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In a quantum many-body system, autocorrelation functions can determine linear responses nearby equilibrium and quantum dynamics far from equilibrium. In this letter, we bring out the connection between the operator complexity and the…
Quantum phase estimation is the workhorse behind any quantum algorithm and a promising method for determining ground state energies of strongly correlated quantum systems. Low-cost quantum phase estimation techniques make use of circuits…
An approximation method which combines the perturbation theory with the variational calculation is constructed for quantum mechanical problems. Using the anharmonic oscillator and the He atom as examples, we show that the present method…
The purpose of this work is to study a finite element method for finding solutions to the eigenvalue problem for the fractional Laplacian. We prove that the discrete eigenvalue problem converges to the continuous one and we show the order…
We present a hardware agnostic error mitigation algorithm for near term quantum processors inspired by the classical Lanczos method. This technique can reduce the impact of different sources of noise at the sole cost of an increase in the…
Entanglement is one of the fundamental properties of a quantum state and is a crucial differentiator between classical and quantum computation. There are many ways to define entanglement and its measure, depending on the problem or…
We develop a scheme to exactly evaluate the correlation energy in the random-phase approximation, based on linear response theory. It is demonstrated that our formula is completely equivalent to a contour integral representation recently…
Understanding the dynamics of equilibration processes in quantum systems as well as their interplay with dissipation and fluctuation is a major challenge in quantum many-body theory. The timescales of such processes are investigated in…
We investigate in this paper an alternative method to simulation based recursive importance sampling procedure to estimate the optimal change of measure for Monte Carlo simulations. We propose an algorithm which combines (vector and…
We propose a simple method to estimate the parameters of a continuously measured quantum system, by fitting correlation functions of the measured signal. We demonstrate the approach in simulation, both on toy examples and on a recent…
Associated to a finite measure on the real line with finite moments are recurrence coefficients in a three-term formula for orthogonal polynomials with respect to this measure. These recurrence coefficients are frequently inputs to modern…
The theory of a novel bond-order potential, which is based on the block Lanczos algorithm, is presented within an orthogonal tight-binding representation. The block scheme handles automatically the very different character of sigma and pi…
We examine and compare several iterative methods for solving large-scale eigenvalue problems arising from nuclear structure calculations. In particular, we discuss the possibility of using block Lanczos method, a Chebyshev filtering based…
The Lanczos algorithm for matrix tridiagonalisation suffers from strong numerical instability in finite precision arithmetic when applied to evaluate matrix eigenvalues. The mechanism by which this instability arises is well documented in…
This paper presents and implements an iterative feedback design algorithm for stabilisation of discrete-time switched systems under arbitrary switching regimes. The algorithm seeks state feedback gains so that the closed-loop switching…
In this paper, we discuss numerical methods for the eigenvalue decomposition of real symmetric matrices. While many existing methods can compute approximate eigenpairs with sufficiently small backward errors, the magnitude of the resulting…
In this paper, a method for recursively computing approximate modal paths is developed. A recursive formulation of the modal path can be obtained either by backward or forward dynamic programming. By combining both methods, a ``two-filter''…
We consider the following constrained Rayleigh quotient optimization problem (CRQopt) $$ \min_{x\in \mathbb{R}^n} x^{T}Ax\,\,\mbox{subject to}\,\, x^{T}x=1\,\mbox{and}\,C^{T}x=b, $$ where $A$ is an $n\times n$ real symmetric matrix and $C$…
An application of an effective numerical algorithm for solving eigenvalue problems which arise in modelling electronic properties of quantum disordered systems is considered. We study the electron states at the localization-delocalization…
We increase the efficiency of a recently proposed time integration scheme for time dependent quantum transport by using the Lanczos method for time evolution. We illustrate our modified scheme in terms of a simple one dimensional model. Our…