PIF2024 - Quantum algorithms for thermal equilibrium (PID2023-150847NA-I00)

We are seeing a dramatic growth in the quality and size of quantum computers and quantum simulators, which are expected to yield numerous scientific breakthroughs in the coming years. In this project, we will push the boundary of the range of fundamental physics problems that can be probed with those new devices. We focus on one of the most pressing questions along these lines: that of studying thermal equilibrium with quantum computers. The key task we want to be able to do is to prepare Gibbs states of a wide range of temperatures by means of various quantum algorithms. This is important both for the exploration of physics at finite temperature, and for the execution of numerous other quantum algorithms for a variety of computational tasks, such as optimization. In doing so, we will extend the range in which this problem is in the complexity class BQP, of problems that can be solved with quantum computers. We will construct abstract algorithms with rigorous mathematical guarantees. The project is of an eminently mathematical physics nature, and relies on a range of theoretical tools from both quantum physics and theoretical algorithmic design. A level of mathematical rigour is typically needed to make our targeted grounded complexity-theoretic statements, such as placing a specific problem in a given complexity class.