Qudit-based variational quantum eigensolver using photonic orbital angular momentum states.

Solving the electronic structure problem is a notorious challenge in quantum chemistry and material science. Variational quantum eigensolver (VQE) is a promising hybrid classical-quantum algorithm for finding the lowest-energy configuration of a molecular system. However, it typically requires many qubits and quantum gates with substantial quantum circuit depth to accurately represent the electronic wave function of complex structures. Here, we propose an alternative approach to solve the electronic structure problem using VQE with a single qudit. Our approach exploits a high-dimensional orbital angular momentum state of a heralded single photon and notably reduces the required quantum resources compared to conventional multi-qubit-based VQE. We experimentally demonstrate that our single-qudit-based VQE can efficiently estimate the ground state energy of hydrogen (H) and lithium hydride (LiH) molecular systems corresponding to two- and four-qubit systems, respectively. We believe that our scheme opens a pathway to perform a large-scale quantum simulation for solving more complex problems in quantum chemistry and material science.