Simultaneous Perturbation Stochastic Approximation of the Quantum Fisher Information

• URL: http://arxiv.org/abs/2103.09232v2
• Date: Wed, 13 Oct 2021 17:55:14 GMT
• Title: Simultaneous Perturbation Stochastic Approximation of the Quantum Fisher Information
• Authors: Julien Gacon, Christa Zoufal, Giuseppe Carleo, Stefan Woerner
• Abstract summary: The Quantum Fisher Information matrix (QFIM) is a central metric in promising algorithms. We propose using simultaneous 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.
• Score: 0.716879432974126
• License: http://creativecommons.org/licenses/by/4.0/
• 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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