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This chapter discusses techniques for implementing linear algebraic operations in quantum circuits, including methods for sequences of matrix-vector operations. The usage of block encodings is demonstrated with its success probability. Subsequently, block-encodings are applied to compute a sequence of matrix-vector products and techniques to minimize resource requirements, and failure probabilities are presented. Finally, two techniques for affine linear operations are presented, each with its advantages and disadvantages.

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Matrix-Vector Multiplications and Affine Linear Operations

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  • 发表日期：

    2026年

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  • Osama M. Raisuddin,
  • Suvranu De

摘要

This chapter discusses techniques for implementing linear algebraic operations in quantum circuits, including methods for sequences of matrix-vector operations. The usage of block encodings is demonstrated with its success probability. Subsequently, block-encodings are applied to compute a sequence of matrix-vector products and techniques to minimize resource requirements, and failure probabilities are presented. Finally, two techniques for affine linear operations are presented, each with its advantages and disadvantages.