Year: 2026
Type: preprint
Abstract: We present an explicit quantum circuit that constructs a block encoding of a generator-representable semiseparable (one-pair) matrix directly from its two generators. For an $N\times N$ semiseparable matrix with $N=2^{n}$, the circuit uses $2n+2$ ancilla qubits and has $O({\rm polylog} N)$ depth, and it realizes a $(2\sqrt{N},\,2n+2,\,2 \sqrt{2}\ \varepsilon)$-block encoding, where $\varepsilon$ is controlled by the accuracy of the state-preparation routines that load the generators. The building blocks of the circuit are cyclic shifts, swaps, and Hadamard gates, each admitting an efficient implementation through the binary decomposition of the relevant indices.
Source: arXiv (Cornell University)
Institutions: University of Pisa, Lawrence Berkeley National Laboratory
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221524110