16、量子计算算法与微激射器中的连续变量量子计算

量子计算算法与微激射器中的连续变量量子计算

1. 量子查询算法计算布尔函数

在量子计算领域，对于布尔函数的计算有多种算法。这里介绍量子算法Q2用于计算布尔函数AND2(x1, x2)的情况。

| X | (|\phi_2\rangle = Q_0U_0 |00\rangle) | (|\phi_{FINAL}\rangle = U_2U_1Q_0U_0 |00\rangle) | (p(AND2 = 1)) |
| — | — | — | — |
| 00 | ((\frac{1}{2}, \frac{1}{2}, \frac{1}{2}, -\frac{1}{2})^T) | ((\frac{1}{2}, \frac{1}{\sqrt{10}}, \sqrt{\frac{2}{5}}, -\frac{1}{2})^T) | (\frac{1}{10}) |
| 01 | ((\frac{1}{2}, \frac{1}{2}, -\frac{1}{2}, -\frac{1}{2})^T) | ((0, -\frac{1}{\sqrt{10}}, \frac{3}{\sqrt{10}}, 0)^T) | (\frac{1}{10}) |
| 10 | ((-\frac{1}{2}, -\frac{1}{2}, \frac{1}{2}, -\frac{1}{2})^T) | ((\frac{1}{2}, -\frac{1}{\sqrt{10}}, -\sqrt{\frac{2}{5}}, -\frac{1}{2})^T) | (\frac{1}{10}) |
| 11 | ((-\frac{1}{2}, -\frac{1}{2}, -\frac{1}{2