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

An active area of investigation in the search for quantum advantage is\nQuantum Machine Learning. Quantum Machine Learning, and Parameterized Quantum\nCircuits in a hybrid quantum-classical setup in particular, could bring\nadvancements in accuracy by utilizing the high dimensionality of the Hilbert\nspace as feature space. But is the ability of a quantum circuit to uniformly\naddress the Hilbert space a good indicator of classification accuracy? In our\nwork, we use methods and quantifications from prior art to perform a numerical\nstudy in order to evaluate the level of correlation. We find a strong\ncorrelation between the ability of the circuit to uniformly address the Hilbert\nspace and the achieved classification accuracy for circuits that entail a\nsingle embedding layer followed by 1 or 2 circuit designs. This is based on our\nstudy encompassing 19 circuits in both 1 and 2 layer configuration, evaluated\non 9 datasets of increasing difficulty. Future work will evaluate if this holds\nfor different circuit designs.\n