Speaker: Nicola Quadri

Title: Variational real-time evolution of U(1)-lattice gauge theories on digital quantum computers

Abstract: Gauge theories are essential for describing the fundamental interactions between particles in the Standard Model. However, simulating real-time dynamics in gauge theories remains the most challenging task for classical computers, since the dimension of the Hilbert space grows exponentially with the system size. Quantum computers can offer a decisive alternative, as the quantum resources required to simulate an exponentially growing Hilbert space only increase polynomially. In this context, many hybrid quantum-classical algorithms—or variational quantum algorithms (VQAs)—have been developed in recent years to exploit the current noisy quantum hardware. One of the most promising algorithms in terms of simulating the real-time evolution of a quantum system is the variational time evolution (VTE), which may require significantly less quantum resources than the Trotterization method that is conventionally employed for quantum dynamics simulations. However, this poses the main problem of finding a variational ansatz that is able to describe the exact state along the entire evolution. We explore the VTE of abelian gauge theories, such as quantum electrodynamics (QED), for a (1+1)-spacetime dimensional lattice. We first discretize and encode continuous QED on qubits. Then, we compare the performance of the VTE using a physically motivated variational ansatz—used so far for stationary VQAs—with the Trotterization method for a growing system size.

Speaker: Oriel Kiss

Title: Quantum Neural Networks for electronic structure calculations

Abstract: In a supervised learning setting, Quantum Neural Networks (QNNs) are quantum machine learning models described by the expectation value of some observable with respect to a quantum state expressed by a Parametrized Quantum Circuit (PQC). In this talk, we present a popular strategy to design this PQC, consisting of alternating encoding and variational layers, and apply this model to the computation of the potential energy surface and forces field for simple molecules. In chemistry applications, these can be used to drive molecular dynamics by integrating the equations of motion. We investigate the performances of our method in terms of accuracy and complexity, which are competitive with classical counterparts. In fact, QNNs can potentially achieve very high effective dimensions in model space, thus suggesting that they might be well suited to tackle complex learning tasks.