Investigation of Floquet engineered non-Abelian geometric phase for holonomic quantum computing

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.

References in corpus (11)

• Non-Abelian Anyons and Topological Quantum Computation
• Fault-Tolerant Quantum Dynamical Decoupling
• Experimental Realization of Universal Geometric Quantum Gates with Solid-State Spins
• Optical holonomic single quantum gates with a geometric spin under a zero field
• Fault-tolerant holonomic quantum computation
• Artificial gauge fields with ultracold atoms
• Floquet analysis of a quantum system with modulated periodic driving
• Ultra-low noise magnetic field for quantum gases
• Dynamical-decoupling-protected nonadiabatic holonomic quantum computation
• Active stabilization of kilogauss magnetic fields to the ppm level for magnetoassociation on ultranarrow Feshbach resonances
• Robust nonadiabatic geometric quantum computation by dynamical correction

Cited by in corpus (1)

• Floquet geometric entangling gates in ground-state manifolds of Rydberg atoms