent paradigms for current quantum devices. The first objective will be to improve the performance of quantum algorithms through optimal control taking into account the coupling of the system with the external environment. We will seek to implement quantum gates in the shortest possible time using several approaches. We will use techniques from optimal quantum control theory, such as the Krotov method, as well as methods based on machine learning. This study aims to reveal concrete examples of how quantum control can relate to quantum computing and provide insights into the design of quantum algorithms in light of optimal quantum control. (AU)