Simulating self-consistent reference states on a quantum computer using optimized custom gates

Self-consistent reference states are a critical starting point for computing many phenomena in physics. The Hartree-Fock (HF) ground state is a ubiquitously used self-consistent reference state for advanced methods to describe both static and dynamic properties of quantum many-body systems. It has been shown that the HF method can be implemented on a superconducting quantum computer by realizing the basis rotation using Givens rotations on a parametrized quantum circuit. In this work, we optimize this procedure by employing optimal control pulse theory to find customized microwave pulses that realize the Givens rotation gate. This leads to a significant reduction in the implementation time of the quantum HF algorithm and a high-fidelity Givens gate. Furthermore, we use machine learning to generalize our method to find optimal pulses for a family of Givens gates parametrized by a continuous variable of the rotation angle. We test the accuracy of our method on exactly solvable nuclear models and observed a good agreement. Thereby, this work contributes towards transformative calculations of quantum simulations on near-term quantum devices.