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A necessary and sufficient condition for a parameter transformation that leaves invariant the energy of a one dimensional autonomous system is obtained. Using a parameter transformation the Hamilton-Jacobi equation is solved by a…
The numerical version of the Hamilton-Jacobi quantization method, recently proposed, is applied to the one dimensional quartic oscillator. A suitable quantization condition is formulated and various energy levels and wave functions are…
This paper is concerned with open quantum memory systems for approximately retaining quantum information, such as initial dynamic variables or quantum states to be stored over a bounded time interval. In the Heisenberg picture of quantum…
We propose an alternative solution to a quantum-mechanical four-particle system in one dimension with two- and three-particle interactions. The solution of the eigenvalue equation in center-of-mass and Jacobi coordinates is considerably…
Dimensional Reduction is applied to \qcd{} in order to compute various renormalization constants in the \drbar{} scheme at higher orders in perturbation theory. In particular, the $\beta$ function and the anomalous dimension of the quark…
The Classic Howard's algorithm, a technique of resolution for discrete Hamilton-Jacobi equations, is of large use in applications for its high efficiency and good performances. A special beneficial characteristic of the method is the…
We present an algorithm for measurement of $k$-local operators in a quantum state, which scales logarithmically both in the system size and the output accuracy. The key ingredients of the algorithm are a digital representation of the…
We introduce an approach for performing quantum state reconstruction on systems of $n$ qubits using a machine-learning-based reconstruction system trained exclusively on $m$ qubits, where $m\geq n$. This approach removes the necessity of…
Dimensionality reduction (DR) algorithms, which reduce the dimensionality of a given data set while preserving the information of the original data set as well as possible, play an important role in machine learning and data mining. Duan…
We investigate a decomposition of a unital Lindblad dynamical map of an open quantum system into two distinct types of mapping on the Hilbert-Schmidt space of quantum states. One component of the decomposed map corresponds to reversible…
We present a tutorial on reduced-rank signal processing, design methods and algorithms for dimensionality reduction, and cover a number of important applications. A general framework based on linear algebra and linear estimation is employed…
Reduced modeling in high-dimensional reproducing kernel Hilbert spaces offers the opportunity to approximate efficiently non-linear dynamics. In this work, we devise an algorithm based on low rank constraint optimization and kernel-based…
In this paper, we propose a decomposition approach for eigenvalue problems with spatial symmetries, including the formulation, discretization as well as implementation. This approach can handle eigenvalue problems with either Abelian or…
We introduce a classical algorithm to approximate the free energy of local, translation-invariant, one-dimensional quantum systems in the thermodynamic limit of infinite chain size. While the ground state problem (i.e., the free energy at…
Quantum computation and quantum control operate by building unitary transformations out of sequences of elementary quantum logic operations or applications of control fields. This paper puts upper bounds on the minimum time required to…
Leveraging an algebraic approach built on minimal realizations and conditional expectations in quantum probability, we propose a method to reduce the dimension of quantum filters in discrete-time, while maintaining the correct distributions…
We consider finite-dimensional many-body quantum systems described by time-independent Hamiltonians and Markovian master equations, and present a systematic method for constructing smaller-dimensional, reduced models that exactly reproduce…
We propose an interpretation of quantum separability based on a physical principle: local time reversal. It immediately leads to a simple characterization of separable quantum states that reproduces results known to hold for binary…
We use the well-known observation that the solutions of Jacobi's differential equation can be represented via non-oscillatory phase and amplitude functions to develop a fast algorithm for computing multi-dimensional Jacobi polynomial…
The quantum mechanical ground state of electrons is described by Density Functional Theory, which leads to large minimization problems. An efficient minimization method uses a selfconsistent field (SCF) solution of large eigenvalue…