论文标题
量子电路的伪维
Pseudo-dimension of quantum circuits
论文作者
论文摘要
我们用伪维数来表征量子电路的表达能力，这是概率概念类别的复杂性的度量。我们证明了量子电路的输出概率分布的伪维数；上限在电路深度和大门的数量上是多项式。使用这些边界，我们表现出一类电路输出状态，其中至少一个具有指数状态的复杂性，此外表明，已知的多项式大小和深度的量子电路是可以pac-learnnnnn的。
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.
