RaCS: Near-Zero-Error Classical Data Encoding on Photonic Quantum Processors via Redundancy-Assisted Coherent-State Codes

Abstract

This work presents a systematic evaluation of near-zero-error encoding strategies for coherent-state quantum communication, comparing homodyne and threshold detection across alphabet sizes $M\in \{3,5,7\}$. Simulations were performed for coherent amplitudes $\alpha \in \{0.20,0.40,0.80\}$ and channel transmittance values $\eta \in [0.5,1.0]$, enabling a detailed characterization of bit-error rate (BER), optimal operating points, and information-theoretic performance. Threshold detection was found to tend to saturate near $\mathrm{BER}\approx 0.5$ for all $M$, consistent with its limited ability to discriminate low-energy coherent states. In contrast, homodyne detection exhibited exponential-like BER suppression, reaching values below ${10}^{-2}$ for $\alpha =0.80$, at $M=5$ and $\eta =1.0$. Error exponent fits further revealed strong scaling behavior, with slopes increasing from 0.8 at $M=3$ to 45 at $M=7$, suggesting the benefits of redundancy-assisted encoding. Optimal amplitude extraction showed that $\alpha =0.80$ within the tested grid minimized BER across all loss conditions examined. Capacity proxy evaluation demonstrated that homodyne in these simulations approaches the theoretical limit ${\log }_2\left(7\right)\approx 2.81$, achieving $C\approx 2.7$ bits, while threshold detection remained substantially below capacity. Additional metrics, including $\Delta C$ and relative BER gain, indicated improvements of up to 2.5 bits and over two orders of magnitude, respectively. All simulations were implemented in Python using PennyLane–Strawberry Fields interfaces, executed entirely on classical hardware to support transparency and reproducibility.