Fluctuation and Noise Letters

FAST MEASUREMENT OF HYPERSPACE VECTORS IN NOISE-BASED LOGIC

László L. Stachó

Published Mar 19, 2012• 12 citations

Abstract

We propose a method to determine single hyperspace vectors (product strings of noise-bits) by classical means with the same effectiveness as the results using time shifted noise-based logic. A system of binary linear equations based on the amplitudes of the hyperspace vector and the reference noise-bits is set up and solved after enough independent information is collected. The resulting error probability (the chance of getting no answer) has approximately an exponential decay with the time of measurement.

DOI: 10.1142/s0219477512500010

Related papers

NEW NOISE-BASED LOGIC REPRESENTATIONS TO AVOID SOME PROBLEMS WITH TIME COMPLEXITY

He Wen, László B. Kish, Andreas Klappenecker +1 more

Instantaneous noise-based logic can avoid time-averaging, which implies significant potential for low-power parallel operations in beyond-Moore-law-chips. However, in its random-telegraph-wave representation, the complete uniform superposition (superposition of all N-bit binary numbers) will be zero with high probability, that is, non-zero with exponentially low probability, thus operations with the uniform superposition would require exponential time-complexity. To fix this deficiency, we modify the amplitudes of the signals of L and H states and achieve an exponential speedup compared to the old situation. Another improvement concerns the identification of a single product-string (hyperspace vector). We introduce "time shifted noise-based logic", which is constructed by shifting each reference signal with a small time delay. This modification implies an exponential speedup of single hyperspace vector identification compared to the former case and it requires the same, O(N) complexity as in quantum computing.

arXiv:1111.3859Fluctuation and Noise LettersMar 19, 201222 citations

FAST MEASUREMENT OF HYPERSPACE VECTORS IN NOISE-BASED LOGIC

László L. Stachó

WORLD SCIENTIFIC eBooksFeb 1, 20221 citation

Entanglement, and Unsorted Database Search in Noise-Based Logic

László B. Kish, Walter C. Daugherity

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.

arXiv:1905.03162Applied SciencesJul 27, 201910 citations

Pairwise XOR & XNOR Operations in Squeezed Instantaneous Noise-Based Logic

Nasir Kenarangui, Arthur Powalka, László B. Kish

Instantaneous noise-based logic (INBL) is a novel computing approach that encodes binary information using stochastic processes. It uses [Formula: see text] orthogonal stochastic reference noises for M noise-bits to construct an exponentially large Hilbert space (hyperspace) of dimension [Formula: see text]. INBL offers a classical alternative to quantum-style parallelism for specific problems with exponential speedup compared with classical algorithms. Building on recent work that introduced pairwise [Formula: see text] and [Formula: see text] operations defined for a symmetric INBL scheme, this paper implements these gates for a squeezed INBL scheme. Hyperspace vectors are product strings corresponding to M-bit long binary numbers. The proposed operations can apply pairwise on hyperspace vectors and their superpositions (sums), while remaining compatible with the squeezed reference system. We validate that the squeezed-scheme [Formula: see text] gate operations have correct Boolean behavior over both bitwise and targeted M-bit strings and demonstrate that the operations preserve instantaneous evaluation. The results show that the [Formula: see text] toolkit, previously developed for symmetric INBL, can be tailored for the squeezed scheme. This development is a key part of the gate set needed for more complex INBL algorithms in the squeezed INBL scheme and advances the objective of gate universality in INBL. It further strengthens the case for INBL as a flexible, classical computing framework that can emulate some structural advantages of quantum computation.

Fluctuation and Noise LettersApr 30, 20260 citations

New XOR & XNOR Operations in Instantaneous Noise-Based Logic

Nasir Kenarangui, Arthur Powalka, László B. Kish

Instantaneous Noise-Based Logic (INBL) is a classical noise-based computing framework that serves as an alternative to quantum computation. However, some of the logic gates remain unimplemented for achieving gate universality over superpositions. INBL encodes M noise-bits using [Formula: see text] orthogonal stochastic reference noises to construct a [Formula: see text]-dimensional product-based Hilbert space (hyperspace). Each vector in this hyperspace is the product of M noise-bits, and each noise-bit corresponds to one of two reference noises. This work introduces INBL implementations of XOR and XNOR gate operations formulated for the symmetric INBL scheme. The resulting gate algorithms support pairwise operations between strings of arbitrary length and naturally extend to superpositions. This offers the potential for substantial gains in computational speed and reductions in hardware complexity. In particular, the XOR and XNOR gates can act on inputs drawn from any combination of individual noise-bits, full bit strings, or superpositions. Diverging from previous methods by Khreishah et al., our approach avoids direct manipulation of the reference noise system, enabling more flexible and general-purpose implementations. We validate NOT, XOR and XNOR operations in symmetric INBL, through simulations using random telegraph waves (RTW), demonstrating practical feasibility without explicit reference noise manipulation.

arXiv:2511.10679Fluctuation and Noise LettersJan 16, 20260 citations

Pairwise XOR and XNOR Gates in Squeezed Instantaneous Noise Based Logic

Nasir Kenarangui, László B. Kish, Arthur Powalka

Instantaneous noise-based logic (INBL) is a novel computing approach that encodes binary information using stochastic processes. It uses 2M orthogonal stochastic reference noises for M noise-bits to construct an exponentially large Hilbert space (hyperspace) of dimension 2^M. INBL offers a classical alternative to quantum-style parallelism for specific problems with exponential speedup compared to classical algorithms. Building on recent work that introduced pairwise XOR and XNOR operations defined for a symmetric INBL scheme, this paper implements these gates for a squeezed INBL scheme. Hyperspace vectors are product strings corresponding to M-bit long binary numbers. The proposed operations can apply pairwise on hyperspace vectors and their superpositions, while remaining compatible with the squeezed reference system. We validate that the squeezed-scheme XOR/XNOR gate operations have correct Boolean behavior over both bitwise and targeted M-bit strings and demonstrate that the operations preserve instantaneous evaluation. The results show that the XOR/XNOR toolkit, previously developed for symmetric INBL, can be tailored for the squeezed scheme. This development is a key part of the gate set needed for more complex INBL algorithms in the squeezed INBL scheme and advances the objective of gate universality in INBL. It further strengthens the case for INBL as a flexible, classical computing framework that can emulate some structural advantages of quantum computation.

arXiv:2602.15032Jan 15, 20260 citations