相关论文: Novel linear algebraic theory and one-hundred-mill…

Sequences of parametrized Lyapunov equations can be encountered in many application settings. Moreover, solutions of such equations are often intermediate steps of an overall procedure whose main goal is the computation of…

In this research, a novel adaptive filtering algorithm is proposed for complex domain signal processing. The proposed algorithm is based on Wirtinger calculus and is called as q-Complex Least Mean Square (q-CLMS) algorithm. The proposed…

Probabilistic ideas and tools have recently begun to permeate into several fields where they had traditionally not played a major role, including fields such as numerical linear algebra and optimization. One of the key ways in which these…

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…

We develop a layered quantum computer architecture, which is a systematic framework for tackling the individual challenges of developing a quantum computer while constructing a cohesive device design. We discuss many of the prominent…

Many areas of machine learning and science involve large linear algebra problems, such as eigendecompositions, solving linear systems, computing matrix exponentials, and trace estimation. The matrices involved often have Kronecker,…

Quantum computation is one of the most promising new paradigms for the simulation of physical systems composed of electrons and atomic nuclei, with applications in chemistry, solid-state physics, materials science, and molecular biology.…

Theoretical concepts in condensed matter physics are typically verified and also developed by exploiting computer simulations mostly in simple models. Predictions based on these usually isotropic models are often at odds with measurement…

In this work we present a rational Krylov subspace method for solving real large-scale polynomial eigenvalue problems with T-even (that is, symmetric/skew-symmetric) structure. Our method is based on the Even-IRA algorithm. To preserve the…

Krylov subspace recycling is a powerful tool for solving long series of large, sparse linear systems that change slowly. In PDE constrained shape optimization, these appear naturally, as hundreds or more optimization steps are needed with…

Quantum computers hold promise to improve the efficiency of quantum simulations of materials and to enable the investigation of systems and properties more complex than tractable at present on classical architectures. Here, we discuss…

We propose a class of randomized quantum algorithms for the task of sampling from matrix functions, without the use of quantum block encodings or any other coherent oracle access to the matrix elements. As such, our use of qubits is purely…

Quantum Layout Synthesis (QLS) plays a crucial role in optimizing quantum circuit execution on physical quantum devices. As we enter the era where quantum computers have hundreds of qubits, we are faced with scalability issues using optimal…

This manuscript explores a variational quantum formulation for nonlinear elasticity problems arising from hyperelastic material models, targeting near term noisy intermediate scale quantum (NISQ) devices. The approach leverages the…

Simulating nonlinear classical dynamics on a quantum computer is an inherently challenging task due to the linear operator formulation of quantum mechanics. In this work, we provide a systematic approach to alleviate this difficulty by…

Computing eigenvalues is a computationally intensive task central to numerous applications in the natural sciences. Toward this end, we investigate the quantum block Krylov subspace projector (QBKSP) algorithm - a multireference quantum…

We present an efficient quantum algorithm to simulate nonlinear differential equations with polynomial vector fields of arbitrary degree on quantum platforms. Models of physical systems that are governed by ordinary differential equations…

Solving the generalized eigenvalue problem is a useful method for finding energy eigenstates of large quantum systems. It uses projection onto a set of basis states which are typically not orthogonal. One needs to invert a matrix whose…

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…

Solving systems of linear equations is a key subroutine in many quantum algorithms. In the last 15 years, many quantum linear solvers (QLS) have been developed, competing to achieve the best asymptotic worst-case complexity. Most QLS assume…