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

TL;DR

This paper demonstrates how Floquet engineering can induce non-Abelian geometric phases in ultracold atoms, enabling holonomic quantum gates without requiring explicit degeneracy, thus offering a new approach for quantum computing.

Contribution

It introduces a Floquet engineering method to realize non-Abelian geometric phases in ultracold atoms, bypassing the need for degeneracy in holonomic quantum computing.

Findings

Successful implementation of non-Abelian gauge structures via Floquet engineering.

High-fidelity single-qubit holonomic gate operations demonstrated.

Limitations similar to traditional degenerate systems are inherited.

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.