Evaluation of Parameterized Quantum Circuits: on the design, and the relation between classification accuracy, expressibility and entangling capability

Quantum computers promise improvements in terms of both computational speedup and increased accuracy. Relevant areas are optimization, chemistry and machine learning, of which we will focus on the latter. Much of the prior art focuses on determining computational speedup, but how do we know if a particular quantum circuit shows promise for achieving high classification accuracy? Previous work by Sim et al. proposed descriptors to characterize and compare Parameterized Quantum Circuits. In this work, we will investigate any potential relation between the classification accuracy and two of these descriptors, being expressibility and entangling capability. We will first investigate different types of gates in quantum circuits and the changes they incur on the decision boundary. From this, we will propose design criteria for constructing circuits. We will also numerically compare the classifications performance of various quantum circuits and their quantified measure of expressibility and entangling capability, as derived in previous work. From this, we conclude that the common approach to layer combinations of rotational gates and conditional rotational gates provides the best accuracy. We also show that, for our experiments on a limited number of circuits, a coarse-grained relationship exists between entangling capability and classification accuracy, as well as a more fine-grained correlation between expressibility and classification accuracy. Future research will need to be performed to quantify this relation.