相关论文: The quantum way to diagonalize hermitean matrices

The quantum mechanical version of the four kinds of classical canonical transformations is investigated by using non-hermitian operator techniques. To help understand the usefulness of this appoach the eigenvalue problem of a harmonic…

We develop a systematic approach to determine and measure numerically the geometry of generic quantum or "fuzzy" geometries realized by a set of finite-dimensional hermitian matrices. The method is designed to recover the semi-classical…

It is well known that a set of non-defect matrices can be simultaneously diagonalized if and only if the matrices commute. In the case of non-commuting matrices, the best that can be achieved is simultaneous block diagonalization. Here we…

Machine learning nowadays becomes a useful instrument in many subjects. In this paper we use interpretable machine learning to build quantum algorithm. By studying the parameters of the machine learning algorithm we were able to construct…

Conjugation covariants of matrices are applied to study the real algebraic variety consisting of complex Hermitian matrices with a bounded number of distinct eigenvalues. A minimal generating system of the vanishing ideal of degenerate…

The random matrix ensembles are applied to the quantum chaotic systems. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the…

We obtain a new inequality for arbitrary Hermitian matrices. We describe particular linear maps called the matrix portrait of arbitrary NxN matrices. The maps are obtained as analogs of partial tracing of density matrices of multipartite…

Quantum machine learning techniques have been proposed as a way to potentially enhance performance in machine learning applications. In this paper, we introduce two new quantum methods for neural networks. The first one is a quantum…

Nuclear magnetic resonance techniques are used to realize a quantum algorithm experimentally. The algorithm allows a simple NMR quantum computer to determine global properties of an unknown function requiring fewer function ``calls'' than…

To simulate the quantum systems at classical or quantum computers, it is necessary to reduce continuous observables (e.g. coordinate and momentum or energy and time) to discrete ones. In this work we consider the continuous observables…

We demonstrate how the inverse scattering problem of a quantum star graph can be solved by means of diagonalization of Hermitian unitary matrix when the vertex coupling is of the scale invariant (or F\"ul\H{o}p-Tsutsui) form. This enables…

We describe a quantum algorithm for finding the smallest eigenvalue of a Hermitian matrix. This algorithm combines Quantum Phase Estimation and Quantum Amplitude Estimation to achieve a quadratic speedup with respect to the best classical…

We consider a set of N linearly coupled harmonic oscillators and show that the diagonalization of this problem can be put in geometrical terms. The matrix techniques developed here allowed for solutions in both the classical and quantum…

We present a systematic method for dealing with time dependent quantum dynamics, based on the quantum brachistochrone and matrix mechanics. We derive the explicit time dependence of the Hamiltonian operator for a number of constrained…

The diagonalization of matrices may be the top priority in the application of modern physics. In this paper, we numerically demonstrate that, for real symmetric random matrices with non-positive off-diagonal elements, a universal scaling…

As a hallmark of pure quantum effect, quantum entanglement has provided unconventional routes to condensed matter systems. Here, from the perspective of quantum entanglement, we disclose exotic quantum physics in non-Hermitian…

The complex-valued quantum mechanics considers quantum motion on the complex plane instead of on the real axis, and studies the variations of a particle complex position, momentum and energy along a complex trajectory. On the basis of…

We present quantum algorithms to efficiently perform discriminant analysis for dimensionality reduction and classification over an exponentially large input data set. Compared with the best-known classical algorithms, the quantum algorithms…

We study the matrix elements of few-body observables, focusing on the off-diagonal ones, in the eigenstates of the two-dimensional transverse field Ising model. By resolving all symmetries, we relate the onset of quantum chaos to the…

While quantum computing provides an exponential advantage in solving system of linear equations, there is little work to solve system of nonlinear equations with quantum computing. We propose quantum Newton's method (QNM) for solving…