Explicit Quantum Circuits for Block Encodings of Certain Sparse Matrices Article Swipe
Daan Camps
,
Lin Lin
,
Roel Van Beeumen
,
Chao Yang
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1137/22m1484298
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1137/22m1484298
Many standard linear algebra problems can be solved on a quantum computer by using recently developed quantum linear algebra algorithms that make use of block encodings and quantum eigenvalue/singular value transformations. A block encoding embeds a properly scaled matrix of interest A in a larger unitary transformation U that can be decomposed into a product of simpler unitaries and implemented efficiently on a quantum computer. Although quantum algorithms can potentially achieve exponential speedup in solving linear algebra problems compared to the best classical algorithm, such a gain in efficiency ultimately hinges on our ability to construct an efficient quantum circuit for the block encoding of A, which is difficult in general, and not trivial even for well structured sparse matrices. Here, in this paper, we give a few examples on how efficient quantum circuits can be explicitly constructed for some well structured sparse matrices and discuss a few strategies used in these constructions. We also provide implementations of these quantum circuits in MATLAB.
Related Topics
Concepts
Linear algebra
Quantum algorithm
Quantum phase estimation algorithm
Eigenvalues and eigenvectors
Mathematics
Quantum computer
Algebra over a field
Quantum
Algorithm
Singular value decomposition
Quantum circuit
Computer science
Quantum error correction
Pure mathematics
Quantum mechanics
Geometry
Physics
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1137/22m1484298
- OA Status
- gold
- Cited By
- 39
- References
- 26
- Related Works
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- OpenAlex ID
- https://openalex.org/W4392662757
All OpenAlex metadata
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https://openalex.org/W4392662757Canonical identifier for this work in OpenAlex
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https://doi.org/10.1137/22m1484298Digital Object Identifier
- Title
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Explicit Quantum Circuits for Block Encodings of Certain Sparse MatricesWork title
- Type
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articleOpenAlex work type
- Language
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enPrimary language
- Publication year
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2024Year of publication
- Publication date
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2024-03-11Full publication date if available
- Authors
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Daan Camps, Lin Lin, Roel Van Beeumen, Chao YangList of authors in order
- Landing page
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https://doi.org/10.1137/22m1484298Publisher landing page
- Open access
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YesWhether a free full text is available
- OA status
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goldOpen access status per OpenAlex
- OA URL
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https://escholarship.org/uc/item/4wv2h6psDirect OA link when available
- Concepts
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Linear algebra, Quantum algorithm, Quantum phase estimation algorithm, Eigenvalues and eigenvectors, Mathematics, Quantum computer, Algebra over a field, Quantum, Algorithm, Singular value decomposition, Quantum circuit, Computer science, Quantum error correction, Pure mathematics, Quantum mechanics, Geometry, PhysicsTop concepts (fields/topics) attached by OpenAlex
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39Total citation count in OpenAlex
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2025: 28, 2024: 9, 2023: 2Per-year citation counts (last 5 years)
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