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arXiv:1201.4829 · Physical Review A

Resonant adiabatic passage with three qubits

Sangchul Oh, Yun-Pil Shim, Jianjia Fei, Mark G. Friesen, Xuedong Hu

Published Feb 21, 2013• 49 citations
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Abstract

We investigate the nonadiabatic implementation of an adiabatic quantum teleportation protocol, finding that perfect fidelity can be achieved through resonance. We clarify the physical mechanisms of teleportation, for three qubits, by mapping their dynamics onto two parallel and mutually coherent adiabatic passage channels. By transforming into the adiabatic frame, we explain the resonance by analogy with the magnetic resonance of a spin-1/2 particle. Our results establish a fast and robust method for transferring quantum states and suggest an alternative route toward high-precision quantum gates.

DOI
10.1103/physreva.87.022332

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Abstract For the past few years, shortcuts to adiabaticity have attracted great attention since they can avoid the necessity of slow driving for adiabatic method while inheriting the partial robustness of the adiabatic dynamics. In this paper, a universal approach to implement quantum state transfer in a three‐state system via optimal transitionless quantum driving is presented. The fast path is optimized for great robustness against uncontrolled systematic error by selecting appropriate experimental parameters. The robustness of the protocol is discussed via numerical simulations. Compared with conventional transitionless quantum driving and adiabatic passage, the protocol via optimized transitionless quantum driving possesses more robustness against the systematic error. Furthermore, decoherence arising from atomic spontaneous emission and dephasing only has a slight impact on the fidelity of quantum state transfer. This work opens up a new avenue for high‐fidelity quantum state transfer in the case of the uncontrolled errors.
Adiabatic passage is a standard tool for achieving robust transfer in quantum systems. We show that in driven nonlinear quantum systems adiabatic passage becomes highly nonrobust when the target is unstable. This occurs for a generic (1:2) resonance, for which the complete transfer corresponds to a hyperbolic fixed point featuring an adiabatic connectivity strongly sensitive to small perturbations of the model. By inverse engineering, we devise high-fidelity and robust partially nonadiabatic trajectories. They localize at the approach of the target near the stable manifold of the separatrix, which drives the dynamics towards the target in a robust way. These results can be applicable to atom-molecule Bose-Einstein condensate conversion and to nonlinear optics.
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Adiabatic quantum operations are ubiquitous in fields such as quantum information processing, quantum control, and magnetic resonance, where their high fidelity and general robustness renders them an essential tool for various applications. This inherent robustness due to adiabaticity can, however, be impaired in cases where the experimental conditions strictly require very fast evolution times. In this thesis, we provide a gradient-based numerical optimization protocol for efficiently engineering adiabatic operations, allowing for the systematic inclusion of robustness criteria against various experimental non-idealities, including inhomogeneities and uncertainties in system parameters, as well as perturbations in the Hamiltonian such as spin-spin interactions. \nThe protocol is implemented in the context of adiabatic passages for magnetic resonance, and \nit is shown that in addition to conventional adiabatic pulses, it can also generate exceptionally fast operations that although slightly deviate from adiabaticity in limited instances, still lead to a high fidelity. \nThe effectiveness of our method for addressing perturbations is also demonstrated by designing a fast adiabatic passage for dipolar-coupled electrons, and numerically comparing its performance with a pulse without such considerations.