Learning from imperfect quantum data via unsupervised domain adaptation with classical shadows

Abstract

Learning from quantum data using classical machine learning models has emerged as a promising paradigm toward realizing quantum advantages. Despite extensive analyses on their performance, clean and fully labeled quantum data from the target domain are often unavailable in practical scenarios, forcing models to be trained on data collected under conditions that differ from those encountered at deployment. This mismatch highlights the need for new approaches beyond the common assumptions of prior work. In this work, we address this issue by employing an unsupervised domain adaptation framework for learning from imperfect quantum data. Specifically, by leveraging classical representations of quantum states obtained via classical shadows, we perform unsupervised domain adaptation entirely within a classical computational pipeline once measurements on the quantum states are executed. We numerically evaluate the framework on quantum phases of matter and entanglement classification tasks under realistic domain shifts. Across both tasks, our method outperforms source-only non-adaptive baselines and target-only unsupervised learning approaches, demonstrating the practical applicability of domain adaptation to realistic quantum data learning.

Figures (6)

• Figure 1: Schematic illustration of unsupervised domain adaptation (UDA) for quantum data. (Upper) The labeled source domain and the unlabeled target domain follow different distributions; as a consequence, the decision boundary learned on the source domain is generally misaligned with the target data. (Lower) A feature-extraction map is learned so that the resulting representation preserves label-relevant structure while reducing domain-specific discrepancies, enabling a decision rule that transfers from the source to the target domain. One such method is a domain-adversarial training as described in Sec. \ref{['sec:uda-method']}.
• Figure 2: Learning pipeline for unsupervised domain adaptation from classical shadow datasets based on CDAN. The input is the labeled source data $(S_{T_{\mathrm{s}}}(\rho^{\mathrm{s}}_i), y)\in\mathcal{D}^{\mathrm{s}}_{N_{\mathrm{s}}}$ or the unlabeled target data $S_{T_{\mathrm{s}}}(\rho^{\mathrm{s}}_j) \in \mathcal{D}^{\mathrm{t}}_{N_{\mathrm{t}}}$, each consisting of Pauli classical shadow. A feature map $\Phi^{\dd}$ converts each shadow record to an input feature tensor $z$ whose size may depend on the domain $d$. The feature extractor $G_{\bm{\theta}_f}$ consists of an input-size adapter $A^{\dd}_{\mathbf{w}_{\dd}}$ to convert $z$ to a fixed-shape input $\tilde{z}$ followed by a CNN that takes $\tilde{z}$ as input. The CNN includes DSBN layers $\mathrm{BN}^{\dd}$. The latent feature $h = G_{\bm{\theta}_f}(z)$ is converted to the label probability distribution via a label classifier $C_{\bm{\theta}_Y}$ to give a label prediction $\hat{y}$ by taking the argmax. The Kronecker product of $h$ and the label probability distribution is fed into a domain discriminator $D_{\bm{\theta}_\mathrm{dom}}$, which outputs a prediction of which domain the given data belongs to. While the feature extractor and the label classifier are trained to minimize the label classification loss $\mathcal{L}_Y$ using labeled source examples, they are simultaneously trained to maximize the domain discrimination loss $\mathcal{L}_\mathrm{dom}$ via GRL. The domain discriminator is adversarially trained to minimize $\mathcal{L}_\mathrm{dom}$. This way, the label-conditional latent feature distributions over the two domains are made similar while keeping the class-label distinguishability.
• Figure 3: The forward mapping of the whole pipeline.
• Figure 4: Ground-state subspace overlap of the target domains for (a) Cluster and (b) ANNNI models with QETU-based algorithmic state-preparation imperfection. Each panel shows $F_{\mathcal{G}}(\bm{x})=\langle \psi | \Pi_{\mathcal{G}(\bm{x})} | \psi \rangle$ at the corresponding Hamiltonian parameters. Only target domains are shown because source states are exact in these simulations.
• Figure 5: Predicted phase diagrams for QETU-based targets obtained by UDA at $T=10^4$ shots per data point. The displayed trial is selected as follows: for each of the $10$ trials, select a model by EnsV using only target-train predictions, and then choose the trial whose target-unseen macro-F1 is closest to the median over the $10$ trials.