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 withdparameters, however, is computationally expensive and generally requiresO(d2)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.
Highlights
Quantum computing promises potential advances in many fields, such as quantum chemistry and physics [1,2,3], biology [4,5,6], optimization [7,8,9,10], finance [11], and machine learning [12,13,14]
We analyze how QN-Simultaneous Perturbation Stochastic Approximation (SPSA) performs compared with Quantum Natural Gradient (QNG) for ground state approximation, and, second, we show how VarQBMs perform when the Gibbs states are prepared with Variational Quantum Imaginary Time Evolution (VarQITE) when the Quantum Fisher Information matrix (QFIM) is approximated using 2-SPSA
We show that Quantum Natural SPSA (QN-SPSA) enables the realization of an approximate VarQBM implementation, where the computational complexity is reduced compared to standard VarQITE-based Gibbs state preparation
Summary
Quantum computing promises potential advances in many fields, such as quantum chemistry and physics [1,2,3], biology [4,5,6], optimization [7,8,9,10], finance [11], and machine learning [12,13,14]. While fault-tolerant quantum computers are not yet in reach, a computational paradigm suitable for near-term, noisy quantum devices is that of variational quantum algorithms These consist of a feedback loop between a classical and a quantum computer, where the objective function, usually based on a parameterized quantum circuit, is evaluated on the quantum computer and a classical counterpart updates the parameters to find their optimal value [15]. One significant drawback of VarQITE and QNG is that it requires evaluating the Quantum Fisher Information matrix (QFIM) at every iteration This operation has a cost scaling quadratically with the number of circuit parameters and is computationally expensive for complex objective function with a large number of variational parameters. For details as well as the proof of convergence, we refer to Sec. 3 in Ref. [29]
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