Matrix encoding method in variational quantum singular value decomposition

• URL: http://arxiv.org/abs/2504.02838v3
• Date: Sun, 03 Aug 2025 06:58:04 GMT
• Title: Matrix encoding method in variational quantum singular value decomposition
• Authors: Alexander I. Zenchuk, Wentao Qi, Junde Wu,
• Abstract summary: We propose the variational quantum singular value decomposition based on encoding the elements of the considered $Ntimes N$ matrix into the state of a quantum system of appropriate dimension.<n> Controlled measurement is involved to avoid small success in ancilla measurement.
• Score: 49.494595696663524
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose the variational quantum singular value decomposition based on encoding the elements of the considered { $N\times N$} matrix into the state of a quantum system of appropriate dimension. This method doesn't use the expansion of this matrix in terms of the unitary matrices. Controlled measurement is involved to avoid small success probability in ancilla measurement. The objective function for maximization algorithm can be obtained probabilistically via measurement of the states of { two} one-qubit subsystems. The circuit requires $O(\log N)$ qubits for realization of this algorithm { whose depths is proportional to $ \log N/\varepsilon$, where $\varepsilon$ is the precision required for calculation of singular values.

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