# Beyond Ans"atze: Learning Quantum Circuits as Unitary Operators

arXiv: https://arxiv.org/abs/2203.00601 · HTML: https://mlsanity.com/paper/2203.00601/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 37 references that are in the map.
- First posted on arXiv 1 Mar 2022.

## Builds on (most cited first, 9 of 9)

- [Neural Architecture Search with Reinforcement Learning](https://mlsanity.com/paper/1611.01578/) (2016)
- [Robust data encodings for quantum classifiers](https://mlsanity.com/paper/2003.01695/) (2020)
- [DeepSat - A Learning framework for Satellite Imagery](https://mlsanity.com/paper/1509.03602/) (2015)
- [Application of Quantum Annealing to Training of Deep Neural Networks](https://mlsanity.com/paper/1510.06356/) (2015)
- [On Circuit-based Hybrid Quantum Neural Networks for Remote Sensing Imagery Classification](https://mlsanity.com/paper/2109.09484/) (2021)
- [Capacity and quantum geometry of parametrized quantum circuits](https://mlsanity.com/paper/2102.01659/) (2021)
- [Quantum versus Classical Generative Modelling in Finance](https://mlsanity.com/paper/2008.00691/) (2020)
- [Synthetic weather radar using hybrid quantum-classical machine learning](https://mlsanity.com/paper/2111.15605/) (2021)
- [Evaluation of Parameterized Quantum Circuits: on the relation between classification accuracy, expressibility and entangling capability](https://mlsanity.com/paper/2003.09887/) (2020)

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

- [On the impact of key design aspects in simulated Hybrid Quantum Neural Networks for Earth Observation](https://mlsanity.com/paper/2410.08677/) (2024)
- [Soft-Quantum Algorithms](https://mlsanity.com/paper/2604.06523/) (2026)

## Abstract (arXiv)

This paper explores the advantages of optimizing quantum circuits on N wires as operators in the unitary group U(2N). We run gradient-based optimization in the Lie algebra mathfrak u(2N) and use the exponential map to parametrize unitary matrices. We argue that U(2N) is not only more general than the search space induced by an ansatz, but in ways easier to work with on classical computers. The resulting approach is quick, ansatz-free and provides an upper bound on performance over all ans"atze on N wires.