aiqbench analysis
This paper introduces an exact quantum algorithm capable of searching for the intersection of multiple constrained sets, overcoming limitations in existing Grover-based methods that typically handle only two sets or suffer from probabilistic failure rates. By deriving a specific phase-matching condition and implementing it within a quantum circuit, the authors achieve a zero theoretical failure rate for this complex search problem, advancing the utility of amplitude amplification techniques.
Exact quantum algorithm for searching of multiple sets intersection
arXiv:2609.36908v1 Announce Type: new Abstract: Grover's algorithm achieves a quadratic speedup for unstructured search when a global oracle for the target set is available. However, its success probability is generally below $100\%$. To overcome this issue, Long presented a modified version of Grover's search algorithm by introducing a phase-matching condition, which can search for the target set with zero theoretical failure rate. Nevertheless, in many applications, the target set is determined by the intersection of multiple constrained sets. Most existing Grover-based methods are limited to the intersection of only two sets and are not always successful in searching for the target set. In this work, based on Long's method, we propose an algorithm for exactly searching the intersection of multiple sets. We derive and prove a phase-matching condition for searching the intersection exactly. Furthermore, we present a quantum circuit that implements exact intersection search. Finally, we support our theoretical results with numerical simulations.
Abstract:Grover's algorithm achieves a quadratic speedup for unstructured search when a global oracle for the target set is available. However, its success probability is generally below $100\%$. To overcome this issue, Long presented a modified version of Grover's search algorithm by introducing a phase-matching condition, which can search for the target set with zero theoretical failure rate. Nevertheless, in many applications, the target set is determined by the intersection of multiple constrained sets. Most existing Grover-based methods are limited to the intersection of only two sets and are not always successful in searching for the target set. In this work, based on Long's method, we propose an algorithm for exactly searching the intersection of multiple sets. We derive and prove a phase-matching condition for searching the intersection exactly. Furthermore, we present a quantum circuit that implements exact intersection search. Finally, we support our theoretical results with numerical simulations.
arXiv:2609.36908 [quant-ph]
(or arXiv:2609.36908v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2609.36908 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Full text under the publisher's open licence · 239 words
