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arXiv · 2002.01490

Pseudo-dimension of quantum circuits

Matthias C. Caro·Ishaun Datta
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Abstract

We characterize the expressive power of quantum circuits with the pseudo-dimension, a measure of complexity for probabilistic concept classes. We prove pseudo-dimension bounds on the output probability distributions of quantum circuits; the upper bounds are polynomial in circuit depth and number of gates. Using these bounds, we exhibit a class of circuit output states out of which at least one has exponential state complexity, and moreover demonstrate that quantum circuits of known polynomial size and depth are PAC-learnable.

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Matthias C. Caro, Ishaun Datta. 2020-11-09. Pseudo-dimension of quantum circuits. https://doi.org/10.1007/s42484-020-00027-5

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