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

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 ηin [0.3,0.95], while non-Gaussian phase noise is incorporated through a differentiable Monte-Carlo mixture of random phase rotations with jitter amplitudes δin [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}_0rangle and langle hat{p}_0rangle 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 $ηge 0.5$. 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.