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This research addresses the critical bottleneck of index-mapping overhead in block-encoding sparse matrices, a foundational requirement for quantum linear system solvers and Hamiltonian simulation. By leveraging coherent permutation to compress multicontrolled X gates and optimize control states under hardware constraints, the proposed framework significantly reduces circuit depth on superconducting backends. The work effectively bridges combinatorial optimization with quantum gate synthesis to improve resource efficiency without altering the underlying algorithmic logic.
Block Encoding of Sparse Matrices via Coherent Permutation
arXiv:2508.21667v4 Announce Type: replace 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 entry-wise 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.
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 entry-wise 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.
16 pages, 8 figures. Published in Physical Review Research
Quantum Physics (quant-ph); Data Structures and Algorithms (cs.DS); Numerical Analysis (math.NA)
arXiv:2508.21667 [quant-ph]
(or arXiv:2508.21667v4 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2508.21667 Focus to learn more arXiv-issued DOI via DataCite
Phys. Rev. Research 8, 033282 (2026)
https://doi.org/10.1103/1nts-v6y9 Focus to learn more DOI(s) linking to related resources
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