July 2021
Beginner to intermediate
274 pages
7h 10m
Chinese
Content preview from 量子计算机编程：从入门到实践
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146
｜
第
9
章
9.1
非整型数据
如何在
QPU
寄存器中编码非整型数据呢？以二进制表示这些值的两种常用方法是
定点
（
fixed point
）和
浮点
（
floating point
）。尽管浮点表示更为灵活（能够用一定数量的比特来
适应我们需要表示的值范围），但考虑到对量子比特的重视和对简单性的渴望，定点表示
在现阶段对我们更有吸引力。
定点表示将寄存器分成两部分，一部分对数值的整数部分进行编码，另一部分对小数部分
进行编码。整数部分使用标准二进制编码来表示，即高位的量子比特表示
2
的幂次增加。
与之相对，在寄存器的小数部分中，量子比特数位的
递减
表示
1/2
的幂次
递增
。
我们通常用
Q
表示法
来描述定点数（请注意，
Q
并不表示
quantum
）。这有助于区分寄存
器中的小数位结束位置和整数位开始位置。
Q
n
.
m
表示在
n
位寄存器中有
m
位为小数，也
就是说，剩余的
(
n
−
m
)
位为整数。当然，我们可以用这一表示法来指定如何使用
QPU
寄
存器编码定点数。图
9-1
显示了以
Q8.6
定点编码方式对值
3.640625
进行编码的八量子比
特寄存器。
量子比特1
量子比特2
量子比特3
量子比特4
量子比特5
量子比特6
量子比特7
量子比特8
图 9-1：值 3.640625 的 Q8.6 定点编码方式，其二进制形式为 11101001
在这个例子中，我们成功地以定点数精确地编码了选定的数值，因为
3.640625 = 2
1
+ 2
0
+
1/2
1
+ 1/2
3
+ 1/2
6
。（太巧了！）当然，我们不可能总是这么幸运。增加定点寄存器整数部
分的位数会扩大它可以编码的整数范围，增加小数部分的位数则会提高小数部分的 ...
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