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.
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.
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.
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.
Instantaneous Noise-Based Logic (INBL) represents a computational paradigm that offers a deterministic alternative to quantum computing, potentially challenging the notion of quantum supremacy without relying on quantum hardware. INBL encodes logical information in orthogonal stochastic processes (“noise-bits”) and exploits their superpositions and nonlinear interactions to achieve an exponentially large computational space of dimension [Formula: see text], where M corresponds to the number of noise-bits analogous to qubits in quantum computing. This approach enables an exponential increase in computational throughput, with a computational speedup scaling on the order of O([Formula: see text], while maintaining hardware complexity comparable to quantum systems. Unlike quantum computers, INBL operates without decoherence, error correction, or probabilistic measurement, yielding deterministic outputs with low error probability. Demonstrated applications include exponential speed-gain compared to classical computers, such as INBL phonebook searches (for number or name lookup) and the implementation of the Deutsch–Jozsa algorithm, illustrating INBL’s capability to perform special-purpose computations with quantum-like exponential speedup using classical-physical noise-based hardware. We present an experimental comparison between the execution speeds of a Classical Turing machine algorithm — which changes the values of odd numbers in an exponentially large set to their next lower even numbers — and its INBL counterpart. Another experimental demonstration of the exponential speedup in finding and removing a given number from an exponentially large, unsorted set of integers.
Exponential parallelism, a defining principle of advanced computational systems, holds promise for transformative impacts across several scientific and industrial domains. This feature paper provides a comparative overview of Quantum Computing (QC) and Instantaneous Noise-based Logic (INBL), focusing on their practical strengths, limitations and applications rather than exhaustive technical depth. Both paradigms leverage exponentially large Hilbert spaces: QC achieves this via quantum superposition, while INBL realizes it through the product space of classical noise processes. Quantum computers attain universality for all computational operations, whereas current INBL frameworks are universal only for Boolean logic; notably, essential superposition operations — such as AND and OR gates — are absent, precluding implementations of algorithms like Shor’s. However, for certain problem classes where full universality is not required, INBL and QC can offer equivalent time and hardware complexity, as observed with the Deutsch–Jozsa algorithm. Remarkably, for search tasks such as phonebook lookup, Grover’s quantum algorithm provides a quadratic [Formula: see text] speedup compared to the classical approach, while INBL achieves an exponential speedup, requiring only logarithmic time in the size N of the phonebook [Formula: see text]. Such INBL algorithms could, in principle, be adapted to quantum hardware to attain similar performance. Importantly, INBL hardware is considerably simpler, being implementable with modest modifications to conventional PC architectures equipped with a true random number generator, and it inherently avoids the decoherence and error correction challenges of quantum systems.
Exponential parallelism, a defining principle of advanced computational systems, holds promise for transformative impacts across several scientific and industrial domains. This feature paper provides a comparative overview of Quantum Computing (QC) and Instantaneous Noise-based Logic (INBL), focusing on their practical strengths, limitations, and applications rather than exhaustive technical depth. Both paradigms leverage exponentially large Hilbert spaces: quantum computing achieves this via quantum superposition, while INBL realizes it through the product space of classical noise processes. Quantum computers attain universality for all computational operations, whereas current INBL frameworks are universal only for Boolean logic; notably, essential superposition operations-such as AND and OR gates-are absent, precluding implementations of algorithms like Shor's. However, for certain problem classes where full universality is not required, INBL and quantum computing can offer equivalent time and hardware complexity, as observed with the Deutsch-Jozsa algorithm. Remarkably, for search tasks such as phonebook lookup, Grover's quantum algorithm provides a quadratic O(n^0.5) speedup compared to the classical approach, while INBL achieves an exponential speedup, requiring only logarithmic time in the size n of the phonebook O(log n). Such INBL algorithms could, in principle, be adapted to quantum hardware to attain similar performance. Importantly, INBL hardware is considerably simpler, being implementable with modest modifications to conventional PC architectures equipped with a true random number generator, and it inherently avoids the decoherence and error correction challenges of quantum systems.
Abstract Instantaneous noise-based logic (INBL) leverages the products and superpositions of uncorrelated noise signals to construct a 2^N-dimensional Hilbert space (‘hyperspace’). This approach has been investigated for complex computational tasks traditionally associated with quantum computing, such as the Deutsch–Jozsa algorithm and phonebook search problems. In this study, we delve into the statistical characteristics of this computational framework. To facilitate simulations, we developed an INBL engine. N noise bits represented by 2N uncorrelated reference noises (random telegraph waves (RTWs)) form a 2^N-dimensional space when used in superpositions. N-long binary strings are the hyperspace vectors formed by the products of the relevant reference noises that represent the corresponding bit values. The superpositions of the 2^N possible products collectively define the 2^N-dimensional universe. To prevent the occurrence of zeros in the time function of the universe signal, we implemented an asymmetric amplitude scheme for the 2N reference noise bits, utilizing different absolute amplitude values for the N uncorrelated waves of low (L) and high (H) bit values. The simulation results indicate that the distribution of discrete amplitudes within the universe waveform (time function) deviates from Gaussianity. This finding reinforces that we cannot assert independence among hyperspace vectors, even though they exhibit zero cross-correlation. Another observation is rare random spikes in the universe waveform; surprisingly, the distribution of their magnitudes (absolute values) conforms to a Gaussian curve. Both the magnitude and the mean frequency of these spikes depend on the number of noise bits N. As N increases, the number of discrete amplitude levels also rises, leading to a broader distribution. Conversely, with a growing N, both the relative magnitudes and frequency of spikes in the superposition diminish. The observed critical statistical properties can affect the implementation of INBL in practical applications, particularly by suggesting potential implications for the energy and supply voltage requirements in processors, although a detailed hardware-level energy model is beyond the scope of this work and is left for future study.