Block encoding of sparse structured matrices coming from ocean acoustics in quantum computing

• URL: http://arxiv.org/abs/2405.18007v2
• Date: Tue, 9 Jul 2024 07:33:45 GMT
• Title: Block encoding of sparse structured matrices coming from ocean acoustics in quantum computing
• Authors: Chunlin Yang, Hongmei Yao, Zexian Li, Zhaobing Fan, Guofeng Zhang, Jianshe Liu,
• Abstract summary: Block encoding is a data input model commonly used in a quantum computer. New base scheme of block encoding is given which generalizes the one in citecamps2024 by removing the constraint that every data item should appear in all columns.
• Score: 2.4487770108795393
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Block encoding is a data input model commonly used in a quantum computer. It is an ingenious technique that embeds a matrix $A$ satisfying $\left\|A/ \alpha \right\| \leq 1$ into a larger unitary matrix $U_{A}$. Its complexity can affect the complexity of quantum algorithms in the framework of block encoding. In this paper, a new base scheme of block encoding is given which generalizes the one in \cite{camps2024explicit} by removing the constraint that every data item should appear in all columns. And applying preamplification and state preparation methods, the base scheme is further improved, which results in lower \textit{figures of merit} than that in special case \cite{sunderhauf2024block}. Then, the construction of oracles in block encoding schemes are discussed in detail. Considering special sparse structured matrices coming from ocean acoustics, two concrete examples are used to illustrate the feasibility of the proposed base scheme of block encoding and their explicit quantum circuits are implemented. Finally, the corresponding \verb|MATLAB| codes are presented to effectively simulate the quantum circuits.

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