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Abstract: In the introductory paper, Physics Letters A 373 2009 911-918,arXiv:0808.3162, about noise-based logic, we showed how simple superpositionsof single logic basis vectors can be achieved in a single wire. Thesuperposition components were the N orthogonal logic basis vectors. Supposingthat the different logic values have -on-off- states only, the resultantdiscrete superposition state represents a single number with N bit accuracy ina 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 vectorsdefined in the introductory paper can be generalized to provide the discretesuperposition of 2^N orthogonal system states. This is equivalent to amulti-valued logic system with 2^2^N logic values per wire. This is a similarsituation to quantum informatics with N qubits, and hence we introduce thenotion of noise-bit. This system has major differences compared to quantuminformatics. The noise-based logic system is deterministic and eachsuperposition element is instantly accessible with the high digital accuracy,via a real hardware parallelism, without decoherence and error correction, andwithout the requirement of repeating the logic operation many times to extractthe probabilistic information. Moreover, the states in noise-based logic do nothave to be normalized, and non-unitary operations can also be used. As anexample, we introduce a string search algorithm which is OM^0.5 times fasterthan Grover-s quantum algorithm where M is the number of string entries,while it has the same hardware complexity class as the quantum algorithm.

Autor: Laszlo B. Kish, Sunil Khatri, Swaminathan Sethuraman


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