Characterization of Training Circuits for Hybrid Quantum-Classical Algorithms*

Performing useful computations with current and near-term quantum computers is becoming increasingly viable due to rapid advances in both algorithms and hardware. A class of algorithms that are promising candidates for demonstrating the utility of near-term quantum computers is the so called hybrid quantum-classical (HQC) algorithms. A common ingredient that plays a crucial role in the algorithmic performance of many HQC algorithms is the parametrized quantum circuit that is tuned to prepare quantum states relevant for (approximately) solving the problem of interest. Despite the importance of these circuits, they are often generated in the absence of a robust theoretical framework. In this work, we introduce several descriptors to characterize a set of parametrized circuits, including a measure of a circuit’s expressibility and how it correlates with algorithmic performance. Ultimately, having a deeper understanding of the qualities associated with an effective parametrized circuit can lead to significant improvements in the overall development of HQC algorithms.