论文标题
参数量子电路的尺寸表达分析
Dimensional Expressivity Analysis of Parametric Quantum Circuits
论文作者
论文摘要
参数量子电路在许多变异量子算法的性能中起着至关重要的作用。为了成功实现此类算法，必须设计有效的量子电路，以足够近似于解决方案空间，同时保持较低的参数计数和电路深度。在本文中，我们开发了一种分析参数量子电路的尺寸表达性的方法。我们的技术允许在电路布局中识别多余的参数，并获得具有最少参数数量的最大表达式ANSATZ。使用混合量子古典方法，我们展示了如何使用量子硬件有效地实施表达性分析，并且我们提供了IBM量子硬件上此过程的原理证明。我们还讨论了对称性的效果，并演示了如何从参数化的ANSATZ中合并或删除对称性。
Parametric quantum circuits play a crucial role in the performance of many variational quantum algorithms. To successfully implement such algorithms, one must design efficient quantum circuits that sufficiently approximate the solution space while maintaining a low parameter count and circuit depth. In this paper, we develop a method to analyze the dimensional expressivity of parametric quantum circuits. Our technique allows for identifying superfluous parameters in the circuit layout and for obtaining a maximally expressive ansatz with a minimum number of parameters. Using a hybrid quantum-classical approach, we show how to efficiently implement the expressivity analysis using quantum hardware, and we provide a proof of principle demonstration of this procedure on IBM's quantum hardware. We also discuss the effect of symmetries and demonstrate how to incorporate or remove symmetries from the parametrized ansatz.
