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arXiv · 2401.09007

Quantum singular value transformation for an arbitrary bounded operator embedded in a unitary operator

Chusei Kiumi·Akito Suzuki
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Abstract

This research extends quantum singular value transformation (QSVT) for general bounded operators embedded in unitary operators on possibly infinite-dimensional Hilbert spaces. Through in-depth mathematical exploration, we have achieved a refined operator-theoretic understanding of QSVT, leading to a more streamlined approach. One of the key discoveries is that polynomial transformations in QSVT inherently apply to the entire operator, rather than being contingent on the selection of a specific basis. We expect that this research will pave the way for applying these insights to a broader range of problems in quantum information processing and provide analytical tools for quantum dynamics, such as quantum walks.

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Chusei Kiumi, Akito Suzuki. 2024-01-17. Quantum singular value transformation for an arbitrary bounded operator embedded in a unitary operator. https://arxiv.org/abs/2401.09007

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