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arXiv:2001.02472 · Physical Review A

Quantum subspace alignment for domain adaptation

Xi He

Published Dec 2, 2020• 9 citations
arXivHTMLPDF

Abstract

Domain adaptation (DA) is used for adaptively obtaining labels of an unprocessed data set with a given related, but different labeled data set. Subspace alignment (SA), a representative DA algorithm, attempts to find a linear transformation to align the subspaces of the two different data sets. The classifier trained on the aligned labeled data set can be transferred to the unlabeled data set to predict the target labels. In this paper, two quantum versions of the SA are proposed to implement the DA procedure on quantum devices. One method, the quantum subspace alignment algorithm (QSA), can achieve quadratic speedup in the number and dimension of given samples. The other method, the variational quantum subspace alignment algorithm (VQSA), can be implemented on near-term quantum devices through a variational hybrid quantum-classical procedure. The results of the numerical experiments on different types of data sets demonstrate that the VQSA can achieve high accuracy in dealing with DA tasks.

DOI
10.1103/physreva.102.062403

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Domain adaptation (DA) is used for adaptively obtaining labels of an unprocessed data set with a given related, but different labeled data set. Subspace alignment (SA), a representative DA algorithm, attempts to find a linear transformation to align the subspaces of the two different data sets. The classifier trained on the aligned labeled data set can be transferred to the unlabeled data set to predict the target labels. In this paper, two quantum versions of the SA are proposed to implement the DA procedure on quantum devices. One method, the quantum subspace alignment algorithm (QSA), can achieve quadratic speedup in the number and dimension of given samples. The other method, the variational quantum subspace alignment algorithm (VQSA), can be implemented on near-term quantum devices through a variational hybrid quantum-classical procedure. The results of the numerical experiments on different types of data sets demonstrate that the VQSA can achieve high accuracy in dealing with DA tasks.
Domain adaptation (DA), the sub-realm of the transfer learning, attempts to deal with machine learning tasks on an unprocessed data domain with the different, but related labeled source domain. However, the classical DA can not efficiently deal with the cross-domain tasks in quantum mechanical scenarios. In this paper, the quantum kernel subspace alignment algorithm is proposed to achieve the procedure of DA by extracting the non-linear features with the quantum kernel method and aligning the two domains with the unitary evolution. The method presented in our work can be implemented on the universal quantum computer with the quantum basic linear algebra subroutines. Based on the algorithmic complexity analysis, the procedure of the QKSA can be implemented with at least quadratic quantum speedup compared with the classical DA algorithms.
The correlation alignment algorithm (CORAL), a representative domain adaptation algorithm, decorrelates and aligns a labeled source domain dataset to an unlabeled target domain dataset to minimize the domain shift such that a classifier can be applied to predict the target domain labels. In this paper, we implement the CORAL on quantum devices by two different methods. One method utilizes quantum basic linear algebra subroutines to implement the CORAL with exponential speedup in the number and dimension of the given data samples. The other method is achieved through a variational hybrid quantum-classical procedure. In addition, the numerical experiments of the CORAL with three different types of data sets, namely, the synthetic data, the synthetic-Iris data, and the handwritten digit data, are presented to evaluate the performance of our paper. The simulation results prove that the variational quantum correlation alignment algorithm can achieve competitive performance compared with the classical CORAL.
Abstract Quantum machine learning is an important application of quantum computing in the era of noisy intermediate-scale quantum devices. Domain adaptation (DA) is an effective method for addressing the distribution discrepancy problem between the training data and the real data when the neural network model is deployed. In this paper, we propose a variational quantum domain adaptation method inspired by the quantum convolutional neural network, named variational quantum domain adaptation (VQDA). The data is first uploaded by a ‘quantum coding module’, then the feature information is extracted by several ‘quantum convolution layers’ and ‘quantum pooling layers’, which is named ‘Feature Extractor’. Subsequently, the labels and the domains of the samples are obtained by the ‘quantum fully connected layer’. With a gradient reversal module, the trained ‘Feature Extractor’ can extract the features that cannot be distinguished from the source and target domains. The simulations on the local computer and IBM Quantum Experience (IBM Q) platform by Qiskit show the effectiveness of the proposed method. The results show that VQDA(with 8 quantum bits) has 91.46% average classification accuracy for DA task between MNIST→USPS (USPS→ MNIST), achieves 91.16% average classification accuracy for gray-scale and color images (with 10 quantum bits), and has 69.25% average classification accuracy on the DA task for color images (also with 10 quantum bits). VQDA achieves a 9.14% improvement in average classification accuracy compared to its corresponding classical domain adaptation method with the same parameter scale for different DA tasks. Simultaneously, the parameters scale is reduced to 43% by using VQDA when both quantum and classical DA methods have similar classification accuracies.
Domain adaptation, a crucial sub-field of transfer learning, aims to utilize known knowledge of one data set to accomplish tasks on another data set. In this paper, we perform one of the most representative domain adaptation algorithms, transfer component analysis (TCA), on quantum devices. Two different quantum implementations of this transfer learning algorithm; namely, the linear-algebra-based quantum TCA algorithm and the variational quantum TCA algorithm, are presented. The algorithmic complexity of the linear-algebra-based quantum TCA algorithm is O(poly(log⁡(ns+nt)))O(\mathrm{poly}(\log (n_{s} + n_{t})))O(poly(log(ns​+nt​))), where nsn_{s}ns​ and ntn_{t}nt​ are input sample size. Compared with the corresponding classical algorithm, the linear-algebra-based quantum TCA can be performed on a universal quantum computer with exponential speedup in the number of given samples. Finally, the variational quantum TCA algorithm based on a quantum-classical hybrid procedure, that can be implemented on the near term quantum devices, is proposed.
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.
The scarcity of labelled data is specifically an urgent challenge in the field of quantum machine learning (QML). Two transfer fusion frameworks are proposed in this paper to predict the labels of a target domain data by aligning its distribution to a different but related labelled source domain on quantum devices. The frameworks fuses the quantum data from two different, but related domains through a quantum information infusion channel. The predicting tasks in the target domain can be achieved with quantum advantages by post-processing quantum measurement results. One framework, the quantum basic linear algebra subroutines (QBLAS) based implementation, can theoretically achieve the procedure of transfer fusion with quadratic speedup on a universal quantum computer. In addition, the other framework, a hardware-scalable architecture, is implemented on the noisy intermediate-scale quantum (NISQ) devices through a variational hybrid quantum-classical procedure. Numerical experiments on the synthetic and handwritten digits datasets demonstrate that the variatioinal transfer fusion (TF) framework can reach state-of-the-art (SOTA) quantum DA method performance.