Related papers: The optimized Rayleigh-Ritz scheme for determining…
The two dimensional set of canonical relations giving rise to minimal uncertainties previously constructed from a q-deformed oscillator algebra is further investigated. We provide a representation for this algebra in terms of a flat…
Besides perturbation theory (which clearly requires the knowledge of the exact unperturbed solution), variational techniques represent the main tool for any investigation of the eigenvalue problem of some semibounded operator H in quantum…
Gradient-based optimization is a key ingredient of variational quantum algorithms, with applications ranging from quantum machine learning to quantum chemistry and simulation. The parameter-shift rule provides a hardware-friendly method for…
We take an additional step towards the optimization of the novel finite-range pseudopotential at constrained Hartree-Fock-Bogolyubov level and implement an optimization procedure within an axial code using harmonic oscillator basis. We…
Eigenvalue estimates that are optimal in some sense have self-evident appeal and leave estimators with a sense of virtue and economy. So, it is natural that ongoing searches for effective strategies for difficult tasks such as estimating…
The eigenstate thermalization hypothesis provides to date the most successful description of thermalization in isolated quantum systems by conjecturing statistical properties of matrix elements of typical operators in the (quasi-)energy…
We provide new information concerning the pseudospectra of the complex harmonic oscillator. Our analysis illustrates two different techniques for getting resolvent norm estimates. The first uses the JWKB method and extends for this…
The spectrum of any quantum model which eigenvalue equation reduces to a three-term recurrence, such as a displaced harmonic oscillator, the Jaynes-Cummings (JC) model, the Rabi model, and a generalized Rabi model, can be determined as…
The power spectrum analysis of spectral fluctuations in complex wave and quantum systems has emerged as a useful tool for studying their internal dynamics. In this paper, we formulate a nonperturbative theory of the power spectrum for…
From characterizing the speed of a thermal system's response to computing natural modes of vibration, eigenvalue analysis is ubiquitous in engineering. In spite of this, eigenvalue problems have received relatively little treatment compared…
A companion paper provides a proposal for cosmic singularity resolution based upon general features of a bouncing unitary cosmological model in the mini-superspace approximation. This paper analyses novel phenomenology that can be…
The one-dimensional harmonic oscillator in a box problem is possibly the simplest example of a two-mode system. This system has two exactly solvable limits, the harmonic oscillator and a particle in a (one-dimensional) box. Each of the two…
Variational Quantum Eigensolver (VQE) is a hybrid algorithm for finding the minimum eigenvalue/vector of a given Hamiltonian by optimizing a parametrized quantum circuit (PQC) using a classical computer. Sequential optimization methods,…
In the existing literature various numerical techniques have been developed to quantize the confined harmonic oscillator in higher dimensions. In obtaining the energy eigenvalues, such methods often involve indirect approaches such as…
Optimization of mutual synchronization between a pair of limit-cycle oscillators with weak symmetric coupling is considered in the framework of the phase reduction theory. By generalizing a previous study on the optimization of…
The variational quantum eigensolver (or VQE) uses the variational principle to compute the ground state energy of a Hamiltonian, a problem that is central to quantum chemistry and condensed matter physics. Conventional computing methods are…
We introduce Rayleigh functional for nonlinear systems. It is defined using the energy functional and the normalization properties of the variables of variation. The key property of the Rayleigh quotient for linear systems is preserved in…
Quantum effects like entanglement and coherent amplification can be used to drastically enhance the accuracy of quantum parameter estimation beyond classical limits. However, challenges such as decoherence and time-dependent errors hinder…
Estimating the overlap between an approximate wavefunction and a target eigenstate of the system Hamiltonian is essential for the efficiency of quantum phase estimation. In this work, we derive upper and lower bounds on this overlap using…
We propose a general strategy for reduced order modeling of systems that display highly nonlinear oscillations. By considering a continuous family of forced periodic orbits defined in relation to a stable fixed point and subsequently…