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Block Encoding Matrices with Single-Entry Columns

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⚡ Quantum Brief
A quantum computing researcher seeks efficient methods to block-encode sparse matrices where each column contains exactly one non-zero entry, representing computational basis vectors. The challenge involves matrices that may have repeating indices. The matrix in question is an N×N structure where columns are basis vectors, formalized as a sum of outer products. This structure resembles permutation matrices but allows duplicates, complicating standard encoding approaches. The query highlights a need for quantum algorithms that can handle such matrices without full permutation constraints. Efficient block encoding could enable faster quantum linear algebra operations for specific applications. No existing solutions or references are provided, leaving the problem open for theoretical or practical contributions. The question targets experts in quantum algorithms and matrix encoding techniques. The discussion underscores a gap in quantum computing literature regarding optimized encoding for non-permutation sparse matrices, potentially impacting quantum machine learning and simulation tasks.
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Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Stack Overflow for Teams is now called Stack Internal. Bring the best of human thought and AI automation together at your work. Bring the best of human thought and AI automation together at your work. Learn more Stack InternalKnowledge at workBring the best of human thought and AI automation together at your work.I am working with an $N \times N$ matrix $A$ whose columns are computational basis vectors: $$ A = [e_{i_0}, e_{i_1}, \dots, e_{i_{N-1}} ] = \sum_{j=0}^{N-1} |i_j\rangle \langle j|, $$ where each $i_j \in \{0, \dots, N-1\}$. The indices $i_j$ may repeat, so $A$ is not necessarily a permutation matrix. Note that every column has Hamming weight $1$.How can one efficiently block encode such a matrix on a quantum computer? Any references or constructive examples would be very helpful.Thanks for contributing an answer to Quantum Computing Stack Exchange!But avoid …Use MathJax to format equations. MathJax reference.To learn more, see our tips on writing great answers.Required, but never shown By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy. Start asking to get answersFind the answer to your question by asking.Explore related questionsSee similar questions with these tags.To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Site design / logo © 2025 Stack Exchange Inc; user contributions licensed under CC BY-SA . rev 2025.11.27.37399

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