Related papers: Symplectic decomposition from submatrix determinan…
We show that deterministic multimode Gaussian channels admit a symmetric-space description. Passing from the n-mode Siegel disk to a doubled version of that space lets general Gaussian dynamics act by a linear-fractional (Mobius)…
We discuss probabilistic models of random covariance structures defined by distributions over sparse eigenmatrices. The decomposition of orthogonal matrices in terms of Givens rotations defines a natural, interpretable framework for…
We review our recent results on pseudo-hermitian random matrix theory which were hitherto presented in various conferences and talks. (Detailed accounts of our work will appear soon in separate publications.) Following an introduction of…
We present methods that can provide an exponential savings in the resources required to perform dynamic parameter estimation using quantum systems. The key idea is to merge classical compressive sensing techniques with quantum control…
When inferring parameters from a Gaussian-distributed data set by computing a likelihood, a covariance matrix is needed that describes the data errors and their correlations. If the covariance matrix is not known a priori, it may be…
We propose a determinant-free approach for simulation-based Bayesian inference in high-dimensional Gaussian models. We introduce auxiliary variables with covariance equal to the inverse covariance of the model. The joint probability of the…
We describe a multi-scale resolution approach to analyzing problems in Quantum Mechanics using Daubechies wavelet basis. The expansion of the wavefunction of the quantum system in this basis allows a natural interpretation of each basis…
We show that the covariance matrix of a quantum state can be reconstructed from position measurements using the simple notion of polar duality, familiar from convex geometry. In particular, all multidimensional Gaussian states (pure or…
We propose a novel approach to estimating the precision matrix of multivariate Gaussian data that relies on decomposing them into a low-rank and a diagonal component. Such decompositions are very popular for modeling large covariance…
Simulation of quantum chemistry is expected to be a principal application of quantum computing. In quantum simulation, a complicated Hamiltonian describing the dynamics of a quantum system is decomposed into its constituent terms, where the…
Multimode Gaussian states are a versatile resource for quantum information technologies and have been realized across a wide range of physical platforms. Recent progress in the large-scale generation of such states provides a key ingredient…
We study the problem of estimating the diagonal of an implicitly given matrix $\Ab$. For such a matrix we have access to an oracle that allows us to evaluate the matrix quadratic form $ \ub^\top \Ab \ub$. Based on this query oracle, we…
Gaussian quantum states of bosonic systems are an important class of states. In particular, they play a key role in quantum optics as all processes generated by Hamiltonians up to second order in the field operators (i.e. linear optics and…
A general method to derive the diagonal representation for a generic matrix valued quantum Hamiltonian is proposed. In this approach new mathematical objects like non-commuting operators evolving with the Planck constant promoted as a…
An approximate diagonalization method is proposed that combines exact diagonalization and perturbation expansion to calculate low energy eigenvalues and eigenfunctions of a Hamiltonian. The method involves deriving an effective Hamiltonian…
A random matrix is likely to be well conditioned, and motivated by this well known property we employ random matrix multipliers to advance some fundamental matrix computations. This includes numerical stabilization of Gaussian elimination…
The problem of diagonalization of Hamiltonians of N-dimensional boson systems by means of time-dependent canonical transformations (CT) is considered, the case of quadratic Hamiltonians being treated in greater detail. The unitary generator…
We introduce a variational Bayesian neural network where the parameters are governed via a probability distribution on random matrices. Specifically, we employ a matrix variate Gaussian \cite{gupta1999matrix} parameter posterior…
Many models for chaotic systems consist of joining two integrable systems with incompatible constants of motion. The quantum counterparts of such models have a propagator which factorizes into two integrable parts. Each part can be…
How could the Fourier and other transforms be naturally discovered if one didn't know how to postulate them? In the case of the Discrete Fourier Transform (DFT), we show how it arises naturally out of analysis of circulant matrices. In…