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

Kosuke Ito; Akira Tanji; Hiroshi Yano; Yudai Suzuki; Naoki Yamamoto

quant-phMar 30, 2026

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

Authors: Kosuke Ito, Akira Tanji, Hiroshi Yano, Yudai Suzuki, Naoki Yamamoto

Organizations: Advanced Material Engineering Division, Toyota Motor Corporation, 1200 Mishuku, Susono, Shizuoka 410-1193, Japan · Quantum Computing Center, Keio University, Hiyoshi 3-14-1, Kohoku, Yokohama, Kanagawa 223-8522, Japan · Department of Applied Physics and Physico-Informatics, Keio University, Hiyoshi 3-14-1, Kohoku, Yokohama, Kanagawa 223-8522, Japan · Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland ·

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 & tables

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. III .

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^{\differential}

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^{\differential}_{\mathbf{w}_{\differential}}

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}^{\differential}

. 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.

Panel of Figure 3 — Figure 3: The forward mapping of the whole pipeline.

Panel of Figure 4 — 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.

Panel of Figure 5 — 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.

Panel of Figure 6 — Figure 6: Predicted phase diagrams of baseline methods for QETU targets. Top row: source-only ERM with $10^{4}$ shots per data point. In each trial, the model is selected by source-domain cross-validation, and the displayed trial is the one whose target-unseen macro-F1 is closest to the median over the $10$ trials. Bottom row: unsupervised clustering baselines based on the shadow kernel with $10^{3}$ shots per data point. For each benchmark, we show the shadow-kernel clustering method that attains the best median target-unseen macro-F1 among the unsupervised shadow-kernel baselines. In each trial, hyperparameters are selected by the corresponding unlabeled criterion using only target-train data, and the displayed trial is the one whose target-unseen macro-F1 is closest to the median over the $10$ trials.

Quantum Machine Learning

Quantum machine learning uses quantum circuits and quantum data to build learning algorithms and study their computational and statistical limits.

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Representation Geometry and Inductive Biases in Quantum Classifiers across Classical Visual Benchmarks

Yu Yamaoka, Weng Ian Chan, Kosuke Mitarai

Center for Quantum Information and Quantum Biology, The University of Osaka, 1-2 Machikaneyama, Toyonaka, 560-0043, Osaka, Japan. · SANKEN, The University of Osaka, 1-5 Yamadaoka, Suita, 565-0871, Osaka, Japan. · Graduate School of Engineering Science, The University of Osaka, 1-3 Machikaneyama, Toyonaka, 560-8531, Osaka, Japan.

Quantum Machine Learning Image Classification Quantum Kernel Methods Quantum Feature Maps

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Quantum Machine Learning (QML) has a theoretical advantage over classical algorithms for specific synthetic data that is computationally hard. However, it remains unclear whether such theoretical advantages play a meaningful role for realistic classical data, such as natural images. Quantum structural properties induced by unitary operations or entanglement introduce inductive biases that differ from those of classical models, potentially leading to distinct learning behavior on real-world data. In a fully quantum learning pipeline, classical real-world data are first encoded into quantum states via a quantum feature mapping, analogous to a classical feature extractor, and a quantum classifier then classifies the resulting states. Quantum feature mappings generate representations that are difficult to realize classically, while also inducing representation-level biases that do not necessarily match the structure of realistic data. To enable a fair comparison at the classifier level, we focus on the classifier and use classical feature extractors that already provide powerful representations for natural images. By controlling the data scale and supervision strength, we analyze how the unitary structure of quantum classifiers affects generalization, and show that their effectiveness depends strongly on the geometry of the input representations. These results indicate that quantum classifiers benefit from classical features that are aligned with quantum feature spaces. Our analysis shows that kernel alignment identifies representations compatible with quantum feature spaces, providing insights into translating classical models into quantum algorithms.

Abstract

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