Improved optimization algorithm for use in variational quantum eigensolvers

Quantum algorithms for treating nuclear and electronic structure problems face a host of challenges in order to run successfully on both near-term and future fault tolerant quantum computers. For variation quantum eigensolvers (VQE), one such challenge is how to optimize parameters dictating the wavefunction efficiently i.e. with few function evaluations in the presence of noisy energy evaluation. This has typically been done with classic optimizers, but these will begin to pose problems as the parameter sets required to treat larger realistic systems grow. Here I present an algorithm that, at the cost of extra Pauli expectation values, allows for a faithful estimation of the parameter gradient of several classes of wavefunctions. I apply this algorithm to the treatment of the deuteron and H₂, and show that it gives a much faster convergence in terms of overall function evaluations when compared to classic optimizers, and this advantage increases with parameter set size. This presents a promising step forward in pushing for treating realistic systems with quantum computers.