论文标题
在Bloch Sphere上量子步行
Quantum walk on the Bloch sphere
论文作者
论文摘要
提出了用于在BLOCH球体上实施离散时间量子步行的方案，该方案与SU（2）组密切相关。旋转簇用作步行者，而其位于Bloch球的位置则由自旋连贯状态描述。与自旋簇相互作用的另一个自旋发挥了硬币的作用，该硬币的状态决定了自旋簇的旋转。计算了Wigner函数，以可视化Walker在Bloch球体上的运动，还可以通过该运动来实现概率分布和标准偏差。确认了Bloch球上量子步行方差的二次增强。与理想的量子步行相比，Bloch球上的步行者状态通常是非正交的，可以通过增加自旋簇中的旋转数量来消除其缺点。
A scheme for implementing the discrete-time quantum walk on the Bloch sphere is proposed, which is closely related to the SU(2) group. A spin cluster serves as the walker, whereas its location on the Bloch sphere is described by the spin coherent state. An additional spin that interacts with the spin cluster plays the role of a coin, whose state determines the rotation of the spin cluster. The Wigner function is calculated to visualize the movement of the walker on the Bloch sphere, with which the probability distribution and the standard deviation are also achieved. The quadratic enhancement of variance for the quantum walk on the Bloch sphere is confirmed. Compared to the ideal quantum walk on a circle, the walker's states on the Bloch sphere are generally nonorthogonal, whose drawbacks can be eliminated by increasing the number of spins in the spin cluster.
