Pulse-based Variational Quantum Optimal Control for hybrid quantum computing

This work studies pulse-based variational quantum algorithms (VQAs), which are designed to determine the ground state of a quantum mechanical system by combining classical and quantum hardware. In contrast to more standard gate-based methods, pulse-based methods aim to directly optimize the laser pulses interacting with the qubits, instead of using some parametrized gate-based circuit. Using the mathematical formalism of optimal control, these laser pulses are optimized. This method has been used in quantum computing before to design pulses for quantum gate implementations, but has only recently been proposed for full optimization in VQAs [1, 2]. Pulse-based methods have several advantages over gate-based methods, such as faster state preparation, simpler implementation and more freedom in moving through the state space [3]. Based on these ideas, we present the development of a variational quantum algorithm employing adjoint-based optimal control techniques. This method can be tailored towards and applied in neutral atom quantum computers. Pulse-based variational quantum optimal control is able to approximate molecular ground states of simple molecules beyond chemical accuracy. Furthermore, it is able to compete with, or even outperform, the gate-based variational quantum eigensolver in terms of total number of quantum evaluations. The total evolution time T and the form of the control Hamiltonian Hc are important factors in the convergence behaviour to the ground state energy, both having influence on the quantum speed limit and the controllability of the system.