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Decomposition of split-step quantum walks for simulating Majorana modes and edge states
Open accessAbstract
We construct a decomposition procedure for converting split-step quantum walks into ordinary quantum walks with alternating coins, and we show that this decomposition enables a feasible linear optical realization of split-step quantum walks by eliminating quantum-control requirements. As salient applications, we show how our scheme will simulate Majorana modes and edge states.
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The split-step DQW described by the operator is equivalent to the two period DQW with alternate coin operations, θ1 and θ2, when the alternate points in position space with zero probability are ignored.
“The split-step DQW described by the operator is equivalent to the two period DQW with alternate coin operations, θ1 and θ2, when the alternate points in position space with zero probability are ignored47.”
From Quantum walks and Dirac cellular automata on a programmable trapped-ion quantum computer (2020) · cites this paper as [47]
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Cites
Observation of topologically protected bound states in photonic quantum walks
Kitagawa, T., Broome, M. A., Fedrizzi, A., Rudner, M. S., Berg, E., Kassal, I., Aspuru-Guzik, A., Demler, E., & White, A. G. (2012) · Nature Communications · doi:10.1038/ncomms1872 · Cited by 607
Photons Walking the Line: A Quantum Walk with Adjustable Coin Operations
Schreiber, A., Cassemiro, K. N., Potoček, V., Gábris, A., Mosley, P. J., Andersson, E., Jex, I., & Silberhorn, C. (2010) · Physical Review Letters · doi:10.1103/physrevlett.104.050502 · Cited by 588
Exploring topological phases with quantum walks
Kitagawa, T., Rudner, M. S., Berg, E., & Demler, E. (2010) · Physical Review A · doi:10.1103/physreva.82.033429 · Cited by 534
A 2D Quantum Walk Simulation of Two-Particle Dynamics
Schreiber, A., Gábris, A., Rohde, P. P., Laiho, K., Štefaňák, M., Potoček, V., Hamilton, C., Jex, I., & Silberhorn, C. (2012) · Science · doi:10.1126/science.1218448 · Cited by 425
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Cardano, F., Massa, F., Qassim, H., Karimi, E., Slussarenko, S., Paparo, D., de Lisio, C., Sciarrino, F., Santamato, E., Boyd, R. W., et al. (2015) · Science Advances · doi:10.1126/sciadv.1500087 · Cited by 207
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Knight, P. L., Roldán, E., & Sipe, J. E. (2003) · Physical Review A · doi:10.1103/physreva.68.020301 · Cited by 176
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Cited by
Sorted by citations
Quantum walks and Dirac cellular automata on a programmable trapped-ion quantum computer
Huerta Alderete, C., Singh, S., Nguyen, N. H., Zhu, D., Balu, R., Monroe, C., Chandrashekar, C. M., & Linke, N. M. (2020) · Nature Communications · doi:10.1038/s41467-020-17519-4 · Cited by 48
Photonic cellular automaton simulation of relativistic quantum fields: Observation of Zitterbewegung
Suprano, A., Zia, D., Polino, E., Poderini, D., Carvacho, G., Sciarrino, F., Lugli, M., Bisio, A., & Perinotti, P. (2024) · Physical Review Research · doi:10.1103/physrevresearch.6.033136 · Cited by 2
Observing Majorana fermion dynamic properties on a NISQ computer
Wang, W.-T., He, X.-G., Kao, H.-C., & Chang, C.-R. (2024) · Chinese Journal of Physics · doi:10.1016/j.cjph.2024.05.006 · Cited by 1
Metadata
- Authors
- Zhang, W.-W., Goyal, S. K., Simon, C., & Sanders, B. C.
- Affiliations
- Indian Institute of Science Education and Research Mohali (IN)
- University of Calgary (CA)
- Canadian Institute for Advanced Research (CA)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2017-05-30
- Volume
- 95
- Issue
- 5
- ISSN
- 0556-2791 (ISSN-L)
- 2469-9926
- 2469-9934
- OpenAlex
- W2601184834
- Cited by
- 17
- References
- 6
- Citations by year
- 2025: 1 · 2024: 4 · 2022: 2 · 2021: 1 · 2020: 3 · 2019: 5 · 2018: 1
- FWCI
- 1.47
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Natural Sciences and Engineering Research Council of Canada
- National Natural Science Foundation of China (11675164)
- China Scholarship Council (201406470022)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Topological Materials and Phenomena
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Keywords
- Majorana modes, edge states
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