# Ansatz-Independent Variational Quantum Classifier

arXiv: https://arxiv.org/abs/2102.01759 · HTML: https://mlsanity.com/paper/2102.01759/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 43 references that are in the map.
- First posted on arXiv 2 Feb 2021.

## Builds on (most cited first, 5 of 5)

- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Power of data in quantum machine learning](https://mlsanity.com/paper/2011.01938/) (2020)
- [Supervised quantum machine learning models are kernel methods](https://mlsanity.com/paper/2101.11020/) (2021)
- [A Domain-agnostic, Noise-resistant, Hardware-efficient Evolutionary Variational Quantum Eigensolver](https://mlsanity.com/paper/1910.09694/) (2019)

## Built on by (most cited first, 3 of 3)

- [Quantum Advantage in Variational Bayes Inference](https://mlsanity.com/paper/2207.03104/) (2022)
- [Quantum Approximation of Normalized Schatten Norms and Applications to Learning](https://mlsanity.com/paper/2206.11506/) (2022)
- [Quantum natural gradient without monotonicity](https://mlsanity.com/paper/2401.13237/) (2024)

## Abstract (arXiv)

The paradigm of variational quantum classifiers (VQCs) encodes textitclassical information as quantum states, followed by quantum processing and then measurements to generate classical predictions. VQCs are promising candidates for efficient utilization of a near-term quantum device: classifiers involving M-dimensional datasets can be implemented with only lceil log2 M rceil qubits by using an amplitude encoding. A general framework for designing and training VQCs, however, has not been proposed, and a fundamental understanding of its power and analytical relationships with classical classifiers are not well understood. An encouraging specific embodiment of VQCs, quantum circuit learning (QCL), utilizes an ansatz: it expresses the quantum evolution operator as a circuit with a predetermined topology and parametrized gates; training involves learning the gate parameters through optimization. In this letter, we first address the open questions about VQCs and then show that they, including QCL, fit inside the well-known kernel method. Based on such correspondence, we devise a design framework of efficient ansatz-independent VQCs, which we call the unitary kernel method (UKM): it directly optimizes the unitary evolution operator in a VQC. Thus, we show that the performance of QCL is bounded from above by the UKM. Next, we propose a variational circuit realization (VCR) for designing efficient quantum circuits for a given unitary operator. By combining the UKM with the VCR, we establish an efficient framework for constructing high-performing circuits. We finally benchmark the relatively superior performance of the UKM and the VCR via extensive numerical simulations on multiple datasets.