https://doi.org/10.1140/epjp/s13360-022-03460-6
Regular Article
Implementation of a holonomic 3-qubit gate using Rydberg superatoms in a microwave cavity
Department of Physics, Ramakrishna Mission Residential College, 700103, Narendrapur, Kolkata, India
Received:
9
April
2022
Accepted:
4
November
2022
Published online:
2
December
2022
Holonomic (i.e., based on geometric phase) quantum gates have been studied extensively in recent years, because they are relatively more immune to environmental effects than normal gates. There have been several physical implementations of such gates, for example, using coupled cavity arrays, ion traps, etc. A particular implementation relevant for our work is one with Rydberg superatoms in a single one-mode microwave cavity given by Zhao et al. Phys Rev A 98:032313 (2018). Zhao et al. (2018) have shown how to design a holonomic two-qubit gate using this scheme. However, their scheme doesn’t straight-forwardly extend to the 3-qubit case. Our work is focused on designing a nonadiabatic holonomic 3-qubit gate with Rydberg superatoms in a single cavity. Our scheme involves sending two species (i.e., with different level structures) of Rydberg superatoms into a two-mode cavity. The computational basis is formed by the four collective ground states of the two species of superatoms that interact with each other via the common cavity mode. For specific values of the gate parameters, we show how the Toffoli gate (controlled-controlled-NOT gate) and Fredkin gate (controlled-swap gate) can be realized.
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