Related papers: Quantum Discriminant Analysis for Dimensionality R…
We propose quantum algorithms, purely quantum in nature, for calculating the determinant and inverse of an $(N-1)\times (N-1)$ matrix (depth is $O(N^2\log N)$) which is a simple modification of the algorithm for calculating the determinant…
Quantum computing is a promising candidate for accelerating machine learning tasks. Limited by the control accuracy of current quantum hardware, reducing the consumption of quantum resources is the key to achieving quantum advantage. Here,…
We study the limitations and fast-forwarding of quantum algorithms for linear ordinary differential equation (ODE) systems with a particular focus on non-quantum dynamics, where the coefficient matrix in the ODE is not anti-Hermitian or the…
We provide a new quantum algorithm that efficiently determines the quality of a least-squares fit over an exponentially large data set by building upon an algorithm for solving systems of linear equations efficiently (Harrow et al., Phys.…
Logistic regression (LR) is an important machine learning model for classification, with wide applications in text classification, image analysis and medicine diagnosis, etc. However, training LR generally entails an iterative gradient…
We give a classical algorithm for linear regression analogous to the quantum matrix inversion algorithm [Harrow, Hassidim, and Lloyd, Physical Review Letters'09, arXiv:0811.3171] for low-rank matrices [Wossnig, Zhao, and Prakash, Physical…
Large machine learning models are revolutionary technologies of artificial intelligence whose bottlenecks include huge computational expenses, power, and time used both in the pre-training and fine-tuning process. In this work, we show that…
Quantum computers promise to enhance machine learning for practical applications. Quantum machine learning for real-world data has to handle extensive amounts of high-dimensional data. However, conventional methods for measuring quantum…
Quantum algorithms for Hamiltonian simulation and linear differential equations more generally have provided promising exponential speed-ups over classical computers on a set of problems with high real-world interest. However, extending…
Quantum algorithms offer significant speed-ups over their classical counterparts in various applications. In this paper, we develop quantum algorithms for the Kalman filter widely used in classical control engineering using the block…
Data compression can be achieved by reducing the dimensionality of high-dimensional but approximately low-rank datasets, which may in fact be described by the variation of a much smaller number of parameters. It often serves as a…
Linear regression is a basic and widely-used methodology in data analysis. It is known that some quantum algorithms efficiently perform least squares linear regression of an exponentially large data set. However, if we obtain values of the…
Quantum computers have the potential to efficiently solve a system of nonlinear ordinary differential equations (ODEs), which play a crucial role in various industries and scientific fields. However, it remains unclear which system of…
Machine learning algorithms perform well on identifying patterns in many different datasets due to their versatility. However, as one increases the size of the dataset, the computation time for training and using these statistical models…
We introduce a new approach for quantum linear algebra based on quantum subspace states and present three new quantum machine learning algorithms. The first is a quantum determinant sampling algorithm that samples from the distribution…
A central task in the field of quantum computing is to find applications where quantum computer could provide exponential speedup over any classical computer. Machine learning represents an important field with broad applications where…
We present a very fast algorithm for general matrix factorization of a data matrix for use in the statistical analysis of high-dimensional data via latent factors. Such data are prevalent across many application areas and generate an…
A diffusion probabilistic model (DPM) is a generative model renowned for its ability to produce high-quality outputs in tasks such as image and audio generation. However, training DPMs on large, high-dimensional datasets such as…
Dimensionality reduction is the fundamental problem for machine learning and pattern recognition. During data preprocessing, the feature selection is often demanded to reduce the computational complexity. The problem of feature selection is…
Quantum machine learning aims to release the prowess of quantum computing to improve machine learning methods. By combining quantum computing methods with classical neural network techniques we aim to foster an increase of performance in…