Mimicking the Probability Distribution of a Two-Dimensional Grover Walk with a Single-Qubit Coin
Open accessAbstract
The nonlocalized case of the spatial density probability of the two-dimensional Grover walk can be obtained using only a two-dimensional coin space and a quantum walk in alternate directions. This significantly reduces the resources necessary for its feasible experimental realization. We present a formal proof of this correspondence and analyze the behavior of the coin-position entanglement as well as the x-y spatial entanglement in our scheme with respect to the Grover one. Our scheme allows us to entangle the two orthogonal directions of the walk more efficiently.
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The implemented split-step quantum walk is proved to realize the Grover search algorithm in the high step-number limit.
“Here we implement a different split-step quantum walk, that is proved to realize the Grover search algorithm in the high step-number limit 53 .”
From Quantum walks of two correlated photons in a 2D synthetic lattice (2022) · cites this paper as [53]
The paper’s proof shows that its alternate-direction walk reproduces the Grover walk’s spatial probability distribution for specified initial conditions. It also says the Grover walk can be used to implement two-dimensional Grover search, but it does not prove that the alternate walk realizes the search algorithm in a high-step-number limit. (LLM, conf=0.87)
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Observation of topologically protected bound states in photonic quantum walks
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Singh, S., Alderete, C. H., Balu, R., Monroe, C., Linke, N. M., & Chandrashekar, C. M. (2021) · Physical Review A · doi:10.1103/physreva.104.062401 · Cited by 13 · see citing works
- Authors
- Di Franco, C., Mc Gettrick, M., & Busch, T.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2011-02-24
- Volume
- 106
- Issue
- 8
- Pages
- 080502-080502
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2070072241
- Cited by
- 96
- References
- 4
- Citations by year
- 2026: 2 · 2025: 7 · 2024: 3 · 2023: 3 · 2022: 6 · 2021: 9 · 2020: 8 · 2019: 9 · 2018: 7 · 2017: 6 · 2016: 10 · 2015: 6 · 2014: 3 · 2013: 7 · 2012: 8
- FWCI
- 5.89
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- Arrow@dit (Dublin Institute of Technology) (acceptedVersion)
- arXiv (Cornell University) (submittedVersion)
- ARAN (University of Galway Research Repository) (Ollscoil na Gaillimhe – University of Galway) (submittedVersion, cc-by-nc-nd)
- Arrow@dit (Dublin Institute of Technology) (submittedVersion)
- Cork Open Research Archive (University College Cork, Ireland) (submittedVersion)
- ARAN (University of Galway Research Repository) (Ollscoil na Gaillimhe – University of Galway) (submittedVersion, cc-by-nc)
- arXiv (Cornell University)
- Research Repository UCD (University College Dublin) (cc-by-nc)
- Funders
- Irish Research Council for Science, Engineering and Technology
- Science Foundation Ireland (05/IN/I852)
- Irish Research Council
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Keywords
- Grover walk, two-dimensional quantum walk, spatial entanglement
- MeSH terms
- Numismatics, Probability, Quantum Theory, Stochastic Processes
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