Related papers: High-Precision Value for the Quartic Anharmonic Os…
We propose a new quantum computational way of obtaining a ground-state energy and expectation values of observables of interacting Hamiltonians. It is based on the combination of the adiabatic quantum evolution to project a ground state of…
We propose a new quantum Monte Carlo algorithm to compute fermion ground-state properties. The ground state is projected from an initial wavefunction by a branching random walk in an over-complete basis space of Slater determinants. By…
The one-dimensional quantum harmonic oscillator problem is examined via the Laplace transform method. The stationary states are determined by requiring definite parity and good behaviour of the eigenfunction at the origin and at infinity.
The total energy of the ground state of the quantum harmonic oscillator is obtained with minimal assumptions. The vacuum energy density of the universe is derived and a cutoff frequency is obtained for the upper bound of the quantum…
The use of special quantum states to achieve sensitivities below the limits established by classically behaving states has enjoyed immense success since its inception. In bosonic interferometers, squeezed states, number states and cat…
Quantum ground-state problems are computationally hard problems; for general many-body Hamiltonians, there is no classical or quantum algorithm known to be able to solve them efficiently. Nevertheless, if a trial wavefunction approximating…
The problem of the harmonic oscillator with a centrally located delta function potential can be exactly solved in one dimension where the eigenfunctions are expressed as superpositions of the Hermite polynomials or as confluent…
The construction of Generalized Intelligent States (GIS) for the $x^4$% -anharmonic oscillator is presented. These GIS families are required to minimize the Robertson-Schr\"odinger uncertainty relation. As a particular case, we will get the…
The Fast Fourier Transform (FFT) is one of the most widely used algorithms in high performance computing, with critical applications in spectral analysis for both signal processing and the numerical solution of partial differential…
We devise a quasilinear quantum algorithm for generating an approximation for the ground state of a quantum field theory (QFT). Our quantum algorithm delivers a super-quadratic speedup over the state-of-the-art quantum algorithm for…
In this paper, we explore an efficient online algorithm for quantum state estimation based on a matrix-exponentiated gradient method previously used in the context of machine learning. The state update is governed by a learning rate that…
We present an approximative calculation of the ground-state energy for the anisotropic anharmonic oscillator Using an instanton solution of the isotropic action $\delta = 0$, we obtain the imaginary part of the ground-state energy for small…
Parallel to the quantization of the complex plane, using the canonical coherent states of a right quaternionic Hilbert space, quaternion field of quaternionic quantum mechanics is quantized. Associated upper symbols, lower symbols and…
A new iterative solver is proposed to efficiently calculate the ground state electronic structure in Density Functional Theory calculations. This algorithm is particularly useful for simulating physical systems considered difficult to…
General positivity constraints linking various powers of observables in energy eigenstates can be used to sharply locate acceptable regions for the energy eigenvalues, provided that efficient recursive methods are available to calculate the…
High-level vibrational calculations have been used to investigate anharmonicity in a wide variety of materials using density-functional-theory (DFT) methods. We have developed a new and efficient approach for describing strongly-anharmonic…
We propose a general-purpose quantum algorithm for preparing ground states of quantum Hamiltonians from a given trial state. The algorithm is based on techniques recently developed in the context of solving the quantum linear systems…
The explicit semiclassical treatment of the logarithmic perturbation theory for the bound-state problem for the spherical anharmonic oscillator is developed. Based upon the $\hbar$-expansions and suitable quantization conditions a new…
The ground-state wave function and the energy gap are calculated for various layer separations d and for up to 24 electrons by the density matrix renormalization group (DMRG) method. Two-particle distribution function and excitonic…
We present a large-scale computational study combining arbitrary-precision arithmetic, sequence acceleration, and the PSLQ integer relation algorithm to discover exact closed-form expressions for fundamental constants arising in asymptotic…