| Abstract: | One of the foundational ideas of the field of quantum computing is the belief that quantum devices can efficiently simulate the dynamics of other quantum systems - a problem recognized as fundamental in condensed matter physics, quantum chemistry, and quantum computing. In this talk, building on recent research efforts aimed at finding pathways to unlock the potential of quantum computers available today and in the future, I'll present two approaches that enhance the capabilities of these devices for quantum simulation by combining quantum computing with classical computing and classical deep learning. In particular, I'll begin by introducing a variational hybrid quantum-classical algorithm to simulate the Lindblad master equation for time-evolving Markovian open quantum systems. This algorithm is based on low-depth variational quantum circuits that can efficiently capture the non-unitary dynamics of the solution. In the second part, I'll present a method that combines “shadow tomography” of quantum states generated on a quantum device with classical deep learning tools, to efficiently simulate the “classical shadow” of a unitary time evolution governed by some Hamiltonian. This approach enables accurate predictions of the time evolution over a broad time range and starting from any initial state. In particular, we demonstrate that this method can accurately predict long-time dynamics when primarily trained on data from shorter time intervals, offering a valuable advantage for applying error mitigation techniques. |