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  • Open Access

Block encoding of sparse matrices via coherent permutation

Abhishek Setty*

  • *Contact author: a.setty@fz-juelich.de
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Phys. Rev. Research 8, 033282 – Published 8 September, 2026

DOI: https://doi.org/10.1103/1nts-v6y9

Abstract

Block encoding of sparse matrices underpins quantum algorithms such as quantum singular value transformation, Hamiltonian simulation, and quantum linear system solvers, yet its efficient gate-level realization remains challenging, with index-mapping oracles constituting one important source of overhead. We introduce a block-encoding framework that focuses on the index-mapping component, where coherent permutation is used as the central mechanism to optimize shift, delete, and insert operations. This provides a unified treatment of index mapping and reduces local multicontrolled X control complexity through structured compression. We further connect coherent amplitude permutation to combinatorial optimization, enabling systematic assignment of control states under hardware connectivity constraints. The resulting construction supports entrywise block encoding for general sparse matrices, with efficiency gains in structured cases. We demonstrate the approach on representative examples and provide resource analysis using IBM superconducting backends, showing significant reductions in circuit depth.

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Phys. Rev. Research 8, 033282– Published 8 September, 2026
  • Received 16 September 2025
  • Accepted 19 August 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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