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arXiv:1201.6171 · Physical Review A

Modeling of quantum-information processing with Ehrenfest guided trajectories: A case study with spin-boson-like couplings

Sai-Yun Ye, Dmitrii V. Shalashilin, Alessio Serafini

Published Sep 13, 2012• 9 citations
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Abstract

We apply a numerical method based on multiconfigurational Ehrenfest trajectories and demonstrate converged results for the Choi fidelity of an entangling quantum gate between two two-level systems interacting through a set of bosonic modes. We consider both spin-boson and rotating-wave Hamiltonians for various numbers of mediating modes (from 1 to 100) and extend our treatment to include finite temperatures. Our results apply to two-level impurities interacting with the same band of a photonic crystal or to two distant ions interacting with the same set of motional degrees of freedom.

DOI
10.1103/physreva.86.032312

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We apply a numerical method based on multiconfigurational Ehrenfest trajectories and demonstrate converged results for the Choi fidelity of an entangling quantum gate between two two-level systems interacting through a set of bosonic modes. We consider both spin-boson and rotating-wave Hamiltonians for various numbers of mediating modes (from 1 to 100) and extend our treatment to include finite temperatures. Our results apply to two-level impurities interacting with the same band of a photonic crystal or to two distant ions interacting with the same set of motional degrees of freedom.
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A generalized version of the coupled coherent states method for coherent states of arbitrary Lie groups is developed. In contrast to the original formulation, which is restricted to frozen-Gaussian basis sets, the extended method is suitable for propagating quantum states of systems featuring diversified physical properties, such as spin degrees of freedom or particle indistinguishability. The approach is illustrated with simple models for interacting bosons trapped in double- and triple-well potentials, most adequately described in terms of SU(2) and SU(3) bosonic coherent states, respectively.
A long-standing challenge in mixed quantum-classical trajectory simulations is the treatment of entanglement between the classical and quantal degrees of freedom. We present a novel approach that describes the emergence of entangled states entirely in terms of independent and deterministic Ehrenfest-like classical trajectories. For a two-level quantum system in a classical environment, this is derived by mapping the quantum system onto a path-integral representation of a spin 1/2. We demonstrate that the method correctly accounts for coherence and decoherence and thus reproduces the splitting of a wave packet in a nonadiabatic scattering problem. This discovery opens up a new class of simulations as an alternative to stochastic surface-hopping, coupled-trajectory, or semiclassical approaches.
We study the interaction between a two-level system and a harmonic oscillator without the rotating-wave approximation (RWA). In quantum optics, this model (sometimes called the spin-boson model) is traditionally thought of as a two-Ievel atom coupled to a single-mode radiation field, but it could also describe (1) a two-level ion in a trap coupled to the motion of its own center of mass or (2) a two-level particle in a solid coupled to a phonon mode. For sufficiently strong coupling, this model is known to exhibit chaos in a variety of semi-classical approximations.1
A long-standing challenge in mixed quantum-classical trajectory simulations is the treatment of entanglement between the classical and quantal degrees of freedom. We present a novel approach which describes the emergence of entangled states entirely in terms of independent and deterministic Ehrenfest-like classical trajectories. For a two-level quantum system in a classical environment, this is derived by mapping the quantum system onto a path-integral representation of a spin-1/2. We demonstrate that the method correctly accounts for coherence and decoherence and thus reproduces the splitting of a wavepacket in a nonadiabatic scattering problem. This discovery opens up a new class of simulations as an alternative to stochastic surface-hopping, coupled-trajectory or semiclassical approaches.