Simultaneous Perturbation Stochastic Approximation of the Quantum Fisher Information

The Quantum Fisher Information matrix (QFIM) is a central metric in promising algorithms, such as Natural Gradient Descent and Variational Imaginary Time Evolution. Computing the full QFIM for model withdparameters, however, computationally expensive generally requiresO(d2)function evaluations. To remedy these increasing costs high-dimensional parameter spaces, we propose using simultaneous perturbation stochastic approximation techniques to approximate at constant cost. We present resulting algorithm successfully apply it prepare Hamiltonian ground states train Boltzmann Machines.