Computer simulations are essential to understand many-body quantum systems. Numerical simulations have a central role in testing models and theoretical predictions, but they can also guide new experiments or the design of new materials.
While the equation governing the evolution of interacting quantum particles (electrons, ions, or spins) is known, the Schroedinger equation, its solution is far from being easy. Computational quantum science aims in general to solve, exactly or approximatively, quantum many-body problems that occur in Nature or that can be engineered in laboratories.
On the other hand, progress in controlling quantum systems is enabling now the fabrication of quantum processing units. These quantum computers could perform computations intractable for conventional -semiconductor based- computers. For instance, Feynman envisioned that only the use of quantum computer would unlock efficient simulations of quantum systems, ranging from quantum chemistry, materials science or high-energy physics. Moreover, quantum computers could also outperform conventional ones also for purely classical problems, such as integer factoring, linear algebra, and data processing, to name a few.
Our group at ICS is following both perspectives. We (1) advance simulations of quantum systems using new accurate methods, including quantum Monte Carlo and machine learning, especially targeting strongly interacting electrons, and correlated quantum spin models.
We also (2) devise new quantum algorithms in the quest for the first realization of practical quantum speed-up. More specifically, we study quantum algorithms for optimization and sampling of classical and quantum partition functions, with applications on classical and quantum spin models.