Solution of Systems of Differential Equations in Quantum Computers

• Grant number: 22/13351-5
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: February 01, 2023
• End date: December 31, 2024
• Field of knowledge: Physical Sciences and Mathematics - Physics - General Physics
• Principal Investigator: Celso Jorge Villas-Bôas
• Grantee: Paulo César Souza Pavoleti
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

With the present project we will work with the implementation of quantum algorithms for the solution of systems of coupled differential equations in IBM quantum computers and we will investigate ways to reduce the complexity of such algorithms. This is a subject that has been studied in our research group for a long time, which made it possible for us to perceive some difficulties in obtaining quantum advantage in many algorithms already proposed. For example, given the complexity of preparing and/or tomography quantum states of very large N dimension, the total complexity of quantum algorithms can be comparable to the complexity of solving the same system in classical computers. Thus, with the present project we will investigate ways to reduce the complexity of extracting information from a quantum computer, that is, ways that do not require tomography and/or knowledge of state amplitudes, for example via encoding the desired information into expected values of the qubits of the quantum computer.