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

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 (sums), 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.