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arXiv · 2103.09232

Simultaneous Perturbation Stochastic Approximation of the Quantum Fisher Information

Julien Gacon·Christa Zoufal·Giuseppe Carleo·Stefan Woerner
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Abstract

The Quantum Fisher Information matrix (QFIM) is a central metric in promising algorithms, such as Quantum Natural Gradient Descent and Variational Quantum Imaginary Time Evolution. Computing the full QFIM for a model with $d$ parameters, however, is computationally expensive and generally requires $\mathcal{O}(d^2)$ function evaluations. To remedy these increasing costs in high-dimensional parameter spaces, we propose using simultaneous perturbation stochastic approximation techniques to approximate the QFIM at a constant cost. We present the resulting algorithm and successfully apply it to prepare Hamiltonian ground states and train Variational Quantum Boltzmann Machines.

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Julien Gacon, Christa Zoufal, Giuseppe Carleo, Stefan Woerner. 2021-03-15. Simultaneous Perturbation Stochastic Approximation of the Quantum Fisher Information. https://doi.org/10.22331/q-2021-10-20-567

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