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

• URL: http://arxiv.org/abs/2401.09007v1
• Date: Wed, 17 Jan 2024 07:06:31 GMT
• Title: Quantum singular value transformation for an arbitrary bounded operator embedded in a unitary operator
• Authors: Chusei Kiumi, Akito Suzuki
• Abstract summary: This research extends quantum singular value transformation (QSVT) for general bounded operators embedded in unitary operators on possibly infinite-dimensional Hilbert spaces. We have achieved a refined operator-theoretic understanding of QSVT, leading to a more streamlined approach.
• Score: 0.65268245109828
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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