Yaroslav Herasymenko (QuTech [TU Delft], QuSoft [CWI, Amsterdam])
In this presentation, I will talk about two problems in quantum computation: (1) how to efficiently simulate a many-body system? And (2) given a simulated quantum state, how to efficiently learn this state from the measurements? In particular, I will focus on the systems composed of fermionic particles, and the settings which are close to non-interacting. Simulations of non-interacting fermions can often be done efficiently on a classical computer. However, for large systems they become prohibitive. To meet this challenge, we provide a quantum algorithm to simulate free-fermion evolutions and thermal states. In particular, I will talk about the speedup that a quantum computer can offer in solving this problem, ranging from a substantial algebraic up to exponential, depending on the system. Switching gears to the quantum learning problem, I will explain how to efficiently learn states which come from quantum circuits dominated by free-fermionic gates. Our learning algorithm is essentially optimal and also applicable to impurity model evolutions, as will be briefly discussed. I will close by describing some open directions in quantum computing for fermionic systems, such as the accelerated simulation of so-called ’sign-free’ interacting systems, and learning of unitaries rather than the states.
The talk will be based on the recent works arXiv:2409.04550 (under review) and arXiv:2402.18665 (PRX Quantum, to appear).
Contact : B. Georgeot