Scheme for Demonstration of Fractional Statistics of Anyons in an Exactly Solvable Model
Open accessAbstract
We propose a scheme to demonstrate fractional statistics of anyons in an exactly solvable lattice model proposed by Kitaev that involves four-body interactions. The required many-body ground state, as well as the anyon excitations and their braiding operations, can be conveniently realized through dynamic laser manipulation of cold atoms in an optical lattice. Because of the perfect localization of anyons in this model, we show that a quantum circuit with only six qubits is enough for demonstration of the basic braiding statistics of anyons. This opens up the immediate possibility of proof-of-principle experiments with trapped ions, photons, or nuclear magnetic resonance systems.
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Following proposals by Han et al. (2007) and Pachos (2007), four- and six-qubit graph states were created to mimic the ground state of the Kitaev spin-lattice model.
“Following proposals by Han et al (2007) and Pachos (2007), four-and six-qubit graph states were created to mimic the ground state of the Kitaev spin-lattice model (Kitaev, 2003).”
From Multiphoton entanglement and interferometry (2012) · cites this paper as Han et al (2007)
Cites
Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
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Measurement-based quantum computation on cluster states
Raussendorf, R., Browne, D. E., & Briegel, H. J. (2003) · Physical Review A · doi:10.1103/physreva.68.022312 · Cited by 1,655 · see citing works
Self-citationEntanglement of Atoms via Cold Controlled Collisions
Jaksch, D., Briegel, H.-J., Cirac, J. I., Gardiner, C. W., & Zoller, P. (1999) · Physical Review Letters · doi:10.1103/physrevlett.82.1975 · Cited by 795 · see citing works
Controlled collisions for multi-particle entanglement of optically trapped atoms
Mandel, O., Greiner, M., Widera, A., Rom, T., Hänsch, T. W., & Bloch, I. (2003) · Nature · doi:10.1038/nature02008 · Cited by 789 · see citing works
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Georgescu, I. M., Ashhab, S., & Nori, F. (2014) · Reviews of Modern Physics · doi:10.1103/revmodphys.86.153 · Cited by 2,932 · see citing works
“The fractional statistics of anyons in the Kitaev model (Kitaev, 2003) involving four-body interactions could be studied using AQS with cold atoms in optical lattices or alternatively using DQS (Han et al., 2007).”
MethodGühne, O., & Tóth, G. (2009) · Physics Reports · doi:10.1016/j.physrep.2009.02.004 · Cited by 2,401 · see citing works
Multiphoton entanglement and interferometry
Pan, J.-W., Chen, Z.-B., Lu, C.-Y., Weinfurter, H., Zeilinger, A., & Żukowski, M. (2012) · Reviews of Modern Physics · doi:10.1103/revmodphys.84.777 · Cited by 1,410 · see citing works
Quantum simulation of frustrated Ising spins with trapped ions
Kim, K., Chang, M.-S., Korenblit, S., Islam, R., Edwards, E. E., Freericks, J. K., Lin, G.-D., Duan, L.-M., & Monroe, C. (2010) · Nature · doi:10.1038/nature09071 · Cited by 750 · see citing works
Self-citationExperimental demonstration of a hyper-entangled ten-qubit Schrödinger cat state
Gao, W.-B., Lu, C.-Y., Yao, X.-C., Xu, P., Gühne, O., Goebel, A., Chen, Y.-A., Peng, C.-Z., Chen, Z.-B., & Pan, J.-W. (2010) · Nature Physics · doi:10.1038/nphys1603 · Cited by 348 · see citing works
Demonstrating Anyonic Fractional Statistics with a Six-Qubit Quantum Simulator
Lu, C.-Y., Gao, W.-B., Gühne, O., Zhou, X.-Q., Chen, Z.-B., & Pan, J.-W. (2009) · Physical Review Letters · doi:10.1103/physrevlett.102.030502 · Cited by 132 · see citing works
- Authors
- Han, Y.-J., Raussendorf, R., & Duan, L.-M.
- Affiliations
- University of Michigan (US)
- Perimeter Institute (CA)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2007-04-12
- Volume
- 98
- Issue
- 15
- Pages
- 150404-150404
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W1975133581
- Cited by
- 96
- References
- 4
- Citations by year
- 2025: 4 · 2024: 3 · 2022: 5 · 2021: 8 · 2020: 4 · 2019: 6 · 2018: 3 · 2017: 5 · 2016: 3 · 2015: 2 · 2014: 10 · 2013: 4 · 2012: 5
- FWCI
- 5.30
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Advanced Condensed Matter Physics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Cold Atom Physics and Bose-Einstein Condensates
- Keywords
- fractional statistics, anyons, Kitaev model, exactly solvable lattice models, four-body interactions, anyon braiding, ultracold atoms in optical lattices, quantum simulation, topological quantum computation
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