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An error avoiding quantum code is presented which is capable of stabilizing Grover's quantum search algorithm against a particular class of coherent errors. This error avoiding code consists of states only which are factorizable in the…
Randomization has emerged as a powerful set of tools for large-scale matrix and tensor decompositions. Randomized algorithms involve computing sketches with random matrices. A prevalent approach is to take the random matrix as a standard…
The assumed computationally difficulty of factoring large integers forms the basis of security for RSA public-key cryptography, which specifically relies on products of two large primes or semi-primes. The best-known factoring algorithms…
We propose a flexible and theoretically supported framework for scalable nonnegative matrix factorization. The goal is to find nonnegative low-rank components directly from compressed measurements, accessing the original data only once or…
Matrices with low numerical rank are omnipresent in many signal processing and data analysis applications. The pivoted QLP (p-QLP) algorithm constructs a highly accurate approximation to an input low-rank matrix. However, it is…
Randomized quantum algorithms have been proposed in the context of quantum simulation and quantum linear algebra with the goal of constructing shallower circuits than methods based on block encodings. While the algorithmic complexities of…
Principal component analysis (PCA) is a dimensionality reduction method in data analysis that involves diagonalizing the covariance matrix of the dataset. Recently, quantum algorithms have been formulated for PCA based on diagonalizing a…
When factorizing binary matrices, we often have to make a choice between using expensive combinatorial methods that retain the discrete nature of the data and using continuous methods that can be more efficient but destroy the discrete…
We consider the problem of computing a QR (or QZ) decomposition of a real, dense, tall and very skinny matrix. That is, the number of columns is tiny compared to the number of rows, rendering most computations completely or partially…
Quantum computing devices are believed to be powerful in solving the prime factorization problem, which is at the heart of widely deployed public-key cryptographic tools. However, the implementation of Shor's quantum factorization algorithm…
Penalized quantile regression (QR) is widely used for studying the relationship between a response variable and a set of predictors under data heterogeneity in high-dimensional settings. Compared to penalized least squares, scalable…
The variational quantum eigensolver is one of the most promising algorithms for near-term quantum computers. It has the potential to solve quantum chemistry problems involving strongly correlated electrons, which are otherwise difficult to…
Randomized algorithms are overwhelming methods for low-rank approximation that can alleviate the computational expenditure with great reliability compared to deterministic algorithms. A crucial thought is generating a standard Gaussian…
Randomized algorithms for low-rank approximation of quaternion matrices have gained increasing attention in recent years. However, existing methods overlook pass efficiency, the ability to limit the number of passes over the input…
Quantum linear system solvers like the Quantum Singular Value Transformation (QSVT) require a block encoding of the system matrix $A$ within a unitary operator $U_A$. Unfortunately, block encoding often results in significant…
We describe an algorithm for sampling a low-rank random matrix $Q$ that best approximates a fixed target matrix $P\in\mathbb{C}^{n\times m}$ in the following sense: $Q$ is unbiased, i.e., $\mathbb{E}[Q] = P$; $\mathsf{rank}(Q)\leq r$; and…
Convolution operations are foundational to classical image processing and modern deep learning architectures, yet their extension into the quantum domain has remained algorithmically and physically costly due to inefficient data encoding…
This paper addresses the Quadratic Multiple Constraints Variable-Sized Bin Packing Problem (QMC-VSBPP), a challenging combinatorial optimization problem that generalizes the classical bin packing problem by incorporating multiple capacity…
Unsplittable flow problems cover a wide range of telecommunication and transportation problems and their efficient resolution is key to a number of applications. In this work, we study algorithms that can scale up to large graphs and…
Quispel-Roberts-Thompson (QRT) maps are a family of birational maps of the plane which provide the simplest discrete analogue of an integrable Hamiltonian system, and are associated with elliptic fibrations in terms of biquadratic curves.…