相关论文: Quantum state transformations and the Schubert cal…
We describe the inequalities on the possible eigenvalues of products of unitary matrices in terms of quantum Schubert calculus. Related problems are the existence of flat connections on the punctured two-sphere with prescribed holonomies,…
The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The…
A theoretical analysis is given of the equation of motion method, due to Alben et al., to compute the eigenvalue distribution (density of states) of very large matrices. The salient feature of this method is that for matrices of the kind…
We review the recent developments in the theory of normal, normal self-dual and general complex random matrices. The distribution and correlations of the eigenvalues at large scales are investigated in the large $N$ limit. The 1/N expansion…
The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The…
Quantum signal processing allows for quantum eigenvalue transformation with Hermitian matrices, in which each eigenspace component of an input vector gets transformed according to its eigenvalue. In this work, we introduce the multivariate…
The random matrix ensembles are applied to the quantum statistical 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 revisit the properties of qubits under Lorentz transformations and, by considering Lorentz invariant quantum states in the Heisenberg formulation, clarify some misleading notation that has appeared in the literature on relativistic…
Mathematical analysis on the existence of eigenvalues is essential because it is equivalent to the occurrence of localization, which is an exceptionally crucial property of quantum walks. We construct the method for the eigenvalue problem…
The usual way to reveal properties of an unknown quantum state, given many copies of a system in that state, is to perform measurements of different observables and to analyze the measurement results statistically. Here we show that the…
Eigenvalue transformations, which include solving time-dependent differential equations as a special case, have a wide range of applications in scientific and engineering computation. While quantum algorithms for singular value…
The kernel trick in supervised learning signifies transformations of an inner product by a feature map, which then restructures training data in a larger Hilbert space according to an endowed inner product. A quantum feature map corresponds…
In this note, we survey some elementary theorems and proofs concerning dynamical matrices theory. Some mathematical concepts and results involved in quantum information theory are reviewed. A little new result on the matrix representation…
State, trace, and moment polynomials are polynomial expressions in several operator or random variables and positive functionals on their products (states, traces or expectations). While these concepts, and in particular their positivity…
We elucidate physical aspects of path signatures by formulating randomised path developments within the framework of matrix models in quantum field theory. Using tools from physics, we introduce a new family of randomised path developments…
Manin matrices are quantum linear transformations of general quantum spaces. In this paper, we study the $q$-analogue of super Manin matrices and obtain several quantum versions of classical identities, such as Jacobi's ratio theorem,…
The randomized quantum marginal problem asks about the joint distribution of the partial traces ("marginals") of a uniform random Hermitian operator with fixed spectrum acting on a space of tensors. We introduce a new approach to this…
Let H be a positive semidefinite matrix partitioned into Hermitian blocks. Then, up to a direct sum operation, H is the average of matrices isometrically congruent to its partial trace. A few corollaries are given, related to important…
Based on the matrix realignment and partial transpose, we develop an approach to entangling power and operator entanglement of quantum unitary operators. We demonstrate efficiency of the approach by studying several unitary operators on…
We introduce a general method for transforming the equations of motion following from a Das-Jevicki-Sakita Hamiltonian, with boundary conditions, into a boundary value problem in one-dimensional quantum mechanics. For the particular case of…