To reproduce the ground-state energy of a one-dimensional transverse-field Ising chain near its critical point, a restricted Boltzmann machine needs a number of weights that grows as the square of the number of qubits, while the training data needed grows only linearly.
Sampling scheme for neuromorphic simulation of entangled quantum systems
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abstract
Due to the complexity of the space of quantum many-body states the computation of expectation values by statistical sampling is, in general, a hard task. Neural network representations of such quantum states which can be physically implemented by neuromorphic hardware could enable efficient sampling. A scheme is proposed which leverages this capability to speed up sampling from so-called neural quantum states encoded by a restricted Boltzmann machine. Due to the complex network parameters a direct hardware implementation is not feasible. We overcome this problem by considering a phase reweighting scheme for sampling expectation values of observables. Applying our method to a set of paradigmatic entangled quantum states we find that, in general, the phase-reweighted sampling is subject to a form of sign problem, which renders the sampling computationally costly. The use of neuromorphic chips could allow reducing computation times and thereby extend the range of tractable system sizes.
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The learnability scaling of quantum states: restricted Boltzmann machines
To reproduce the ground-state energy of a one-dimensional transverse-field Ising chain near its critical point, a restricted Boltzmann machine needs a number of weights that grows as the square of the number of qubits, while the training data needed grows only linearly.