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Non-Abelian Berry connections for quantum computation
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In the holonomic approach to quantum computation, information is encoded in a degenerate eigenspace of a parametric family of Hamiltonians and manipulated by the associated holonomic gates. These are realized in terms of the non-Abelian Berry connection and are obtained by driving the control parameters along adiabatic loops. We show how it is possible for a specific model to explicitly determine the loops generating any desired logical gate, thus producing a universal set of unitary transformations. In a multipartite system unitary transformations can be implemented efficiently by sequences of local holonomic gates. Moreover, a conceptual scheme for obtaining the required Hamiltonian family, based on frequently repeated pulses, is discussed, together with a possible process whereby the initial state can be prepared and the final one can be measured.
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“Davies did not consider time-dependent system Hamiltonians in [43], but it is possible to generalize his derivation to allow for slowly varying system Hamiltonians [37, 44, 45]. That is, whenever the time scale of the variation of H C ( t ) is much longer than the inverse of the typical Bohr frequency (of H S ), it is possible to add H C ( t ) to the system Hamiltonian in Eq. (23), necessitating a”
From Internal consistency of fault-tolerant quantum error correction in light of rigorous derivations of the quantum Markovian limit (2006) · cites this paper as [44]
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Metadata
- Authors
- Pachos, J., Zanardi, P., & Rasetti, M.
- Affiliations
- Institute for Scientific Interchange (IT)
- ORCID
- Pachos, Jiannis
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 1999-12-13
- Volume
- 61
- Issue
- 1
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W1965228711
- Cited by
- 316
- References
- 9
- Citations by year
- 2026: 5 · 2025: 7 · 2024: 12 · 2023: 15 · 2022: 21 · 2021: 19 · 2020: 13 · 2019: 12 · 2018: 7 · 2017: 4 · 2016: 10 · 2015: 4 · 2014: 8 · 2013: 6 · 2012: 8
- FWCI
- 12.79
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (acceptedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- PORTO@Iris (submittedVersion)
- PORTO Publications Open Repository TOrino (Politecnico di Torino) (submittedVersion)
- 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 Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- holonomic quantum computation, universal gate set, multipartite systems, state preparation and measurement
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