The DOI matches its Crossref record; 48 of the 48 references it cites were found in a registry or an index.
Relationship between quantum walks and relativistic quantum mechanics
Open accessAbstract
Quantum walk models have been used as an algorithmic tool for quantum computation and to describe various physical processes. This article revisits the relationship between relativistic quantum mechanics and the quantum walks. We show the similarities of the mathematical structure of the decoupled and coupled forms of the discrete-time quantum walk to that of the Klein-Gordon and Dirac equations, respectively. In the latter case, the coin emerges as an analog of the spinor degree of freedom. Discrete-time quantum walk as a coupled form of the continuous-time quantum walk is also shown by transforming the decoupled form of the discrete-time quantum walk to the Schr\"odinger form. By showing the coin to be a means to make the walk reversible and that the Dirac-like structure is a consequence of the coin use, our work suggests that the relativistic causal structure is a consequence of conservation of information. However, decoherence (modeled by projective measurements on position space) generates entropy that increases with time, making the walk irreversible and thereby producing an arrow of time. The Lieb-Robinson bound is used to highlight the causal structure of the quantum walk to put in perspective the relativistic structure of the quantum walk, the maximum speed of walk propagation, and earlier findings related to the finite spread of the walk probability distribution. We also present a two-dimensional quantum walk model on a two-state system to which the study can be extended.
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“We notice that our analysis agrees with the works [42-46] that studied the continuum limit, i.e. when the lattice spacings and the time steps are sent to 0, of QWs in comparison with the Dirac or the Klein-Gordon equations 3 .”
From Quantum field as a quantum cellular automaton: The Dirac free evolution in one dimension (2015) · cites this paper as [45]
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“Consistency of the + (1 1)-dimensional Dirac QW has been argued in [6], and for the + (1 1)-dimensional massless case in [8].”
From The Dirac equation as a quantum walk: higher dimensions, observational convergence (2014) · cites this paper as [8]
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Cites
Quantum Mechanics and Path Integrals
Miguel Blasco, L. D. (1966) · Students Quarterly Journal · doi:10.1049/sqj.1966.0063 · Cited by 9,884
Fernández, T. A. (2006) · conference · Cited by 5,362
Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems
Engel, G. S., Calhoun, T. R., Read, E. L., Ahn, T.-K., Mančal, T., Cheng, Y.-C., Blankenship, R. E., & Fleming, G. R. (2007) · Nature · doi:10.1038/nature05678 · Cited by 3,315
Aharonov, Y., Davidovich, L., & Zagury, N. (1993) · Physical Review A · doi:10.1103/physreva.48.1687 · Cited by 1,622
The finite group velocity of quantum spin systems
Lieb, E. H., & Robinson, D. W. (1972) · Communications in Mathematical Physics · doi:10.1007/bf01645779 · Cited by 1,463
Quantum computation and decision trees
Farhi, E., & Gutmann, S. (1998) · Physical Review A · doi:10.1103/physreva.58.915 · Cited by 1,215
Environment-assisted quantum walks in photosynthetic energy transfer
Mohseni, M., Rebentrost, P., Lloyd, S., & Aspuru-Guzik, A. (2008) · The Journal of Chemical Physics · doi:10.1063/1.3002335 · Cited by 1,189
Quantum random-walk search algorithm
Shenvi, N., Kempe, J., & Whaley, K. B. (2003) · Physical Review A · doi:10.1103/physreva.67.052307 · Cited by 1,150
Lieb-Schultz-Mattis in higher dimensions
Hastings, M. B. (2004) · Physical Review B · doi:10.1103/physrevb.69.104431 · Cited by 685
Lieb-Robinson Bounds and the Generation of Correlations and Topological Quantum Order
Bravyi, S., Hastings, M. B., & Verstraete, F. (2006) · Physical Review Letters · doi:10.1103/physrevlett.97.050401 · Cited by 664
Research works printed but not linked: 3
- G. V. Riazanov, 1958, Sov. Phys. JETP, 6, 1107
- A. Ambainis, 2001, Proceeding of the 33rd ACM Symposium on Theory of Computing
- A. M. Childs, 2003, Proceedings of the 35th ACM Symposium on Theory of Computing
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Quantum walks: a comprehensive review
Venegas-Andraca, S. E. (2012) · Quantum Information Processing · doi:10.1007/s11128-012-0432-5 · Cited by 934
Programmable quantum simulations of spin systems with trapped ions
Monroe, C. R., Campbell, W. C., Duan, L.-M., Gong, Z., Gorshkov, A. V., Hess, P., Islam, R., Kim, K., Linke, N. M., Pagano, G., et al. (2021) · Reviews of Modern Physics · doi:10.1103/revmodphys.93.025001 · Cited by 891
Programmable Quantum Simulations of Spin Systems with Trapped Ions
Monroe, C., Campbell, W. C., Duan, L. M., Gong, Z. X., Gorshkov, A. V., Hess, P., Islam, R., Kim, K., Linke, N., Pagano, G., et al. (2019) · arXiv · doi:10.48550/arxiv.1912.07845 · Cited by 806
Quantum walks: a comprehensive reviewPreprint
Venegas-Andraca, S. E. (2012) · Cited by 533
Attal, S., Petruccione, F., Sabot, C., & Sinayskiy, I. (2012) · Journal of Statistical Physics · doi:10.1007/s10955-012-0491-0 · Cited by 165
Metadata
- Authors
- Chandrashekar, C. M., Banerjee, S., & Srikanth, R.
- Affiliations
- University of Waterloo (CA)
- Chennai Mathematical Institute (IN)
- Raman Research Institute (IN)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2010-06-25
- Volume
- 81
- Issue
- 6
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2089766148
- Cited by
- 109
- References
- 48
- Citations by year
- 2026: 1 · 2025: 5 · 2024: 7 · 2023: 1 · 2022: 9 · 2021: 10 · 2020: 11 · 2019: 12 · 2018: 9 · 2017: 4 · 2016: 7 · 2015: 5 · 2014: 6 · 2013: 8 · 2012: 8
- FWCI
- 7.45
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- arXiv (Cornell University)
- 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 › Physics and Astronomy › Nuclear and High Energy Physics › Noncommutative and Quantum Gravity Theories
- Keywords
- quantum walks, relativistic quantum mechanics, Klein-Gordon equation, Dirac equation, discrete-time quantum walks, continuous-time quantum walks, coin operator, reversibility, information conservation, arrow of time, decoherence, entropy (information theory), Lieb-Robinson bound, causal structure, two-dimensional quantum walk, two-level system
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