论文标题
随机量子步行
Randomizing Quantum Walk
论文作者
论文摘要
沃克在标准“离散时间量子步行（DTQW）”中的演变由硬币和偏移统一操作员确定。有条件的换档操作员将步行者的位置移到右或向左按单位步长大小，同时由硬币操作员指定运动方向。可以通过在每个特定间隔中随机选择步骤大小来推广此情况。例如，掷骰子的掷骰值可用于指定硬币后的步长。让我们称之为这样的量子步行“离散时间随机步骤量子步行（DTRSQW）”。每当步行者遵循DTRSQW时，就会获得完全随机的概率分布。我们还分析了另外两种类型的量子步行，即“离散的非偏置量子步行（DTUBQW）”和“离散时间有偏见的量子步行（DTBQW）”。在第一种类型中，步长保持不同于单位大小，但对于左右移位，则相同，而在第二种类型中，左右移位也可能不同。发现DTUBQW中的概率分布遵循一定规则。 DTRSQW的标准偏差（$σ$）高于DTQW，因此DTRSQW的传播速度更快。 DTUBQW的$σ$显示出比DTQW更快的锯齿行为，对于旋转角度和步骤的某些特定值。
The evolution of a walker in standard "Discrete-time Quantum Walk (DTQW)" is determined by coin and shift unitary operators. The conditional shift operator shifts the position of the walker to right or left by unit step size while the direction of motion is specified by the coin operator. This scenario can be generalized by choosing the step size randomly at each step in some specific interval. For example, the value of the roll of a dice can be used to specify the step size after throwing the coin. Let us call such a quantum walk "Discrete-time Random Step Quantum Walk (DTRSQW)". A completely random probability distribution is obtained whenever the walker follows the DTRSQW. We have also analyzed two more types of quantum walks, the "Discrete-time Un-biased Quantum Walk (DTUBQW)" and the "Discrete-time Biased Quantum Walk (DTBQW)". In the first type, the step size is kept different than unit size but the same for left and right shifts, whereas in the second type left and right shifts can also be different. The probability distribution in DTUBQW is found to follow a certain rule. The standard deviation ($σ$) of DTRSQW is higher than DTQW and hence DTRSQW spreads faster. The $σ$ of DTUBQW shows sawtooth behavior with faster spread than DTQW for some specific values of rotation angles and steps.
