New XOR & XNOR Operations in Instantaneous Noise-Based Logic

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 Khreishahet 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.