Driven geometric phase gates with trapped ions

Abstract

We describe a hybrid laser-microwave scheme to implement twoqubit geometric phase gates in crystals of trapped ions. The proposed gates can attain errors below the fault-tolerance threshold in the presence of thermal, dephasing, laser-phase and microwave-intensity noise. Moreover, our proposal is technically less demanding than previous schemes, since it does not require a laser arrangement with interferometric stability. The laser beams are tuned close to a single vibrational sideband to entangle the qubits, while strong microwave drivings provide the geometric character to the gate, and thus protect the qubits from these different sources of noise. A thorough analytic and numerical study of the performance of these gates in realistic noisy regimes is presented. A. Magnus expansion for the driven single-sideband Hamiltonian 28 Appendix B. Stochastic processes for the noise sources 31 References 372. Driven single-sideband geometric phase gates Two-ion crystals as the hardware for quantum logic gatesLet us start by describing the system under consideration: a two-ion (N = 2) crystal confined in a linear Paul trap [10]. Under certain conditions [11], such radio-frequency traps provide an effective quadratic confining potential, which is characterized by the so-called axial ω z , and radial {ω x , ω y } trap frequencies. Moreover, when {ω x , ω y } ω z , the ion equilibrium positions arrange in a string along the trap z-axis. As customary in these cases, when the particles only 2 During the completion of this work, we became aware of the results of [9]. In this work, the authors have also generalized the scheme described in [8] to the near-resonance regime where faster gates can be achieved. Moreover, they have presented an experimental realization of these ideas, showing that two-qubit gates with errors ε 2,q ≈ 2.6 × 10 −2 can be achieved using this hybrid laser-microwave scheme.

Quantization of time-dependent non-central singular potential systems in three dimensions by using the Nikiforov-Uvarov method

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Quantum transport of energy in controlled synthetic quantum magnets

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Floquet engineering to entanglement protection of distant nitrogen vacancy centers

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