Chemistry Department, Marquette University, PO Box 1881, Milwaukee, Wisconsin 53201, USA.
J Chem Phys. 2012 Aug 14;137(6):064301. doi: 10.1063/1.4742309.
We demonstrate theoretically that it may be possible to encode states of a multi-qubit system into the progression of quantized motional∕vibrational levels of an ion trapped in a weakly anharmonic potential. Control over such register of quantum information is achieved by applying oscillatory radio-frequency fields shaped optimally for excitation of the desired state-to-state transitions. Anharmonicity of the vibrational spectrum plays a key role in this approach to the control and quantum computation, since it allows resolving different state-to-state transitions and addressing them selectively. Optimal control theory is used to derive pulses for implementing the four-qubit version of Shor's algorithm in a single step. Accuracy of the qubit-state transformations, reached in the numerical simulations, is around 0.999. Very detailed insight is obtained by analysis of the time-evolution of state populations and by spectral analysis of the optimized pulse.
我们从理论上证明，将多量子比特系统的状态编码到被困在弱非谐势中的离子的量子化运动/振动能级的进展中是可能的。通过应用最佳形状的振荡射频场来激发所需的态-态跃迁，可以实现对这种量子信息寄存器的控制。振动谱的非谐性在这种控制和量子计算方法中起着关键作用，因为它允许解析不同的态-态跃迁并选择性地处理它们。最优控制理论用于导出脉冲，以在单个步骤中实现 Shor 算法的四量子比特版本。在数值模拟中达到的量子比特状态变换的精度约为 0.999。通过分析状态种群的时间演化和优化脉冲的频谱分析，可以获得非常详细的见解。
