Related papers: Contour Integral-based Quantum Algorithm for Estim…
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…
Quantum signal processing (QSP) and the quantum singular value transformation (QSVT) are pivotal tools for simplifying the development of quantum algorithms. These techniques leverage polynomial transformations on the eigenvalues or…
Extracting eigenvalues and eigenvectors of exponentially large matrices will be an important application of near-term quantum computers. The Variational Quantum Eigensolver (VQE) treats the case when the matrix is a Hamiltonian. Here, we…
The learning process for multi layered neural networks with many nodes makes heavy demands on computational resources. In some neural network models, the learning formulas, such as the Widrow-Hoff formula, do not change the eigenvectors of…
We present a quantum algorithm to compute the entanglement spectrum of arbitrary quantum states. The interesting universal part of the entanglement spectrum is typically contained in the largest eigenvalues of the density matrix which can…
We transform the problem of solving linear system of equations $A\mathbf{x}=\mathbf{b}$ to a problem of finding the right singular vector with singular value zero of an augmented matrix $C$, and present two quantum algorithms for solving…
Accurately predicting response properties of molecules such as the dynamic polarizability and hyperpolarizability using quantum mechanics has been a long-standing challenge with widespread applications in material and drug design. Classical…
Efficient numerical characterization is a key problem in composite material analysis. To follow accuracy improvement in image tomography, memory efficient methods of numerical characterization have been developed. Among them, an FFT based…
In this paper, we propose an eigenvalue analysis -- of system dynamics models -- based on the Mutual Information measure, which in turn will be estimated via the Kernel Density Estimation method. We postulate that the proposed approach…
Powerful generative artificial intelligence from large language models (LLMs) harnesses extensive computational resources for inference. In this work, we investigate the transformer architecture, a key component of these models, under the…
An algorithm named EigenWave is described to compute eigenvalues and eigenvectors of elliptic boundary value problems. The algorithm, based on the recently developed WaveHoltz scheme, solves a related time-dependent wave equation as part of…
We present a new algorithm that computes eigenvalues and eigenvectors of a Hermitian positive definite matrix while solving a linear system of equations with Conjugate Gradient (CG). Traditionally, all the CG iteration vectors could be…
Variational algorithms for strongly correlated chemical and materials systems are one of the most promising applications of near-term quantum computers. We present an extension to the variational quantum eigensolver that approximates the…
Quantum computational approaches to some classic target identification and localization algorithms, especially for radar images, are investigated, and are found to raise a number of quantum statistics and quantum measurement issues with…
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…
The Harrow-Hassidim-Lloyd (HHL) algorithm is a quantum algorithm for solving systems of linear equations that, in principle, offers an exponential improvement in scaling with the system size compared to classical approaches. In this work,…
Quantum process tomography (QPT) plays a central role in characterizing quantum gates and circuits, diagnosing quantum devices, calibrating hardware, and supporting quantum error correction. However, conventional QPT methods face challenges…
Entanglement is one of the fundamental properties of a quantum state and is a crucial differentiator between classical and quantum computation. There are many ways to define entanglement and its measure, depending on the problem or…
Fine-grained spectral properties of quantum Hamiltonians, including both eigenvalues and their multiplicities, provide useful information for characterizing many-body quantum systems as well as for understanding phenomena such as…
We present a quantum algorithm for solving the finite-horizon discrete-time Linear Quadratic Gaussian (LQG) control problem, which integrates optimal control and state estimation in the presence of stochastic disturbances and noise.…