Direct Probe of Topological Invariants Using Bloch Oscillating Quantum Walks
Open accessAbstract
The topology of a single-particle band structure plays a fundamental role in understanding a multitude of physical phenomena. Motivated by the connection between quantum walks and such topological band structures, we demonstrate that a simple time-dependent, Bloch-oscillating quantum walk enables the direct measurement of topological invariants. We consider two classes of one-dimensional quantum walks and connect the global phase imprinted on the walker with its refocusing behavior. By disentangling the dynamical and geometric contributions to this phase, we describe a general strategy to measure the topological invariant in these quantum walks. As an example, we propose an experimental protocol in a circuit QED architecture where a superconducting transmon qubit plays the role of the coin, while the quantum walk takes place in the phase space of a cavity.
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The circuit-based implementations reported to date are a DQW on a three-qubit NMR system, a CQW on a two-qubit photonic processor, and a split-step QW on superconducting circuits.
“The implementation of a DQW on a three-qubit NMR system36, a CQW on a two-qubit photonic processor37 and a split-step QW on superconducting circuits38,39 are the circuit-based implementations reported to date.”
From Quantum walks and Dirac cellular automata on a programmable trapped-ion quantum computer (2020) · cites this paper as [38]
The paper describes a split-step quantum walk in a superconducting circuit-QED architecture, but calls it a proposed experimental realization, not a reported implementation (p. 1). Its “Experimental realization” section likewise presents an experimental blueprint (p. 4). (LLM, conf=0.89)
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Cites
Universal Computation by Quantum Walk
Childs, A. M. (2009) · Physical Review Letters · doi:10.1103/physrevlett.102.180501 · Cited by 1,002 · see citing works
Observation of a Topological Transition in the Bulk of a Non-Hermitian System
Zeuner, J. M., Rechtsman, M. C., Plotnik, Y., Lumer, Y., Nolte, S., Rudner, M. S., Segev, M., & Szameit, A. (2015) · Physical Review Letters · doi:10.1103/physrevlett.115.040402 · Cited by 730 · see citing works
Self-citationObservation 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 · see citing works
Self-citationPhotons 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 · see citing works
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 · see citing works
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Quantum walks on a programmable two-dimensional 62-qubit superconducting processor
Gong, M., Wang, S., Zha, C., Chen, M.-C., Huang, H.-L., Wu, Y., Zhu, Q., Zhao, Y., Li, S., Guo, S., et al. (2021) · Science · doi:10.1126/science.abg7812 · Cited by 331 · see citing works
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 · see citing works
Entanglement transfer, accumulation and retrieval via quantum-walk-based qubit–qudit dynamics
Giordani, T., Innocenti, L., Suprano, A., Polino, E., Paternostro, M., Spagnolo, N., Sciarrino, F., & Ferraro, A. (2021) · New Journal of Physics · doi:10.1088/1367-2630/abdbe1 · Cited by 1 · see citing works
- Authors
- Ramasesh, V. V., Flurin, E., Rudner, M., Siddiqi, I., & Yao, N. Y.
- Affiliations
- University of California, Berkeley (US)
- University of Copenhagen (DK)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2017-03-27
- Volume
- 118
- Issue
- 13
- Pages
- 130501-130501
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2529776492
- Cited by
- 105
- References
- 5
- Citations by year
- 2026: 5 · 2025: 8 · 2024: 11 · 2023: 8 · 2022: 10 · 2021: 16 · 2020: 16 · 2019: 13 · 2018: 12 · 2017: 5 · 2016: 1
- FWCI
- 6.17
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Research at the University of Copenhagen (University of Copenhagen) (submittedVersion)
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Adolph C. and Mary Sprague Miller Institute for Basic Research in Science, University of California Berkeley
- U.S. Department of Energy (DE-AC02-05CH11231)
- Army Research Office (W911NF-15-1-0496)
- Air Force Office of Scientific Research (FA9550-12-1-0378)
- Seventh Framework Programme (FP7/2007-2013)
- Research Executive Agency (PIIF-GA-2013-627838)
- National Science Foundation
- Laboratory Directed Research and Development Program of Lawrence Berkeley National Laboratory
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Keywords
- topological invariants, quantum walks, Bloch oscillations, topological band structure, global phase, refocusing, circuit quantum electrodynamics, transmon qubits, one-dimensional quantum walk
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