Evaluation of Parameterized Quantum Circuits: on the relation between classification accuracy, expressibility and entangling capability
This addresses the problem of evaluating quantum circuit design for machine learning, but it is incremental as it builds on prior methods and quantifications.
The study investigated whether a quantum circuit's ability to uniformly address the Hilbert space correlates with classification accuracy in parameterized quantum circuits, finding a strong correlation for circuits with single embedding layers and 1-2 layers across 19 circuits and 9 datasets.
An active area of investigation in the search for quantum advantage is Quantum Machine Learning. Quantum Machine Learning, and Parameterized Quantum Circuits in a hybrid quantum-classical setup in particular, could bring advancements in accuracy by utilizing the high dimensionality of the Hilbert space as feature space. But is the ability of a quantum circuit to uniformly address the Hilbert space a good indicator of classification accuracy? In our work, we use methods and quantifications from prior art to perform a numerical study in order to evaluate the level of correlation. We find a strong correlation between the ability of the circuit to uniformly address the Hilbert space and the achieved classification accuracy for circuits that entail a single embedding layer followed by 1 or 2 circuit designs. This is based on our study encompassing 19 circuits in both 1 and 2 layer configuration, evaluated on 9 datasets of increasing difficulty. Future work will evaluate if this holds for different circuit designs.