Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Dong, Dekuan, Li, Yingzhou, Xue, Jungong
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7083075996
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