Block Encoding of Sparse Matrices via Coherent Permutation
arXiv:2508.21667v3 Announce Type: replace-cross Abstract: Block encoding of sparse matrices underpins powerful quantum algorithms such as quantum singular value transformation, Hamiltonian simulation, and quantum linear solvers, yet its efficient gate-level realization for general sparse matrices remains a major challenge. We introduce a unified framework that addresses key obstacles including the overhead of multi-controlled X (MCX) gates, amplitude reordering, and hardware connectivity, enabling simplified block encoding constructions with explicit gate-level implementations. Central to our approach is a connection to combinatorial optimization, which enables systematic assignment of control qubits to satisfy nearest-neighbor connectivity constraints, along with coherent permutation oper
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Abstract:Block encoding of sparse matrices underpins powerful quantum algorithms such as quantum singular value transformation, Hamiltonian simulation, and quantum linear solvers, yet its efficient gate-level realization for general sparse matrices remains a major challenge. We introduce a unified framework that addresses key obstacles including the overhead of multi-controlled X (MCX) gates, amplitude reordering, and hardware connectivity, enabling simplified block encoding constructions with explicit gate-level implementations. Central to our approach is a connection to combinatorial optimization, which enables systematic assignment of control qubits to satisfy nearest-neighbor connectivity constraints, along with coherent permutation operators that preserve superposition while enabling structured amplitude reordering. We demonstrate our methods on structured sparse matrices, achieving systematic reductions in control overhead and circuit depth. Our framework bridges the gap between theoretical formulations and hardware-efficient quantum circuit implementations.
Subjects:
Quantum Physics (quant-ph); Data Structures and Algorithms (cs.DS); Numerical Analysis (math.NA)
Cite as: arXiv:2508.21667 [quant-ph]
(or arXiv:2508.21667v3 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2508.21667
arXiv-issued DOI via DataCite
Submission history
From: Abhishek Setty [view email] [v1] Fri, 29 Aug 2025 14:30:08 UTC (909 KB) [v2] Fri, 19 Sep 2025 13:52:51 UTC (901 KB) [v3] Fri, 3 Apr 2026 16:53:35 UTC (896 KB)
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