Investigation of Floquet engineered non-Abelian geometric phase for holonomic quantum computing
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| Main Authors: | , , , , , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866909129127231488 |
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| author | Cooke, Logan W. Tashchilina, Arina Protter, Mason Lindon, Joseph Ooi, Tian Marsiglio, Frank Maciejko, Joseph LeBlanc, Lindsay J. |
| author_facet | Cooke, Logan W. Tashchilina, Arina Protter, Mason Lindon, Joseph Ooi, Tian Marsiglio, Frank Maciejko, Joseph LeBlanc, Lindsay J. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_12957 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Investigation of Floquet engineered non-Abelian geometric phase for holonomic quantum computing Cooke, Logan W. Tashchilina, Arina Protter, Mason Lindon, Joseph Ooi, Tian Marsiglio, Frank Maciejko, Joseph LeBlanc, Lindsay J. Quantum Physics Quantum Gases Atomic Physics 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. |
| title | Investigation of Floquet engineered non-Abelian geometric phase for holonomic quantum computing |
| topic | Quantum Physics Quantum Gases Atomic Physics |
| url | https://arxiv.org/abs/2307.12957 |