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

arXiv: https://arxiv.org/abs/2003.09887 · HTML: https://mlsanity.com/paper/2003.09887/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Mar 2020.

## Built on by (most cited first, 2 of 2)

- [Beyond Ans"atze: Learning Quantum Circuits as Unitary Operators](https://mlsanity.com/paper/2203.00601/) (2022)
- [Towards Efficient Ansatz Architecture for Variational Quantum Algorithms](https://mlsanity.com/paper/2111.13730/) (2021)

## Abstract (arXiv)

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.