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.

翻译：我们用假二元来描述量子电路的表达力,这是概率概念等级的复杂度。我们证明在量子电路的输出概率分布上有伪二元界限;上界是电路深度和门数的多元线。我们利用这些界限展示了一组电路输出状态,其中至少有一组电路输出状态具有指数性复杂度,此外,我们还证明已知多元体大小和深度的量子电路是PAC可忽略的。