Gate-Based Path integral Quantum Control applied to quantum chemistry

Abstract

Abstract The Path integral Quantum Control (PiQC) algorithm was recently introduced as a new approach
for computing optimal controls in continuous-time open and closed quantum systems. In this work,
we adapt the PiQC algorithm to optimize parametrized quantum circuits and refer to this version
of PiQC as the Gate-Based PiQC (GB-PiQC) algorithm. We apply GB-PiQC and the original
continuous-time version of PiQC for ground state preparation of electronic structure problems, and
benchmark them against the Variational Quantum Eigensolver (VQE), optimized using the stan-
dard Simultaneous Perturbation Stochastic Approximation (SPSA) optimizer, on a set of standard
benchmark molecular Hamiltonians. For a fair comparison, we optimize the hyperparameters of the
algorithms for each molecule. We find that both PiQC algorithms exhibit greater robustness than
SPSA to variations in the target Hamiltonian induced by changes in interatomic distance, when
hyperparameters for both methods are fixed at values tuned near equilibrium. Furthermore, PiQC
algorithms also achieve superior performance compared to SPSA in most instances under this fixed-
hyperparameter setting, particularly at stretched interatomic distances, where the Hartree–Fock
(HF) solution becomes less accurate and its error grows relative to equilibrium