Drawing from hats by noise-based logic

Zhang, Bruce; Kish, László B.; Granqvist, Claes G.

doi:10.1080/17445760.2016.1140168

Cited by 9 publications

(35 citation statements)

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“…Bob's job is to measure S(t) and decide which is the actual superposition from these different possibilities. To identify strings, statistical methods exist, e.g., [9,11,12,14] and some of them, like the time-shifted RTW scheme [9] and the Stacho [11] method, require only polynomial computation complexity versus the number of noise-bits. However, these methods used on superposition would require exponential complexity with expanding M (except when the job is to identify a single string and the rest of the superposition is known [14]).…”

Section: Deterministic Measurement and Evaluation Of Entangled Statesmentioning

confidence: 99%

“…In the present situation, S 2 (t) 0 (see Equations (7) and (8)), Bob needs to evaluate which value of the second bit is entangled with the 0 value of the first bit. This string can be evaluated in various known statistical ways, e.g., [9,11,14] but here we again propose a deterministic tool by utilizing the reference wires:…”

Section: Deterministic Measurement and Evaluation Of Entangled Statesmentioning

confidence: 99%

“…However, the NBL schemes and their modes of operations are substantially different, even if some of the computational goals may be the same. While the explorations of NBL are still taking place, it is already clear that in certain demonstrated cases, the robustness and controllability of classical physical systems and information offer strong advantages [14,15] over quantum informatics. Some NBL schemes can offer solutions that either reach beyond the abilities of quantum informatics or offer alternative means with identical potential and less cost, similarly to recent achievements by Ewin Tang in classical computing [16,17].…”

mentioning

confidence: 99%

“…Computer simulation[14] of the product-string of the number 2 (binary number 00000000000000000000000000000010) in an M = 32 noise-bit INBL scheme.…”

mentioning

confidence: 99%

“…Computer simulation[14] of a random telegraph wave carrying the high-bit value of a noise-bit in the asymmetric instantaneous-noise-based logic (INBL) scheme.Appl. Sci.…”

mentioning

confidence: 99%

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Entanglement, and Unsorted Database Search in Noise-Based Logic

Kish

Daugherity

2019

Applied Sciences

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We explore the collapse of “wavefunction” and the measurement of entanglement in the superpositions of hyperspace vectors in classical physical instantaneous-noise-based logic (INBL). We find both similarities with and major differences from the related properties of quantum systems. Two search algorithms utilizing the observed features are introduced. For the first one we assume an unsorted names database set up by Alice that is a superposition (unknown by Bob) of up to n = 2N strings; those we call names. Bob has access to the superposition wave and to the 2N reference noises of the INBL system of N noise bits. For Bob, to decide if a given name x is included in the superposition, once the search has begun, it takes N switching operations followed by a single measurement of the superposition wave. Thus, the time and hardware complexity of the search algorithm is O[log(n)], which indicates an exponential speedup compared to Grover’s quantum algorithm in a corresponding setting. An extra advantage is that the error probability of the search is zero. Moreover, the scheme can also check the existence of a fraction of a string, or several separate string fractions embedded in an arbitrarily long, arbitrary string. In the second algorithm, we expand the above scheme to a phonebook with n names and s phone numbers. When the names and numbers have the same bit resolution, once the search has begun, the time and hardware complexity of this search algorithm is O[log(n)]. In the case of one-to-one correspondence between names and phone numbers (n = s), the algorithm offers inverse phonebook search too. The error probability of this search algorithm is also zero.

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Section: Deterministic Measurement and Evaluation Of Entangled Statesmentioning

confidence: 99%

Section: Deterministic Measurement and Evaluation Of Entangled Statesmentioning

confidence: 99%

mentioning

confidence: 99%

“…Computer simulation[14] of the product-string of the number 2 (binary number 00000000000000000000000000000010) in an M = 32 noise-bit INBL scheme.…”

mentioning

confidence: 99%

“…Computer simulation[14] of a random telegraph wave carrying the high-bit value of a noise-bit in the asymmetric instantaneous-noise-based logic (INBL) scheme.Appl. Sci.…”

mentioning

confidence: 99%

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Entanglement, and Unsorted Database Search in Noise-Based Logic

Kish

Daugherity

2019

Applied Sciences

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‘Quantum supremacy’ revisited: low-complexity, deterministic solutions of the original Deutsch–Jozsa problem in classical physical systems

Kish¹

2023

R. Soc. open sci.

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The original Deutsch–Jozsa (oDJ) problem is for an oracle (realized here as a database) of size N , where, according to their claim, the deterministic solution of the problem on a classical Turing computer requires O( N ) computational complexity. They produced the famous Deutsch–Jozsa quantum algorithm that offered an exponential speed-up over the classical computer, namely O[log( N )] complexity for the solution in a quantum computer. In this paper, the problem is implemented on an instantaneous noise-based logic processor. It is shown that, similarly to the quantum algorithm, the oDJ problem can deterministically be solved with O[log( N )] complexity. The implication is that by adding a truly random coin to a classical Turing machine and using this classical-physical algorithm can also speed up the deterministic solution of the Deutsch–Jozsa problem exponentially, similarly to the quantum algorithm. Then it is realized that the same database and the solution of the Deutsch–Jozsa problem can also be realized by using an identical algorithmic structure in a simpler way, even without noise/random coin. The only lost function in this new system, as compared with noise-based logic, is the ability to do generic parallel logic operations over the whole database. As the latter feature is not needed for the oDJ problem, it is concluded that the problem can be solved on a classical computer with O[log( N )] complexity even without a random coin. Therefore, while the oDJ algorithm is a historically important step in the developments of quantum computers, it is insufficient to prove quantum supremacy. Note, there is also a simplified Deutsch–Jozsa problem proposed later, which is more popular in the field; however, it is irrelevant for the present paper.

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Noise-Based Logic Gates by Operations on the Reference System

Kish

Daugherity

2018

Fluct. Noise Lett.

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We propose a new, low-complexity solution to realize multi-input-bit gates acting on exponentially large superpositions in noise-based logic processors. Two examples are shown, the NOT gate and the CNOT gate. The operations can be executed and repeated with polynomial time and hardware complexity. The lack of a solution of this problem had been one of the major issues prohibiting the efficient realization of Shor's algorithm by Instantaneous Noise-Based Logic, which runs on a classical Turing computer with a true random number generator. With the method described in this paper, we are one step closer to this goal.

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Drawing from hats by noise-based logic

Cited by 9 publications

References 9 publications

Entanglement, and Unsorted Database Search in Noise-Based Logic

Entanglement, and Unsorted Database Search in Noise-Based Logic

‘Quantum supremacy’ revisited: low-complexity, deterministic solutions of the original Deutsch–Jozsa problem in classical physical systems

Noise-Based Logic Gates by Operations on the Reference System

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