Quantum expectation-maximization algorithm

Miyahara, Hidekazu; Aihara, Kazuyuki; Lechner, Wolfgang

doi:10.1103/physreva.101.012326

Cited by 9 publications

(8 citation statements)

References 22 publications

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“…Quantum computers embody a physically feasible computational model which may exceed the limit of conventional computers, and have been researched vigorously for several decades. In particular, the amplitude estimation algorithm [1][2][3][4][5][6] has attracted a lot of attention as a fundamental subroutine of a wide range of application-oriented quantum algorithms, such as the Monte Carlo integration [7][8][9][10][11][12][13] and machine learning tasks [14][15][16][17][18][19][20]. However, those quantum amplitude estimation algorithms are assumed to work on ideal quantum computers, and their performance on noisy computers should be carefully investigated.…”

Section: Introductionmentioning

confidence: 99%

Modified Grover operator for amplitude estimation

Uno,

Suzuki,

Hisanaga

et al. 2020

Preprint

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In this paper, we propose a quantum amplitude estimation method that uses a modified Grover operator and quadratically improves the estimation accuracy in the ideal case, as in the conventional one using the standard Grover operator. Under the depolarizing noise, the proposed method can outperform the conventional one in the sense that it can in principle achieve the ultimate estimation accuracy characterized by the quantum Fisher information in the limit of a large number of qubits, while the conventional one cannot achieve the same value of ultimate accuracy. In general this superiority requires a sophisticated adaptive measurement, but we numerically demonstrate that the proposed method can outperform the conventional one and approach to the ultimate accuracy, even with a simple non-adaptive measurement strategy.

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Section: Introductionmentioning

confidence: 99%

Modified Grover operator for amplitude estimation

Uno,

Suzuki,

Hisanaga

et al. 2020

Preprint

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“…Independent of this work, Miyahara, Aihara, and Lechner extended the q-means algorithm [18] for Gaussian Mixture Models [29]. The techniques used in [29] are similar to ours.…”

Section: Previous Workmentioning

confidence: 99%

“…Independent of this work, Miyahara, Aihara, and Lechner extended the q-means algorithm [18] for Gaussian Mixture Models [29]. The techniques used in [29] are similar to ours. The main difference is that in their work the update step is performed using a hard-clustering approach (as in the k-means algorithm), that is for updating the centroid and the covariance matrices of a cluster j, only the data points for which cluster j is nearest are taken into account.…”

Section: Previous Workmentioning

confidence: 99%

“…We would like to thank the authors of [29] for sharing an early version of their manuscript with us. Part of this research was supported by the projects: ANR QuDATA and QuantERA QuantAlgo.…”

Section: Acknowledgementsmentioning

confidence: 99%

“…Techniques illustrated in [29] can also be used to quantize the CEM algorithm which needs a hard-clustering step. Among the different possible approaches, the random and the small EM greatly benefit from a faster algorithm, as we can spend more time exploring the space of the parameters by starting from different initial seeds, and thus avoid local minima of the likelihood.…”

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confidence: 99%

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Quantum Expectation-Maximization for Gaussian Mixture Models

Kerenidis,

Luongo,

Prakash

2019

Preprint

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The Expectation-Maximization (EM) algorithm is a fundamental tool in unsupervised machine learning. It is often used as an efficient way to solve Maximum Likelihood (ML) estimation problems, especially for models with latent variables. It is also the algorithm of choice to fit mixture models: generative models that represent unlabelled points originating from k different processes, as samples from k multivariate distributions. In this work we define and use a quantum version of EM to fit a Gaussian Mixture Model. Given quantum access to a dataset of n vectors of dimension d, our algorithm has convergence and precision guarantees similar to the classical algorithm, but the runtime is only polylogarithmic in the number of elements in the training set, and is polynomial in other parameters -as the dimension of the feature space, and the number of components in the mixture. We generalize further the algorithm in two directions. First, we show how to fit any mixture model of probability distributions in the exponential family. Then, we show how to use this algorithm to compute the Maximum a Posteriori (MAP) estimate of a mixture model: the Bayesian approach to likelihood estimation problems. We discuss the performance of the algorithm on datasets that are expected to be classified successfully by those algorithms, arguing that on those cases we can give strong guarantees on the runtime.

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Quantum‐inspired hybrid algorithm for image classification and segmentation: Q‐Means++ max‐cut method

Roy,

Rudra

2024

Int J Imaging Syst Tech

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Finding brain tumors is a crucial step in medical diagnosis that can have a big impact on how patients turn out. Conventional detection techniques can be laborious and demand a lot of computing power. Brain tumor detection could be made more effective and precise, thanks to the quickly developing field of quantum computing. In this article, we propose a quantum machine learning (QML)‐based method for brain tumor extraction and detection based on quantum computing. To implement our strategy, we use a Hybrid Quantum‐Classical Convolutional Neural Network (HQC‐CNN) that has been trained using a collection of brain MRI images. Additionally, we employ Batchwise Q‐Means++ Clustering for segmenting the images and a Max‐cut approach with Adiabatic Quantum Computation (AQC) to extract the tumor region from the segmented MRI image. Our results highlight the strength of Quanvolutional Layer in Neural Network and reduced time complexity exponentially or quadratically in clustering and max‐cut algorithms respectively and see the potential of quantum computing for improving the accuracy and speed of medical diagnosis and have implications for the future of healthcare technology.

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Quantum expectation-maximization algorithm

Cited by 9 publications

References 22 publications

Modified Grover operator for amplitude estimation

Modified Grover operator for amplitude estimation

Quantum Expectation-Maximization for Gaussian Mixture Models

Quantum‐inspired hybrid algorithm for image classification and segmentation: Q‐Means++ max‐cut method

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