Investigation of Floquet engineered non-Abelian geometric phase for holonomic quantum computing
arXiv:2307.12957 · doi:10.1103/PhysRevResearch.6.013057
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 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 , 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 (43)
- Non-Abelian Anyons and Topological Quantum Computation
- Optical Magnetometry
- Dynamical Decoupling of Open Quantum Systems
- Holonomic Quantum Computation
- Geometric quantum computation with NMR
- Geometric Manipulation of Trapped Ions for Quantum Computation
- Quantum Error Correction for Beginners
- Fault-Tolerant Quantum Dynamical Decoupling
- Experimental Realization of Nonadiabatic Holonomic Quantum Computation
- Non-adiabatic holonomic quantum computation
- Experimental Realization of Universal Geometric Quantum Gates with Solid-State Spins
- Experimental Realization of Non-Abelian Geometric Gates
- Symmetrizing Evolutions
- Non-Abelian Berry connections for quantum computation
- Non-Adiabatic Holonomic Quantum Computation in Decoherence-Free Subspaces
- The Peierls substitution in an engineered lattice potential
- Artificial gauge fields in materials and engineered systems
- A Short Introduction to Topological Quantum Computation
- Optical holonomic single quantum gates with a geometric spin under a zero field
- Experimental Realization of Nonadiabatic Shortcut to Non-Abelian Geometric Gates
- Quantum Holonomies for Quantum Computing
- Nonadiabatic geometric quantum computation with cat qubits via invariant-based reverse engineering
- Fault-tolerant holonomic quantum computation
- Artificial gauge fields with ultracold atoms
- Floquet analysis of a quantum system with modulated periodic driving
- Non-Abelian adiabatic geometric transformations in a cold Strontium gas
- Ultra-low noise magnetic field for quantum gases
- Dynamical-decoupling-protected nonadiabatic holonomic quantum computation
- Complete unitary qutrit control in ultracold atoms
- Product Integral Formalism and Non-Abelian Stokes Theorem
- Optimal design strategy for non-Abelian geometric phases using Abelian gauge fields based on quantum metric
- Experimental Realization of Nonadiabatic Holonomic Single-Qubit Quantum Gates with Two Dark Paths in a Trapped Ion
- Wilson loop and Wilczek-Zee phase from a non-Abelian gauge field
- Active stabilization of kilogauss magnetic fields to the ppm level for magnetoassociation on ultranarrow Feshbach resonances
- Highly-Degenerate Photonic Waveguide Structures for Holonomic Computation
- Decoherence-Suppressed Non-adiabatic Holonomic Quantum Computation
- Atom-Orbital Qubits under Holonomic Quantum Control
- Conditions for Equivalent Noise Sensitivity of Geometric and Dynamical Quantum Gates
- Non-Abelian geometric phases in periodically driven systems
- Robust nonadiabatic geometric quantum computation by dynamical correction
- An SU(2) geometric phase induced by periodically driven Raman process in an ultracold dilute Bose gas
- Error-Resilient Floquet Geometric Quantum Computation
- Measurement and Significance of Wilson Loops in Synthetic Gauges Fields