Foundation Model for Unified Characterization of Optical Quantum States

TL;DR

The paper addresses the challenge of characterizing optical quantum states across a wide range of complexity without full tomography. It introduces OSFM, a foundation model trained in a pretraining–finetuning fashion on homodyne marginals, with a three-axes state complexity space (m, xi, r). It demonstrates out-of-distribution generalization to higher-complexity states and strong transfer to downstream tasks such as Wigner negativity, fidelity, and QFI for families including photon-subtracted/added states, N00N, cat, and highly squeezed states. It shows robust few-shot performance, surpassing baselines, and reveals organized clustering of state families in learned latent space. This framework paves the way for scalable, efficient certification of optical quantum states relevant to computation, communication, and metrology.

Abstract

Machine learning methods have been used to infer specific properties of limited families of optical quantum states, but a unified model that predicts a broad range of properties for practically relevant-especially multimode non-Gaussian-states without full tomography is still lacking. Here we introduce the first foundation model for the characterization of optical quantum states across a wide range of complexity, defined by three key factors: non-Gaussianity, number of modes, and degree of squeezing. We show that a single model pretrained on low-complexity states can be directly applied to characterize states of higher complexity. With limited fine-tuning, the model adapts to downstream tasks such as predicting quantum fidelity and Wigner negativity over a broad class of experimentally relevant states, including strongly non-Gaussian Schrödinger cat states, multimode systems with up to ten modes, and highly squeezed states with squeezing levels up to 10.4dB. Our results establish a unified framework for characterizing optical quantum states from limited measurement data, enabling efficient certification of quantum states relevant to optical quantum information computation, communication and metrology.

Figures (8)

• Figure 1: Dataset characterization and three-stage framework of transfer learning for optical states. All optical quantum states considered are represented in an $(m,\xi,r)$-space spanned by the number of modes $m$, the squeezing degree $\xi$, and the stellar rank $r$, three axes that correlate with the difficulty of classical simulation. In Stage 1, a representation network $\mathcal{E}$ encodes partial measurements and a generation network $\mathcal{G}$ predicts the corresponding outcome statistics. Pretraining is performed on states that are relatively tractable for classical simulation. In Stage 2, we test the model on states outside the pretraining distribution, evaluating its ability to generalize the learned representation to more complex quantum states. In Stage 3, the pretrained model is fine-tuned for downstream quantum property prediction tasks, focusing on representative families of optical states.
• Figure 2: Representation learning and prediction on homodyne measurement statistics.a, Comparison between the predicted and true homodyne marginal distributions for test states with different parameters. b, Classical fidelity $\mathcal{F}$ decreases with stellar rank $r$ for both in-distribution (ID; within the pretraining distribution) and out-of-distribution (OOD; outside it) data. c, 2D embeddings of state representation vectors colored by stellar rank, showing smooth hierarchical organization in the representation space. d, Classical fidelity $\mathcal{F}$ versus the number of modes $m$. For Gaussian states ($r=0$), $\mathcal{F}$ remains high and essentially unchanged across $m$. For non-Gaussian states ($r>0$), $\mathcal{F}$ increases with $m$ and tends to plateau.
• Figure 3: Fine-tuning for downstream quantum property prediction tasks on state families that lie far outside the pretraining distribution.a, Comparison of prediction accuracies on Wigner negativity for OSFM with and without pretraining, and for a shallow feedforward neural network baseline, across multimode photon-subtracted/added states with $m=5,7,$ and $10$. b, Predictions of purity and fidelity for N00N states, a non-Gaussian family with finite stellar rank exceeding the pretraining range. c, Predictions of size and fidelity for Schrödinger cat states, which possess infinite stellar rank. d, Predictions of quantum Fisher information (QFI) and fidelity for highly squeezed states.
• Figure 4: The 2D embeddings of diverse optical states using t-SNE. The figure shows the 2D embeddings of state representation vectors learned by the pretrained OSFM based on limited homodyne measurement statistics. Distinct clusters of optical states emerge, and largely reflect the ordering in mode number $m$, squeezing degree $\xi$, and stellar rank $r$.
• Figure 5: Structure of OSFM during pretraining and fine-tuning.