Robson Barry, St Clair Jim
The Dirac Foundation, Oxfordshire, UK; Ingine Inc, USA.
Linux Foundation Public Health, San Franciso, USA.
Comput Biol Med. 2022 Apr;143:105323. doi: 10.1016/j.compbiomed.2022.105323. Epub 2022 Feb 16.
This paper reviews some basic principles of Quantum Mechanics, Quantum Computing, and Artificial Intelligence in terms of a specific unifying theme. This theme relates to the hyperbolic or split-complex imaginary numbers and their equivalent matrices, rediscovered by Dirac, and the underlying mathematics of the previously described Q-UEL language based on them. Hyperbolic imaginary numbers h have the property hh = +1: contrast the more familiar i such that ii = -1. Examples of analogous matrices include that for the Hadamard gate as used in quantum computing and the Pauli spin matrices, and all Hermitian matrices of interest in quantum computing can readily be derived from these. They also relate to Dirac dualization, spinor projectors of Quantum Field Theory, the non-wave-like part of quantum theory, collapse of the wave function, and a dualized form of classical probability theory that has advantages in automated reasoning for medicine.
本文从一个特定的统一主题出发，回顾了量子力学、量子计算和人工智能的一些基本原理。这个主题涉及双曲或分裂复数虚数及其等价矩阵，由狄拉克重新发现，以及基于它们的先前描述的Q-UEL语言的基础数学。双曲虚数h具有hh = +1的性质：对比更熟悉的i，其ii = -1。类似矩阵的例子包括量子计算中使用的哈达玛门的矩阵以及泡利自旋矩阵，并且量子计算中所有感兴趣的厄米矩阵都可以很容易地从这些矩阵推导出来。它们还与狄拉克对偶化、量子场论的旋量投影器、量子理论的非波状部分、波函数坍缩以及经典概率论的对偶形式相关，这种对偶形式在医学自动推理中具有优势。
