Related papers: Integrals for lower bounds to the exact energy
The well-known algorithm for quantum phase estimation requires that the considered unitary is available as a conditional transformation depending on the quantum state of an ancilla register. We present an algorithm converting an unknown…
Hamiltonian quantum gates controlled by classical electromagnetic fields form the basis of any realistic model of quantum computers. In this letter, we derive a lower bound on the field energy required to implement such gates and relate…
A method for determination of bound state energies for an asymmetric quantum well with an arbitrary shape of the bottom is suggested. It is shown that how the equation determining the energy levels can be easily derived if one knows the…
The fundamental problem faced in quantum chemistry is the calculation of molecular properties, which are of practical importance in fields ranging from materials science to biochemistry. Within chemical precision, the total energy of a…
The first fully relativistic, rigorous QED calculations of the self-energy correction to the fine-structure levels of heavy muonic atoms are reported. We discuss nuclear model and parameter dependence for this contribution as well as…
We present a complete prescription for the numerical calculation of surface Green's functions and self-energies of semi-infinite quasi-onedimensional systems. Our work extends the results of Sanvito et al. [1] generating a robust algorithm…
An exact invariant is derived for $n$-degree-of-freedom Hamiltonian systems with general time-dependent potentials. The invariant is worked out in two equivalent ways. In the first approach, we define a special {\it Ansatz\/} for the…
We give a lower bound for the energy of a quantum particle in the infinite square well. We show that the bound is exact and identify the well-known element that fulfils the equality. Our approach is not directly dependent on the…
General analytic energy bounds are derived for N-boson systems governed by semirelativistic Hamiltonians of the form H=\sum_{i=1}^N \sqrt(p_i^2+m^2) + \sum_{1=i<j}^N V(r_{ij}), where V(r) is a static attractive pair potential. A…
Vacuum polarization corrections to the energy levels of bound electrons are calculated using a perturbative path integral formalism. We apply quantum electrodynamics in a framework which treats the strong binding nuclear field to all…
Variational methods play an important role in the study of quantum many-body problems, both in the flavor of classical variational principles based on tensor networks as well as of quantum variational principles in near-term quantum…
We introduce an effective thermodynamics for multipartite entangled pure states and derive an upper bound on extractable energy with feedback control from a subsystem under a local Hamiltonian. The inequality that gives the upper bound…
For a prototype quadratic Hamiltonian describing a driven, dissipative system, exact matrix elements of the reduced density matrix are obtained from a generating function in terms of the normal characteristic functions. The approach is…
Direct dynamics methods using Gaussian wavepackets have to rely only on local properties, such as gradients and hessians at the center of the wavepacket, so as to be compatible with the usual quantum chemistry methods. Matrix elements of…
In this work, we investigate the amount of energy that can be extracted or charged through unitary operations when only minimal information about the state is known. Assuming knowledge of only the mean energy of the state, we start by…
A solution to the quantum Zermelo problem for control Hamiltonians with general energy resource bounds is provided. Interestingly, the energy resource of the control Hamiltonian and the control time define a pair of conjugate variables that…
The method reducing the solution of the Schroedinger equation for several types of power potentials to the solution of the eigenvalue problem for the infinite system of algebraic equations is developed. The finite truncation of this system…
We propose a hybrid quantum-classical algorithm to compute approximate solutions of binary combinatorial problems. We employ a shallow-depth quantum circuit to implement a unitary and Hermitian operator that block-encodes the weighted…
Holonomic quantum computation is analyzed from geometrical viewpoint. We develop an optimization scheme in which an arbitrary unitary gate is implemented with a small circle in a complex projective space. Exact solutions for the Hadamard,…
An exactly solvable position-dependent mass Schr\"odinger equation in two dimensions, depicting a particle moving in a semi-infinite layer, is re-examined in the light of recent theories describing superintegrable two-dimensional systems…