Optimal design for model training is a critical topic in machine learning. Active learning aims at obtaining improved models by querying samples with maximum uncertainty according to the estimation model for artificially labeling; this has the additional advantage of achieving successful performances with a reduced number of labeled samples. We analyze its capability as an assistant for the design of experiments, extracting maximum information for learning with the minimal cost in fidelity loss, or reducing total operation costs of labeling in the laboratory. We present two typical applications as quantum information retrieval in qutrits and phase boundary prediction in many-body physics. For an equivalent multinomial classification problem, we achieve the correct rate of 99% with less than 2% of samples labeled. We reckon that active-learning-inspired physics experiments will remarkably save budget without loss of accuracy.
Optimal design for model training is a critical topic in machine learning. Active learning aims at obtaining improved models by querying samples with maximum uncertainty according to the estimation model for artificially labeling; this has the additional advantage of achieving successful performances with a reduced number of labeled samples. We analyze its capability as an assistant for the design of experiments, extracting maximum information for learning with the minimal cost in fidelity loss, or reducing total operation costs of labeling in the laboratory. We present two typical applications as quantum information retrieval in qutrits and phase boundary prediction in many-body physics. For an equivalent multinomial classification problem, we achieve the correct rate of 99% with less than 2% of samples labeled. We reckon that active-learning-inspired physics experiments will remarkably save budget without loss of accuracy.
Active learning is a machine learning method aiming at optimal design for model training. At variance with supervised learning, which labels all samples, active learning provides an improved model by labeling samples with maximal uncertainty according to the estimation model. Here, we propose the use of active learning for efficient quantum information retrieval, which is a crucial task in the design of quantum experiments. Meanwhile, when dealing with large data output, we employ active learning for the sake of classification with minimal cost in fidelity loss. Indeed, labeling only 5% samples, we achieve almost 90% rate estimation. The introduction of active learning methods in the data analysis of quantum experiments will enhance applications of quantum technologies.
Quantum machine learning, as an extension of classical machine learning that harnesses quantum mechanics, facilitates effiient learning from data encoded in quantum states. Training a quantum neural network typically demands a substantial labeled training set for supervised learning. Human annotators, often experts, provide labels for samples through additional experiments, adding to the training cost. To mitigate this expense, there is a quest for methods that maintain model performance over fully labeled datasets while requiring fewer labeled samples in practice, thereby extending few-shot learning to the quantum realm. Quantum active learning estimates the uncertainty of quantum data to select the most informative samples from a pool for labeling. Consequently, a QML model is supposed to accumulate maximal knowledge as the training set comprises labeled samples selected via sampling strategies. Notably, the QML models trained within the QAL framework are not restricted to specific types, enabling performance enhancement from the model architecture's perspective towards few-shot learning. Recognizing symmetry as a fundamental concept in physics ubiquitous across various domains, we leverage the symmetry inherent in quantum states induced by the embedding of classical data for model design. We employ an equivariant QNN capable of generalizing from fewer data with geometric priors. We benchmark the performance of QAL on two classification problems, observing both positive and negative results. QAL effectively trains the model, achieving performance comparable to that on fully labeled datasets by labeling less than 7\% of the samples in the pool with unbiased sampling behavior. Furthermore, we elucidate the negative result of QAL being overtaken by random sampling baseline through miscellaneous numerical experiments. (character count limit, see the main text)
Abstract Active learning (AL) is a family of machine learning (ML) algorithms that predates the current era of artificial intelligence. Unlike traditional approaches that require labeled samples for training, AL iteratively selects unlabeled samples to be annotated by an expert. This protocol aims to prioritize the most informative samples, leading to improved model performance compared to training with all labeled samples. In recent years, AL has gained increasing attention, particularly in the field of physics. This paper presents a comprehensive and accessible introduction to the theory of AL reviewing the latest advancements across various domains. Additionally, the potential integration of AL is explored with quantum ML, envisioning a synergistic fusion of these two fields rather than viewing AL as a mere extension of classical ML into the quantum realm.
Abstract Training a quantum machine learning model generally requires a large labeled dataset, which incurs high labeling and computational costs. To reduce such costs, a selective training strategy, called active learning (AL), chooses only a subset of the original dataset to learn while maintaining the trained model’s performance. Here, we design and implement two AL-enpowered variational quantum classifiers to investigate the potential applications and effectiveness of AL in quantum machine learning. Firstly, we build a programmable free-space photonic quantum processor, which enables the programmed implementation of various hybrid quantum-classical computing algorithms. Then, we code the designed variational quantum classifier with AL into the quantum processor, and execute comparative tests for the classifiers with and without the AL strategy. The results validate the great advantage of AL in quantum machine learning, as it saves at most 85 % labeling efforts and 91.6 % percent computational efforts compared to the training without AL on a data classification task. Our results inspire AL’s further applications in large-scale quantum machine learning to drastically reduce training data and speed up training, underpinning the exploration of practical quantum advantages in quantum physics or real-world applications.
Pattern recognition is a central topic in learning theory, with numerous applications such as voice and text recognition, image analysis and computer diagnosis. The statistical setup in classification is the following: we are given an i.i.d. training set ( X 1 , Y 1 ), ... , ( X n , Y n ), where X i represents a feature and Y i ∊{0, 1} is a label attached to that feature. The underlying joint distribution of ( X , Y ) is unknown, but we can learn about it from the training set, and we aim at devising low error classifiers f: X → Y used to predict the label of new incoming features. In this paper, we solve a quantum analogue of this problem, namely the classification of two arbitrary unknown mixed qubit states. Given a number of 'training' copies from each of the states, we would like to 'learn' about them by performing a measurement on the training set. The outcome is then used to design measurements for the classification of future systems with unknown labels. We found the asymptotically optimal classification strategy and show that typically it performs strictly better than a plug-in strategy, which consists of estimating the states separately and then discriminating between them using the Helstrom measurement. The figure of merit is given by the excess risk equal to the difference between the probability of error and the probability of error of the optimal measurement for known states. We show that the excess risk scales as n −1 and compute the exact constant of the rate.
Hamiltonian learning is an important procedure in quantum system identification, calibration, and successful operation of quantum computers. Through queries to the quantum system, this procedure seeks to obtain the parameters of a given Hamiltonian model and description of noise sources. Standard techniques for Hamiltonian learning require careful design of queries and $O({\ensuremath{\epsilon}}^{\ensuremath{-}2})$ queries in achieving learning error $\ensuremath{\epsilon}$ due to the standard quantum limit. With the goal of efficiently and accurately estimating the Hamiltonian parameters within learning error $\ensuremath{\epsilon}$ through minimal queries, we introduce an active learner that is given an initial set of training examples and the ability to interactively query the quantum system to generate new training data. To ensure applicability on near-term quantum hardware, the active learner operates in batch mode as opposed to sequentially, proposing batches of queries to be made during learning. We formally specify and experimentally assess the performance of this Hamiltonian active learning (HAL) algorithm for learning the six parameters of a two-qubit cross-resonance Hamiltonian on four different superconducting IBM quantum devices. Compared with standard techniques for the same problem and a specified learning error, HAL achieves more than a 95 reduction in queries required, and upwards of 33 reduction over a sequential active learner. Moreover, with access to prior information on a subset of Hamiltonian parameters and given the ability to select queries with linearly (or exponentially) longer system interaction times during learning, HAL can exceed the standard quantum limit and achieve Heisenberg (or super-Heisenberg) limited convergence rates during learning.