Block Encoding of Non-Unitary Matrices Into Quantum Framework
Varun Puram, K. M. George, Johnson P. Thomas · 2025
Block encoding of non-unitary matrices in a quantum framework is a transformative technique for broadening the capabilities of quantum algorithms, allowing them to address a wider range of computational challenges. This paper introduces a novel embedding method to construct unitary matrices from non-unitary matrices, enabling their efficient encoding into quantum circuits. Utilizing the Gram-Schmidt process, the proposed approach embeds an$n \times n$non-unitary matrix$A$into a$2 n \times 2 n$unitary matrix$U_{A}$. When Compared to conventional methods such as Singular Value Decomposition (SVD), our approach achieves a 20 % faster execution time while maintaining high accuracy. Block encoding method has the potential to significantly advance quantum computing applicability by building unitary matrices from non-unitary ones in areas like optimization, quantum machine learning, and large-scale quantum simulations.