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arXiv:2302.06449 · Fluctuation and Noise Letters

XOR and XNOR Gates in Instantaneous Noise-Based Logic

Mohammad B. Khreishah, Walter C. Daugherity, László B. Kish

Published May 14, 2023• 7 citations
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Abstract

In this paper, we propose a new method of applying the XOR and XNOR gates on exponentially large superpositions in Instantaneous Noise-Based Logic. These new gates are repeatable, and they can achieve an exponential speedup in computation with polynomial hardware complexity.
DOI
10.1142/s0219477523500414

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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.
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 for 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.
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 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 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.
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.