Non-Abelian Berry connections for quantum computation
Open accessAbstract
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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The Davies derivation can be generalized to allow for slowly varying system Hamiltonians, whenever the time scale of variation of H_C(t) is much longer than the inverse of the typical Bohr frequency of H_S.
“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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- 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 › Computer Science › Artificial Intelligence › 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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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