In recent years, various quantum algorithms have been proposed to approach problems in chemistry, machine learning, and combinatorial optimization. While the problem specifications may differ, these belong to a class called “variational quantum algorithms”: those that are well-suited for execution on small, noisy quantum computers by dividing up computational tasks between quantum and classical computing resources. A current challenge in the field is to scale these algorithms to approach larger and more difficult problem instances. To address this challenge, we investigated a common component in variational quantum algorithms that is crucial to the performance: parameterized quantum circuits. To make a more informed decision on which parameterized circuits to use for a given algorithm, we define several descriptors, namely expressibility and entangling capability, that can be used to compare and contrast circuit designs. While a thorough benchmark study is necessary to understand which circuits are better suited to particular algorithms, methods and results from this study can be useful for both algorithm development and design of experiments for near-term quantum computers.
