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

TL;DR

DifGa presents a differentiable, Gaussian-only error-mitigation framework for continuous-variable photonic circuits subject to Gaussian loss and weak non-Gaussian phase noise. By embedding a six-parameter trainable Gaussian recovery layer inside a multi-mode Gaussian circuit and optimizing end-to-end on quadrature observables, the method achieves near-perfect reconstruction under moderate loss and demonstrates robust generalization when non-Gaussian noise is present via differentiable Monte-Carlo mixtures. Key contributions include detailed demonstrations of (i) large gains in quadrature accuracy with ancilla-assisted mitigation, (ii) smooth, differentiable loss landscapes enabling gradient-based optimization, and (iii) predictable linear-scale runtimes with Monte-Carlo sampling, guiding practical parameter choices. The work provides a hardware-ready, scalable pathway for observable-level noise suppression in near-term CV photonic processors, complementing non-Gaussian quantum error-correction approaches without requiring non-Gaussian resources.

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.

Figures (10)

• Figure 1: Overview of DifGa, a fully differentiable, Gaussian-only error mitigation framework for continuous-variable photonic circuits. The pipeline comprises ideal Gaussian encoding, physically motivated Gaussian loss and weak non-Gaussian phase noise, and a trainable Gaussian recovery layer optimized end-to-end via automatic differentiation, without logical encoding or non-Gaussian resource states.
• Figure 2: Gaussian loss mitigation performance using DifGa. Final reconstruction error $\mathcal{L}$ after $60$ gradient-descent steps (learning rate $0.06$) versus transmissivity $\eta\in\{0.30,0.41,0.52,0.63,0.74,0.85,0.95\}$, with fixed input $(0.6,0.3,0.8,0.4,0.1)$ and entangler $(0.7,0.2)$.
• Figure 3: Single-mode versus multi-mode mitigation at fixed loss $\eta=0.55$. Final reconstruction error for single-mode baseline (SM base: $1.71\times10^{-1}$), single-mode mitigated (SM mit: $\sim10^{-44}$), multi-mode baseline (MM base: $9.997\times10^{-2}$), and multi-mode mitigated (MM mit: $\sim10^{-41}$).
• Figure 4: Non-Gaussian phase noise landscape. Log-scale reconstruction error as a function of phase jitter $\delta$ and loss transmissivity $\eta$.
• Figure 5: Generalization under non-Gaussian phase noise. Comparison of Gaussian-trained and NG-trained recovery layers.