Year: 2026
Type: article
Abstract: ABSTRACT Two preparation algorithms are presented and analyzed for generating quantum circuits that implement cycle shift transformations with arbitrary integer steps on superpositions, such as quantum images. The two algorithms extend the Toffoli‐based state‐of‐the‐art method by exploiting the fact that larger powers of two lead to cheaper cycle shift circuits; consequently, injecting appropriate larger powers into the sequence that realizes a desired shift step can significantly reduce the total cost. Greedy and dynamic programming methods are leveraged to decide between the two nearest powers of two for a given remaining shift distance. Theoretical analysis supports the algorithms' correctness and shows that preparation‐time complexities remain on par with the existing approach. Experimental testing using realistic Toffoli decomposition cost models indicates that the greedy algorithm reduces the circuit cost in an increasing tendency as the width of the host register increases, approaching a drop of in over of cases. The dynamic programming algorithm is shown to consistently match the best case scenario of both previous algorithms and even improves it further in over of cases, by a modest amount. Additional testing, approximating quasi‐realistic noisy conditions, indicates that the two proposed methods achieve parity in noise robustness with the current state‐of‐the‐art.
Source: Advanced Quantum Technologies
DOI: 10.1002/qute.70445
Institution: Aristotle University of Thessaloniki
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $4,430
Funder: Hellenic Academic Libraries Link
OpenAlex ID: W7213263373