This content originally appeared on HackerNoon and was authored by Eigenvector Initialization Publication
:::info Authors:
(1) Nhat A. Nghiem, Department of Physics and Astronomy, State University of New York (email: nhatanh.nghiemvu@stonybrook.edu);
(2) Tzu-Chieh Wei, Department of Physics and Astronomy, State University of New York and C. N. Yang Institute for Theoretical Physics, State University of New York.
:::
Table of Links
Acknowledgements, Declarations, Data Availability Statement, and References
Appendix A: Review of Chebyshev Approach
Here we make a review of Chebyshev approach that was employed in [2], which is essentially built upon quantum walk technique [6, 8]. What we will describe below is more or less a summary of Section 4 in Ref. [2], the result of which was used in our main text.
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\ The so-called walk operator is defined as:
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\ Let |λ⟩ and λ be eigenvector and eigenvalue of A/d (note that the scaling by d doesn’t have further systematic problem, as the spectrum remains the same, only eigenvalues got scaled by a factor). Within the subspace spanned by T |λ⟩ and ST |λ⟩, W admits the following block form:
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\ The proof can be found in Lemma 15 of [2]. The above form of W possess the following remarkable property (Lemma 16 of [2]),
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:::info This paper is available on arxiv under CC 4.0 license.
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This content originally appeared on HackerNoon and was authored by Eigenvector Initialization Publication
Eigenvector Initialization Publication | Sciencx (2024-06-15T15:00:28+00:00) An Improved Method for Quantum Matrix Multiplication: Appendix A. Retrieved from https://www.scien.cx/2024/06/15/an-improved-method-for-quantum-matrix-multiplication-appendix-a/
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