Logistic regression, the Support Vector Machine (SVM), and least squares are well-studied methods in the statistical and computer science community, with various practical applications. High-dimensional data arriving on a real-time basis makes the design of online learning algorithms that produce sparse solutions essential. The seminal work of \hyperlink{cite.langford2009sparse}{Langford, Li, and Zhang (2009)} developed a method to obtain sparsity via truncated gradient descent, showing a near-optimal online regret bound. Based on this method, we develop a quantum sparse online learning algorithm for logistic regression, the SVM, and least squares. Given efficient quantum access to the inputs, we show that a quadratic speedup in the time complexity with respect to the dimension of the problem is achievable, while maintaining a regret of $O(1/\sqrt{T})$ , where $T$ is the number of iterations.Logistic regression, the Support Vector Machine (SVM), and least squares are well-studied methods in the statistical and computer science community, with various practical applications. High-dimensional data arriving on a real-time basis makes the design of online learning algorithms that produce sparse solutions essential. The seminal work of \hyperlink{cite.langford2009sparse}{Langford, Li, and Zhang (2009)} developed a method to obtain sparsity via truncated gradient descent, showing a near-optimal online regret bound. Based on this method, we develop a quantum sparse online learning algorithm for logistic regression, the SVM, and least squares. Given efficient quantum access to the inputs, we show that a quadratic speedup in the time complexity with respect to the dimension of the problem is achievable, while maintaining a regret of $O(1/\sqrt{T})$, where $T$ is the number of iterations.

arXiv:2411.03925Nov 6, 20240 citations

Variational Quantum Linear Solver Enhanced Quantum Support Vector Machine

Yi, Jianming, Suresh, Kalyani, Moghiseh, Ali +1 more

Nov 26, 20250 citations

Quantum Support Vector Machine Based on Gradient Descent

Hong Li, Nan Jiang, Rui Zhang +2 more

International Journal of Theoretical PhysicsMar 1, 202211 citations

Quantum Sparse Support Vector Machines

Seyran Saeedi, Tom J. Arodz

We analyze the computational complexity of Quantum Sparse Support Vector Machine, a linear classifier that minimizes the hinge loss and the $L_1$ norm of the feature weights vector and relies on a quantum linear programming solver instead of a classical solver. Sparse SVM leads to sparse models that use only a small fraction of the input features in making decisions, and is especially useful when the total number of features, $p$ , approaches or exceeds the number of training samples, $m$ . We prove a $Ω(m)$ worst-case lower bound for computational complexity of any quantum training algorithm relying on black-box access to training samples; quantum sparse SVM has at least linear worst-case complexity. However, we prove that there are realistic scenarios in which a sparse linear classifier is expected to have high accuracy, and can be trained in sublinear time in terms of both the number of training samples and the number of features.We analyze the computational complexity of Quantum Sparse Support Vector Machine, a linear classifier that minimizes the hinge loss and the $L_1$ norm of the feature weights vector and relies on a quantum linear programming solver instead of a classical solver. Sparse SVM leads to sparse models that use only a small fraction of the input features in making decisions, and is especially useful when the total number of features, $p$, approaches or exceeds the number of training samples, $m$. We prove a $Ω(m)$ worst-case lower bound for computational complexity of any quantum training algorithm relying on black-box access to training samples; quantum sparse SVM has at least linear worst-case complexity. However, we prove that there are realistic scenarios in which a sparse linear classifier is expected to have high accuracy, and can be trained in sublinear time in terms of both the number of training samples and the number of features.

arXiv:1902.01879Feb 5, 20196 citations

Quantum support vector machine without iteration

Rui Zhang, Jian Wang, Nan Jiang +1 more

arXiv:2206.00909Information SciencesMar 27, 202343 citations

O(1/\sqrt{T})

, where

T

is the number of iterations.

We analyze the computational complexity of Quantum Sparse Support Vector Machine, a linear classifier that minimizes the hinge loss and the

L_1

norm of the feature weights vector and relies on a quantum linear programming solver instead of a classical solver. Sparse SVM leads to sparse models that use only a small fraction of the input features in making decisions, and is especially useful when the total number of features,

p

, approaches or exceeds the number of training samples,

m

. We prove a

Ω(m)

worst-case lower bound for computational complexity of any quantum training algorithm relying on black-box access to training samples; quantum sparse SVM has at least linear worst-case complexity. However, we prove that there are realistic scenarios in which a sparse linear classifier is expected to have high accuracy, and can be trained in sublinear time in terms of both the number of training samples and the number of features.