Noise-based logic hyperspace with the superposition of 2^N states in a single wire

Details Noise-based logic hyperspace with the superposition of 2^N states in a single wire Noise-based logic hyperspace with the superposition of 2^N states in a single wire

2009-01-26

arxiv.org/abs/0901.3947v5

Physics Letters A 373 (2009) 1928-1934

Physics

General Physics

Accepted for publication in Phys.Lett. A on March 21, 2009. The corrected proof is accessible at PLA (Article in press) or at

Scientific paper

10.1016/j.physleta.2009.03.059

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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