# A Novel Single-Layer Quantum Neural Network for Approximate SRBB-Based Unitary Synthesis

arXiv: https://arxiv.org/abs/2412.03083 · HTML: https://mlsanity.com/paper/2412.03083/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 31 references that are in the map.
- First posted on arXiv 4 Dec 2024.

## Builds on (most cited first, 6 of 6)

- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [Best Approximate Quantum Compiling Problems](https://mlsanity.com/paper/2106.05649/) (2021)
- [Efficient decomposition of unitary matrices in quantum circuit compilers](https://mlsanity.com/paper/2101.02993/) (2021)
- [Scalable quantum circuits for n-qubit unitary matrices](https://mlsanity.com/paper/2304.14096/) (2023)
- [Sketching the Best Approximate Quantum Compiling Problem](https://mlsanity.com/paper/2205.04025/) (2022)

## Built on by (most cited first, 1 of 1)

- [Approximate Quantum State Preparation Through Proximal Policy Optimization](https://mlsanity.com/paper/2607.21121/) (2026)

## Abstract (arXiv)

In this work, a novel quantum neural network is introduced as a means to approximate any unitary evolution through the Standard Recursive Block Basis (SRBB) and is subsequently redesigned with the number of CNOTs asymptotically reduced by an exponential contribution. This algebraic approach to the problem of unitary synthesis exploits Lie algebras and their topological features to obtain scalable parameterizations of unitary operators. First, the original SRBB-based scalability scheme, already known in the literature only from a theoretical point of view, is reformulated for efficient algorithm implementation and complexity management. Remarkably, 2-qubit operators emerge as a special case of the original scaling scheme. Furthermore, an algorithm is proposed to reduce the number of CNOT gates in the scalable variational quantum circuit, thus deriving a new implementable scaling scheme that requires only one layer of approximation. The single layer CNOT-reduced quantum neural network is implemented, and its performance is assessed with a variety of different unitary matrices, both sparse and dense, up to 6 qubits via the PennyLane library. The effectiveness of the approximation is measured with different metrics in relation to two optimizers: a gradient-based method and the Nelder-Mead method. The approximate CNOT-reduced SRBB-based synthesis algorithm is also tested on real hardware and compared with other valid approximation and decomposition methods available in the literature.