arXiv subjects

Akira Tanji

Publications and source records attributed to Akira Tanji.

4 recordsLinked to original sources

arXiv2026

Adaptive identification of low-degree polynomials in quantum singular value transformation: application to nonlinear quantum properties estimation

Estimating properties of unknown quantum states via quantum singular value transformation (QSVT) often requires high-degree polynomials to handle small eigenvalues of density matrices. Specifically, the existing approaches determine the polynomial degree by relying on overly conservative worst-case bounds based on the minimum non-zero eigenvalue or the rank of the density matrices. In this work, we propose a spectral cutoff method that truncates the negligible eigenvalue tail depending on the task, the target accuracy, and the state, which enables the use of significantly lower-degree polynomials. To implement this, we develop a two-stage algorithm to estimate nonlinear properties, particularly von Neumann entropy and R{\'e}nyi entropy. In the first stage, we execute a search algorithm to identify the spectral cutoff directly from the unknown quantum state. In the second stage, we estimate the nonlinear properties utilizing QSVT with the degree of polynomial adaptively determined by the cutoff. This two-stage algorithm significantly improves the overall estimation cost compared to known bounds, even without knowing the minimum eigenvalue or the rank.

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arXiv2026

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

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.

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arXiv2025

Quantum phase classification via partial tomography-based quantum hypothesis testing

Quantum phase classification is a fundamental problem in quantum many-body physics, traditionally approached using order parameters or quantum machine learning techniques such as quantum convolutional neural networks (QCNNs). However, these methods often require extensive prior knowledge of the system or large numbers of quantum state copies for reliable classification. In this work, we propose a classification algorithm based on the quantum Neyman-Pearson test, which is theoretically optimal for distinguishing between two quantum states. While directly constructing the optimal test for many-body systems via full state tomography is intractable due to the exponential growth of the Hilbert space, we introduce a partitioning strategy that applies hypothesis tests to subsystems rather than the entire state, effectively reducing the required number of quantum state copies while maintaining classification accuracy. We validate our approach through numerical simulations, demonstrating its advantages over conventional methods, including the order parameter-based classifier, the QCNN, and the recently developed classical machine learning algorithm enhanced with quantum data. Our results show that the proposed method achieves lower classification error probabilities with fewer required quantum state copies compared to all of these baselines, while also reducing the training cost relative to the QCNN and the classical machine learning algorithm enhanced with quantum data, and further decreasing the classical computational time in comparison with the latter. We additionally demonstrate scalability of our method in numerical experiments up to systems with 81 qubits. These findings highlight the potential of quantum hypothesis testing as a powerful tool for quantum phase classification, particularly in experimental settings where quantum measurements are combined with classical post-processing.

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arXiv2024

Quantum Inception Score

Motivated by the great success of classical generative models in machine learning, enthusiastic exploration of their quantum version has recently started. To depart on this journey, it is important to develop a relevant metric to evaluate the quality of quantum generative models; in the classical case, one such example is the (classical) inception score (cIS). In this paper, as a natural extension of cIS, we propose the quantum inception score (qIS) for quantum generators. Importantly, qIS relates the quality to the Holevo information of the quantum channel that classifies a given dataset. In this context, we show several properties of qIS. First, qIS is greater than or equal to the corresponding cIS, which is defined through projection measurements on the system output. Second, the difference between qIS and cIS arises from the presence of quantum coherence, as characterized by the resource theory of asymmetry. Third, when a set of entangled generators is prepared, there exists a classifying process leading to the further enhancement of qIS. Fourth, we harness the quantum fluctuation theorem to characterize the physical limitation of qIS. Finally, we apply qIS to assess the quality of the one-dimensional spin chain model as a quantum generative model, with the quantum convolutional neural network as a quantum classifier, for the phase classification problem in the quantum many-body physics.

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