布尔函数的量子计算表示
Representation of Boolean functions in terms of quantum computation
摘要：
本文综述了量子物理与离散数学的关系。考虑布尔函数的酉表示。描述了定义布尔函数代数范式的Zhegalkin多项式与量子逻辑电路之间的关系。结果表明，量子信息方法提供了一种简单的算法，利用真值表构造Zhegalkin多项式。所开发的方法和算法具有任意布尔函数的推广性，具有多位输入和多位输出。这样的推广允许我们使用多值逻辑（k值逻辑，其中k是素数）。开发的方法和算法可以显着提高量子技术的实现。所提出的方法是从经典机器逻辑过渡到量子硬件的基线。
英文摘要：
The relationship between quantum physics and discrete mathematics is reviewed in this article. The Boolean functions unitary representation is considered. The relationship between Zhegalkin polynomial, which defines the algebraic normal form of Boolean function, and quantum logic circuits is described. It is shown that quantum information approach provides simple algorithm to construct Zhegalkin polynomial using truth table. Developed methods and algorithms have arbitrary Boolean function generalization with multibit input and multibit output. Such generalization allows us to use many-valued logic (k-valued logic, where k is a prime number). Developed methods and algorithms can significantly improve quantum technology realization. The presented approach is the baseline for transition from classical machine logic to quantum hardware.
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