Pseudo-dimension of quantum circuits
Quantum Physics
2020-11-10 v3 Machine Learning
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.
Cite
@article{arxiv.2002.01490,
title = {Pseudo-dimension of quantum circuits},
author = {Matthias C. Caro and Ishaun Datta},
journal= {arXiv preprint arXiv:2002.01490},
year = {2020}
}
Comments
22 pages, 1 figure; corrected Lemma 3.8, this does not change our results