{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T18:24:35Z","timestamp":1765045475956,"version":"build-2065373602"},"reference-count":21,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2021,1,7]],"date-time":"2021-01-07T00:00:00Z","timestamp":1609977600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Quantum search algorithms provide a way to speed up combinatorial search, and have found several applications in modern quantum technology. In particular, spatial search on graphs, based on continuous-time quantum walks (CTQW), represents a promising platform for the implementation of quantum search in condensed matter systems. CTQW-based algorithms, however, work exactly on complete graphs, while they are known to perform poorly on realistic graphs with low connectivity. In this paper, we put forward an alternative search algorithm, based on structuring the oracle operator, which allows one to improve the localization properties of the walker by tuning only the on-site energies of the graph, i.e., without altering its topology. As such, the proposed algorithm is suitable for implementation in systems with low connectivity, e.g., rings of quantum dots or superconducting circuits. Oracle parameters are determined by Hamiltonian constraints, without the need for numerical optimization.<\/jats:p>","DOI":"10.3390\/sym13010096","type":"journal-article","created":{"date-parts":[[2021,1,10]],"date-time":"2021-01-10T23:03:42Z","timestamp":1610319822000},"page":"96","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Improving Quantum Search on Simple Graphs by Pretty Good Structured Oracles"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7523-7289","authenticated-orcid":false,"given":"Matteo G. A.","family":"Paris","sequence":"first","affiliation":[{"name":"Quantum Technology Lab &amp; Applied Quantum Mechanics Group, Dipartimento di Fisica Aldo Pontremoli, Universit\u00e0 degli Studi di Milano, I-20133 Milano, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8112-4907","authenticated-orcid":false,"given":"Claudia","family":"Benedetti","sequence":"additional","affiliation":[{"name":"Quantum Technology Lab &amp; Applied Quantum Mechanics Group, Dipartimento di Fisica Aldo Pontremoli, Universit\u00e0 degli Studi di Milano, I-20133 Milano, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9251-0731","authenticated-orcid":false,"given":"Stefano","family":"Olivares","sequence":"additional","affiliation":[{"name":"Quantum Technology Lab &amp; Applied Quantum Mechanics Group, Dipartimento di Fisica Aldo Pontremoli, Universit\u00e0 degli Studi di Milano, I-20133 Milano, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,7]]},"reference":[{"key":"ref_1","unstructured":"Aaronson, S., and Ambainis, A. 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