Operational Natural Gradients For Variational Quantum Algorithms*

One of the obvious uses for a quantum computer is as a co-processor for a quantum machine learning problems. Combining this with traditional optimisation and machine learning techniques would give an efficient process to approximate the ground state of a given Hamiltonian.

Given a quantum computer, gradient descent can be used to optimise a quantum circuit ansatz (using the parameter shift rule) but may have problems with local minima. This can be improved, in terms of higher accuracies/fewer iterations of optimisation, via quantum natural gradient optimisation (based on natural gradient optimisation) [1]. However the quantum natural gradient requires more samples per iteration, possibly requiring more samples than other gradient descent algorithms [2].

Here I will present an alternate natural gradient technique for ground state minimisation that abstracts away the wave function and focuses on the output distribution used to compute the Energy. This process requires the same number of samples as (non-natural) gradient descent algorithms but achieves similar accuracies to the quantum natural gradient.

[1] J. Stokes, J. Izaac, N. Killoran, G. Carleo Quantum, 4, 269 (2020)
[2] D. Wiecrichs, C. Gogolin, M. Kastoryano, arXiv:2004.14666