Investigation of Floquet engineered non-Abelian geometric phase for
holonomic quantum computing
- URL: http://arxiv.org/abs/2307.12957v2
- Date: Wed, 6 Mar 2024 17:32:59 GMT
- Title: Investigation of Floquet engineered non-Abelian geometric phase for
holonomic quantum computing
- Authors: Logan W. Cooke, Arina Tashchilina, Mason Protter, Joseph Lindon, Tian
Ooi, Frank Marsiglio, Joseph Maciejko, Lindsay J. LeBlanc
- Abstract summary: We present an experiment in ultracold $87$Rb atoms where atomic spin states are dressed by modulated RF fields to induce periodic driving of a family of Hamiltonians linked through a tuneable parameter space.
The adiabatic motion through this parameter space leads to the holonomic evolution of the degenerate spin states in $SU(2)$, characterized by a non-Abelian connection.
Results indicate that while the Floquet engineering technique removes the need for explicit degeneracies, it inherits many of the same limitations present in degenerate systems.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Holonomic quantum computing (HQC) functions by transporting an adiabatically
degenerate manifold of computational states around a closed loop in a
control-parameter space; this cyclic evolution results in a non-Abelian
geometric phase which may couple states within the manifold. Realizing the
required degeneracy is challenging, and typically requires auxiliary levels or
intermediate-level couplings. One potential way to circumvent this is through
Floquet engineering, where the periodic driving of a nondegenerate Hamiltonian
leads to degenerate Floquet bands, and subsequently non-Abelian gauge
structures may emerge. Here we present an experiment in ultracold $^{87}$Rb
atoms where atomic spin states are dressed by modulated RF fields to induce
periodic driving of a family of Hamiltonians linked through a fully tuneable
parameter space. The adiabatic motion through this parameter space leads to the
holonomic evolution of the degenerate spin states in $SU(2)$, characterized by
a non-Abelian connection. We study the holonomic transformations of spin
eigenstates in the presence of a background magnetic field, characterizing the
fidelity of these single-qubit gate operations. Results indicate that while the
Floquet engineering technique removes the need for explicit degeneracies, it
inherits many of the same limitations present in degenerate systems.
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