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

TL;DR

This paper extends noise-based logic to create a hyperspace with 2^N superposition states in a single wire, enabling deterministic, high-accuracy multi-valued logic with potential computational advantages over quantum algorithms.

Contribution

It generalizes noise-based logic to superpose 2^N states, introduces the concept of noise-bit, and demonstrates a faster string search algorithm compared to Grover's quantum algorithm.

Findings

Superposition of 2^N states in a single wire achieved.

Noise-based logic is deterministic and hardware-efficient.

Proposed string search algorithm is faster than Grover's algorithm.

Abstract

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.