DifGa: Differentiable Error Mitigation for Multi-Mode Gaussian and Non-Gaussian Noise in Quantum Photonic Circuits

Abstract: We introduce DifGa, a fully differentiable error-mitigation framework for continuous-variable (CV) quantum photonic circuits operating under Gaussian loss and weak non-Gaussian noise. The approach is demonstrated using analytic simulations with the default.gaussian backend of PennyLane, where quantum states are represented by first and second moments and optimized end-to-end via automatic differentiation. Gaussian loss is modeled as a beam splitter interaction with an environmental vacuum mode of transmissivity $η\in [0.3,0.95]$, while non-Gaussian phase noise is incorporated through a differentiable Monte-Carlo mixture of random phase rotations with jitter amplitudes $δ\in [0,0.7]$. The core architecture employs a multi-mode Gaussian circuit consisting of a signal, ancilla, and environment mode. Input states are prepared using squeezing and displacement operations with parameters $(r_s,\varphi_s,α)=(0.60,0.30,0.80)$ and $(r_a,\varphi_a)=(0.40,0.10)$, followed by an entangling beam splitter with angles $(θ,φ)=(0.70,0.20)$. Error mitigation is achieved by appending a six-parameter trainable Gaussian recovery layer comprising local phase rotations and displacements, optimized by minimizing a quadratic loss on the signal-mode quadratures $\langle \hat{x}_0\rangle$ and $\langle \hat{p}_0\rangle$ using gradient descent with fixed learning rate $0.06$ and identical initialization across experiments. Under pure Gaussian loss, the optimized recovery suppresses reconstruction error to near machine precision ($<10^{-30}$) for moderate loss ($η\ge 0.5$). When non-Gaussian phase noise is present, noise-aware training using Monte Carlo averaging yields robust generalization, reducing error by more than an order of magnitude compared to Gaussian-trained recovery at large phase jitter. Runtime benchmarks confirm linear scaling with the number of Monte Carlo samples.