Quantum circuits for the realization of equivalent forms of one-dimensional discrete-time quantum walks on near-term quantum hardware
Open accessAbstract
Quantum walks are a promising framework for developing quantum algorithms and quantum simulations. They represent an important test case for the application of quantum computers. Here we present different forms of discrete-time quantum walks (DTQWs) and show their equivalence for physical realizations. Using an appropriate digital mapping of the position space on which a walker evolves to the multiqubit states of a quantum processor, we present different configurations of quantum circuits for the implementation of DTQWs in one-dimensional position space. We provide example circuits for a five-qubit processor and address scalability to higher dimensions as well as larger quantum processors.
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The quantum circuit for the time evolution operator has a similar circuit depth to the approach proposed in Ref. [20,21] without limitation.
“It has a similar circuit depth to the approach proposed in Ref. [20,21] without limitation (see Figure 1(b)).”
From Quantum Entanglement in Dirac Dynamics via Continuous-Time Quantum Walks in a Quantum Circuit Framework (2024) · cites this paper as [21]
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- Authors
- Singh, S., Alderete, C. H., Balu, R., Monroe, C., Linke, N. M., & Chandrashekar, C. M.
- Affiliations
- Homi Bhabha National Institute (IN)
- National Institute of Astrophysics, Optics and Electronics (MX)
- DEVCOM Army Research Laboratory (US)
- Joint Center for Quantum Information and Computer Science (US)
- ORCID
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2021-12-01
- Volume
- 104
- Issue
- 6
- ISSN
- 0556-2791 (ISSN-L)
- 2469-9926
- 2469-9934
- OpenAlex
- W3216172383
- Cited by
- 13
- References
- 87
- Citations by year
- 2026: 1 · 2025: 3 · 2024: 4 · 2023: 1 · 2022: 4
- FWCI
- 0.80
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- arXiv (Cornell University)
- Funders
- Consejo Nacional de Ciencia y Tecnología (455378)
- National Science Foundation (PHY-1430094)
- Department of Science and Technology, Ministry of Science and Technology (SB/S2/RJN-192/2014)
- U.S. Army (FA520919PA139)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- discrete-time quantum walks, one-dimensional quantum walk, quantum circuit design, near-term quantum devices, quantum simulation, scalability
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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