Products between block-encodings

• URL: http://arxiv.org/abs/2509.15779v1
• Date: Fri, 19 Sep 2025 09:10:11 GMT
• Title: Products between block-encodings
• Authors: Dekuan Dong, Yingzhou Li, Jungong Xue,
• Abstract summary: We present resource-efficient methods for matrix-matrix, Kronecker, and Hadamard products between block-encodings.<n>Our constructions significantly reduce the number of ancilla qubits, achieving exponential qubit savings for sequences of matrix-matrix multiplications.
• Score: 1.2744523252873352
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Block-encoding is a standard framework for embedding matrices into unitary operators in quantum algorithms. Efficient implementation of products between block-encoded matrices is crucial for applications such as Hamiltonian simulation and quantum linear algebra. We present resource-efficient methods for matrix-matrix, Kronecker, and Hadamard products between block-encodings that apply to rectangular matrices of arbitrary dimensions. Our constructions significantly reduce the number of ancilla qubits, achieving exponential qubit savings for sequences of matrix-matrix multiplications, with a moderate increase in gate complexity. These product operations also enable more complex block-encodings, including a compression gadget for time-dependent Hamiltonian simulation and matrices represented as sums of Kronecker products, each with improved resource requirements.

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