基于噪声的单线2^N态叠加逻辑超空间
Noise-based logic hyperspace with the superposition of 2^N states in a single wire
摘要：
在关于基于噪声的逻辑的介绍性论文[Physics Letters A 373（2009）911-918]，arXiv：0808.3162中，我们展示了如何在单线中实现单个逻辑基向量的简单叠加。叠加分量是N个正交逻辑基向量。假设不同的逻辑值仅具有“开/关”状态，所得到的离散叠加状态表示单线中具有N位精度的单个数，其中N是基中正交逻辑向量的数目。在本文中，我们证明了在引言中定义的逻辑超空间（乘积）向量可以推广到提供2^N个正交系统状态的离散叠加。这相当于一个多值逻辑系统，每条线有2^（2^N）个逻辑值。这与具有N个量子比特的量子信息学类似，因此我们引入了噪声比特的概念。这个系统与量子信息学有很大的不同。基于噪声的逻辑系统是确定性的，并且每个叠加元件可以通过实际的硬件并行性以高数字精度立即访问，而不需要去相干和纠错，并且不需要多次重复逻辑运算以提取概率信息。此外，基于噪声的逻辑中的状态不必被归一化，并且也可以使用非酉运算。作为一个例子，我们引入了一个字符串搜索算法，它比Grover的量子算法（其中M是字符串条目的数量）快O（M^0.5）倍，而它与量子算法具有相同的硬件复杂度。
英文摘要：
In the introductory paper, [Physics Letters A 373 (2009) 911-918], arXiv:0808.3162, about noise-based logic, we showed how simple superpositions of single logic basis vectors can be achieved in a single wire. The superposition components were the N orthogonal logic basis vectors. Supposing that the different logic values have "on/off" states only, the resultant discrete superposition state represents a single number with N bit accuracy in a single wire, where N is the number of orthogonal logic vectors in the base. In the present paper, we show that the logic hyperspace (product) vectors defined in the introductory paper can be generalized to provide the discrete superposition of 2^N orthogonal system states. This is equivalent to a multi-valued logic system with 2^(2^N) logic values per wire. This is a similar situation to quantum informatics with N qubits, and hence we introduce the notion of noise-bit. This system has major differences compared to quantum informatics. The noise-based logic system is deterministic and each superposition element is instantly accessible with the high digital accuracy, via a real hardware parallelism, without decoherence and error correction, and without the requirement of repeating the logic operation many times to extract the probabilistic information. Moreover, the states in noise-based logic do not have to be normalized, and non-unitary operations can also be used. As an example, we introduce a string search algorithm which is O(M^0.5) times faster than Grover's quantum algorithm (where M is the number of string entries), while it has the same hardware complexity class as the quantum algorithm.
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