Benchmarking of Different Optimizers in the Variational Quantum
  Algorithms for Applications in Quantum Chemistry
Classical optimizers play a crucial role in determining the accuracy and
convergence of variational quantum algorithms. In literature, many optimizers,
each having its own architecture, have been employed expediently for different
applications. In this work, we consider a few popular optimizers and assess
their performance in variational quantum algorithms for applications in quantum
chemistry in a realistic noisy setting. We benchmark the optimizers with
critical analysis based on quantum simulations of simple molecules, such as
Hydrogen, Lithium Hydride, Beryllium Hydride, water, and Hydrogen Fluoride. The
errors in the ground-state energy, dissociation energy, and dipole moment are
the parameters used as yardsticks. All the simulations were carried out with an
ideal quantum circuit simulator, a noisy quantum circuit simulator, and a noisy
simulator with noise embedded from the IBM Cairo quantum device to understand
the performance of the classical optimizers in ideal and realistic quantum
environments. We used the standard unitary coupled cluster (UCC) ansatz for
simulations, and the number of qubits varied from two, starting from the
Hydrogen molecule to ten qubits, in Hydrogen Fluoride. Based on the performance
of these optimizers in the ideal quantum circuits, the conjugate gradient (CG),
limited-memory Broyden-Fletcher-Goldfarb-Shanno bound (L_BFGS)B), and
sequential least squares programming (SLSQP) optimizers are found to be the
best-performing gradient-based optimizers. While constrained optimization by
linear approximation (COBYLA) and POWELL perform most efficiently among the
gradient-free methods. However, in noisy quantum circuit conditions,
Simultaneous Perturbation Stochastic Approximation (SPSA), POWELL, and COBYLA
are among the best-performing optimizers.
Harshdeep Singh Sabyashachi Mishra Sonjoy Majumder