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The spectral density operator $hat{rho}(omega)=delta(omega-hat{H})$ plays a central role in linear response theory as its expectation value, the dynamical response function, can be used to compute scattering cross-sections. In this work, we describe a near optimal quantum algorithm providing an approximation to the spectral density with energy resolution $Delta$ and error $epsilon$ using $mathcal{O}left(sqrt{logleft(1/epsilonright)left(logleft(1/Deltaright)+logleft(1/epsilonright)right)}/Deltaright)$ operations. This is achieved without using expensive approximations to the time-evolution operator but exploiting instead qubitization to implement an approximate Gaussian Integral Transform (GIT) of the spectral density. We also describe appropriate error metrics to assess the quality of spectral function approximations more generally.
We study quantum anomaly detection with density estimation and multivariate Gaussian distribution. Both algorithms are constructed using the standard gate-based model of quantum computing. Compared with the corresponding classical algorithms, the res
We investigate an algorithm named histogram transform ensembles (HTE) density estimator whose effectiveness is supported by both solid theoretical analysis and significant experimental performance. On the theoretical side, by decomposing the error te
The resolvent of supersymmetric Dirac Hamiltonian is studied in detail. Due to supersymmetry the squared Dirac Hamiltonian becomes block-diagonal whose elements are in essence non-relativistic Schrodinger-type Hamiltonians. This enables us to find a
A brief outline of the Lorentz Integral Transform (LIT) method is given. The method is well established and allows to treat reactions into the many-body continuum with bound-state like techniques. The energy resolution that can be achieved is studied
We investigate the quantum Cramer-Rao bounds on the joint multiple-parameter estimation with the Gaussian state as a probe. We derive the explicit right logarithmic derivative and symmetric logarithmic derivative operators in such a situation. We com