Metrology-oriented bulk-optics implementation of a stochastic NOT gate: Unified error budget and tolerance analysis

Abstract

Stochastic computing represents real-valued quantities by the relative frequency of ones in a binary pulse train, enabling compact arithmetic with an accuracy that improves with stream length. Here, we report a metrology-oriented, bulk optics realisation of a stochastic NOT primitive for a polarisation-encoded bit stream (1≡H, 0≡V), implemented as a passive exchange of two orthogonal linear polarisations. Two practical architectures are considered: (A) a folded, single-output polarising beam splitter (PBS)-based module with two PBS cubes and two half-wave plates (HWPs) and (B) a compact 3 × HWP in-line chain. Using a unified Jones calculus model coupled to stochastic bit stream simulation, we quantify how finite extinction/leakage, waveplate angle, and retardance errors, arm imbalance, detector noise, and contrast threshold decision settings propagate into computation level metrics (p̂ transfer, bias/RMSE, BER, and contrast margin). A harmonised head-to-head comparison under common decision settings (γ = 0.60, erasure window 0.35) reveals distinct sensitivity profiles for the two layouts and provides actionable tolerance guidance for teaching grade implementations and for calibrated error budget studies. The full reproducible Colab workflows and derived datasets are provided as Supplementary materials, together with an alignment/calibration protocol and a phase reference/compensation note for phase sensitive use cases.