Photonic Causal Tensor Processor (PCTP): Hardware Architecture, Non-Commutative Optical Logic, and Topological State Execution

Linear optical computing has emerged as a promising paradigm to bypass the thermodynamic constraints of von Neumann architectures and the Landauer dissipation limit (Emin = kBT ln2). However, existing integrated photonic accelerators remain fundamentally Markovian: they are restricted to commutative matrix-vector multiplications that systematically erase computational history during state aggregation. Here, we present the hardware architecture and operational principles of the Photonic Causal Tensor Processor (PCTP). Grounded in Causal Quaternionic Field Theory (CQFT), the PCTP natively executes the non-commutative Causal Tensor Product (⊠) governed by a rigorous chronological index (τ). We demonstrate how the four algebraic components of the quaternion (qa, qi, qj, qk) are directly mapped onto physical, orthogonal degrees of freedom of coherent optical wavepackets: real amplitude and longitudinal carrier phase, polarization states on the Poincaré sphere, and transverse orbital angular momentum (OAM) modes. We provide the physical layout of non-reciprocal causal logic gates utilizing low-loss Silicon Nitride (Si3N4) waveguides, magneto-optic Bismuth Iron Garnet (BIG) Faraday isolators, and synthetic diamond nitrogen-vacancy (NV) phase latches. The proposed processor executes deterministic causal tensor algebra at the speed of light with near-zero thermodynamic entropy generation, establishing an empirical hardware framework for post-quantum computing.