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.
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.
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 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.
Quantum Supremacy is an expression coined to indicate that there are some hard computational problems that quantum computers can solve exponentially faster than a classical-physical Turing machine (that is, a digital computer). Noise-based Logic (NBL) is a deterministic computation scheme that utilizes a digital computer and a physical true random number generator (TRNG). Recently, several computational problems have been identified where NBL also deterministically offered an exponential speedup compared to a digital computer. In the case of phonebook search, at proper conditions, NBL can even be exponentially faster than Grover's quantum algorithm that offers only a polynomial speedup compared to a digital computer. The newest result is the implementation of the Deutsch-Jozsa problem in NBL. The Deutsch-Jozsa quantum algorithm was historically the first one that was able to offer quantum supremacy. NBL offers the same speedup class. Open philosophical questions emerge about the role of true randomness in the speedup.
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.