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Advanced Quantum Technologies

From Conventional to Unconventional Geometric Gates: What Can We Learn?

Wenli Zhang, Daolin Yang, Yonggang Peng, Yujun Zheng

Published Aug 1, 2026• 0 citations
Publisher

Abstract

ABSTRACT Geometric quantum gates play crucial role in quantum computation, and the diffident types of geometric gates are constructed, including conventional and unconventional geometric gates. The physical natures of the conventional geometric gates with zero dynamical phase are investigated widely. In this paper, we analyze the physical natures of the unconventional geometric gates, and present the unconventional geometric gate is related with the Levi–Civita connection. We establish its physical constraint, and demonstrate the results by employing two‐level system.

DOI
10.1002/qute.70395

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A different way to realize nonadiabatic geometric quantum computation is proposed by varying parameters in the Hamiltonian for nuclear-magnetic resonance, where the dynamical and geometric phases are implemented separately without the usual operational process. Therefore the phase accumulated in the geometric gate is a pure geometric phase for any input state. In comparison with the conventional geometric gates by rotating operations, our approach simplifies experimental implementations making them robust to certain experimental errors. In contrast to the unconventional geometric gates, our approach distinguishes the total and geometric phases and offers a wide choice of the relations between the dynamical and geometric phases.
Nonadiabatic geometric quantum computation in decoherence-free subspaces has received increasing attention due to the merits of its high-speed implementation and robustness against both control errors and decoherence. However, all the previous schemes in this direction have been based on the conventional geometric phases, of which the dynamical phases need to be removed. In this paper, we put forward a scheme of nonadiabatic geometric quantum computation in decoherence-free subspaces based on unconventional geometric phases, of which the dynamical phases do not need to be removed. Specifically, by using three physical qubits undergoing collective dephasing to encode one logical qubit, we realize a universal set of geometric gates nonadiabatically and unconventionally. Our scheme not only maintains all the merits of nonadiabatic geometric quantum computation in decoherence-free subspaces, but also avoids the additional operations required in the conventional schemes to cancel the dynamical phases.
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