Related papers: Improved Quantum Algorithms for Eigenvalues Findin…

We apply the framework of block-encodings, introduced by Low and Chuang (under the name standard-form), to the study of quantum machine learning algorithms and derive general results that are applicable to a variety of input models,…

Solving eigenproblem of the Laplacian matrix of a fully connected weighted graph has wide applications in data science, machine learning, and image processing, etc. However, this is very challenging because it involves expensive matrix…

Optimization problems in disciplines such as machine learning are commonly solved with iterative methods. Gradient descent algorithms find local minima by moving along the direction of steepest descent while Newton's method takes into…

Vectorized quantum block encoding provides a way to embed classical data into Hilbert space, offering a pathway for quantum models, such as Quantum Transformers (QT), that replace classical self-attention with quantum circuit simulations to…

The matrix functions can be defined by Cauchy's integral formula and can be approximated by the linear combination of inverses of shifted matrices using a quadrature formula. In this paper, we show a concrete construction of a framework to…

This paper introduces an algorithm designed to approximate quantum transformation matrix with a restricted number of gates by using the block decomposition technique. Addressing challenges posed by numerous gates in handling large qubit…

Group convolutions and cross-correlations, which are equivariant to the actions of group elements, are commonly used in mathematics to analyze or take advantage of symmetries inherent in a given problem setting. Here, we provide efficient…

The development of quantum computers has been the stimulus that enables the realization of Quantum Machine Learning (QML), an area that integrates the calculational framework of quantum mechanics with the adaptive properties of classical…

Estimating the eigenvalues of non-normal matrices is a foundational problem with far-reaching implications, from modeling non-Hermitian quantum systems to analyzing complex fluid dynamics. Yet, this task remains beyond the reach of standard…

Quantum computing can provide speedups in solving many problems as the evolution of a quantum system is described by a unitary operator in an exponentially large Hilbert space. Such unitary operators change the phase of their eigenstates…

Quantum error correction is a critical component for scaling up quantum computing. Given a quantum code, an optimal decoder maps the measured code violations to the most likely error that occurred, but its cost scales exponentially with the…

Recent advancements in quantum computing (QC) and machine learning (ML) have garnered significant attention, leading to substantial efforts toward the development of quantum machine learning (QML) algorithms to address a variety of complex…

Quantum algorithms can enhance machine learning in different aspects. Here, we study quantum-enhanced least-square support vector machine (LS-SVM). Firstly, a novel quantum algorithm that uses continuous variable to assist matrix inversion…

Large-scale eigenvalue problems pose a significant challenge to classical computers. While there are efficient quantum algorithms for unitary or Hermitian matrices, eigenvalue problems for non-normal matrices remain open in quantum…

The Quantum Singular Value Transformation (QSVT) is a technique that provides a unified framework for describing many of the quantum algorithms discovered to date. We implement a noise-free simulation of the technique to investigate how it…

Matrices with the displacement structures of circulant, Toeplitz, and Hankel types as well as matrices with structures generalizing these types are omnipresent in computations of sciences and engineering. In this paper, we present efficient…

Despite extensive research efforts, few quantum algorithms for classical optimization demonstrate realizable quantum advantage. The utility of many quantum algorithms is limited by high requisite circuit depth and nonconvex optimization…

Leveraging the extraordinary phenomena of quantum superposition and quantum correlation, quantum computing offers unprecedented potential for addressing challenges beyond the reach of classical computers. This paper tackles two pivotal…

We propose a variational method for constructing the eigenvalues and generalized eigenvalues for an arbitrary $N\times N$ complex matrix. The quantum part of our algorithm is based on encoding the matrix elements into the pure state of a…

Solving real-world optimization problems with quantum computing requires choosing between a large number of options concerning formulation, encoding, algorithm and hardware. Finding good solution paths is challenging for end users and…