Related papers: Special functions in quantum phase estimation
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…
Quantum phase estimation (QPE) is the key subroutine of several quantum computing algorithms as well as a central ingredient in quantum computational chemistry and quantum simulation. While QPE strategies have focused on the estimation of a…
The perturbation method in supersymmetric quantum mechanics (SUSYQM) is used to study whether the spheroidal equations have the shape-invariance property. Expanding the super-potential term by term in the parameter alpha and solving it, we…
A previous article showed that alternative expressions for calculating oblate spheroidal radial functions of both kinds can provide accurate values over very large parameter ranges using double precision arithmetic, even where the…
In the present paper, first the mathematical basic properties of the exceptional points are discussed. Then, their role in the description of real physical quantum systems is considered. Most interesting value is the phase rigidity of the…
Quantum mechanical wave functions have phases. These phases either initial or acquired during time evolution usually do not enter the final expressions for observable physical quantities. Nevertheless in many cases the observable physical…
Quantum parameter estimation plays a key role in many fields like quantum computation, communication and metrology. Optimal estimation allows one to achieve the most precise parameter estimates, but requires accurate knowledge of the model.…
Quantum amplitude estimation is a key subroutine in a number of powerful quantum algorithms, including quantum-enhanced Monte Carlo simulation and quantum machine learning. Maximum-likelihood quantum amplitude estimation (MLQAE) is one of a…
Phase difference function is established by means of phase transfer function between time domains of source and interference point. The function reveals a necessary interrelation between outcome of two-beam interference, source's frequency…
An algorithm for computing eigenvalues and eigenfunctions of the angular spheroidal wave equation, based on a known but scarcely used method, is developed. By requiring the regularity of the wave function, represented by its series…
Quantum phase estimation is one of the key algorithms in the field of quantum computing, but up until now, only approximate expressions have been derived for the probability of error. We revisit these derivations, and find that by ensuring…
The spin-weighted spheroidal equations in the case s=1/2 is thoroughly studied in the paper by means of the perturbation method in supersymmetry quantum mechanics. The first-five terms of the super-potential in the series of the parameter…
The effect of non-sphericity of the quantum dot on the eigenvalues and eigenfunctions has been investigated for the case of both the finite and infinite barrier. The ground and excited state energies have been calculated for prolate and…
Generalized prolate spheroidal functions (GPSFs) arise naturally in the study of bandlimited functions as the eigenfunctions of a certain truncated Fourier transform. In one dimension, the theory of GPSFs (typically referred to as prolate…
We study the simultaneous estimation of multiple phases as a discretised model for the imaging of a phase object. We identify quantum probe states that provide an enhancement compared to the best quantum scheme for the estimation of each…
A quantum mechanical observer might be describable as having a reference system that is a superposition of classical inertial reference frames. The present paper suggests a possible weighting function in such superpositions, determined by…
Quantum-phase-estimation algorithms are critical subroutines in many applications for quantum computers and in quantum-metrology protocols. These algorithms estimate the unknown strength of a unitary evolution. By using coherence or…
The efficiency of parameter estimation of quantum channels is studied in this paper. We introduce the concept of programmable parameters to the theory of estimation. It is found that programmable parameters obey the standard quantum limit…
For Hill's equation on [0,infinity) we prove new characterizations of the spectral function rho(lambda) and the spectral density function f(lambda) based on analysis involving a companion system of first order differential equations in…
Since the early 1960s, the fields of signal processing, data transmission, channel equalisation, filter design and others have been technologically developed and modernised as a result of the research carried out by D. Slepian and his…