# A quantum neural network framework for scalable quantum circuit approximation of unitary matrices

arXiv: https://arxiv.org/abs/2405.00012 · HTML: https://mlsanity.com/paper/2405.00012/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Feb 2024.

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

- [Quantum State Preparation with the QNN-based SRBB Algorithm](https://mlsanity.com/paper/2503.13647/) (2025)

## Abstract (arXiv)

In this paper, we develop a Lie group theoretic approach for parametric representation of unitary matrices. This leads to develop a quantum neural network framework for quantum circuit approximation of multi-qubit unitary gates. Layers of the neural networks are defined by product of exponential of certain elements of the Standard Recursive Block Basis, which we introduce as an alternative to Pauli string basis for matrix algebra of complex matrices of order 2n. The recursive construction of the neural networks implies that the quantum circuit approximation is scalable i.e. quantum circuit for an (n+1)-qubit unitary can be constructed from the circuit of n-qubit system by adding a few CNOT gates and single-qubit gates.