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Block-encoding structured matrices for data input in quantum computing

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arxiv 2302.10949 v2 pith:XZ45UMUA submitted 2023-02-21 quant-ph

Block-encoding structured matrices for data input in quantum computing

Christoph S\"underhauf , Earl Campbell , Joan Camps This is my paper
classification quant-ph
keywords matricesblockdataencodinginputcircuitsquantumaccording
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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The cost of data input can dominate the run-time of quantum algorithms. Here, we consider data input of arithmetically structured matrices via block encoding circuits, the input model for the quantum singular value transform and related algorithms. We demonstrate how to construct block encoding circuits based on an arithmetic description of the sparsity and pattern of repeated values of a matrix. We present schemes yielding different subnormalisations of the block encoding; a comparison shows that the best choice depends on the specific matrix. The resulting circuits reduce flag qubit number according to sparsity, and data loading cost according to repeated values, leading to an exponential improvement for certain matrices. We give examples of applying our block encoding schemes to a few families of matrices, including Toeplitz and tridiagonal matrices.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

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    quant-ph 2026-05 unverdicted novelty 6.0

    Presents LCU block-encodings for SLAC derivative operators, applies Shannon wavelets and preconditioning, and obtains O(d n^3 α^(k) log(1/ε)) gate complexity for d-dimensional PDEs via QLSA.

  2. Quantum algorithm for solving differential equations using SLAC derivatives

    quant-ph 2026-05 unverdicted novelty 5.0

    Efficient quantum block-encodings of SLAC first-order derivative and Laplacian operators are built with LCU, state preparation, wavelet multi-scale transforms, and preconditioning to solve PDEs via QLSA with analyzed ...

  3. Unitaria: Quantum Linear Algebra via Block Encodings

    quant-ph 2026-05 accept novelty 4.0

    Unitaria is a new open-source Python library that provides a high-level, composable interface for block encodings in quantum computing, enabling automatic circuit generation and classical simulation-based verification.