Trained quantum neural networks are Gaussian processes

arXiv:2402.08726v1 Announce Type: cross
Abstract: We study quantum neural networks made by parametric one-qubit gates and fixed two-qubit gates in the limit of infinite width, where the generated function is the expectation value of the sum of single-qubit observables over all the qubits. First, we prove that the probability distribution of the function generated by the untrained network with randomly initialized parameters converges in distribution to a Gaussian process whenever each measured qubit is correlated only with few other measured …

abstract arxiv cs.lg distribution function gates gaussian processes generated math.mp math-ph math.pr networks neural networks parametric probability processes prove quant-ph quantum quantum neural networks qubit qubits study type value