scholarly journals Variational Quantum Fidelity Estimation

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 248 ◽  
Author(s):  
Marco Cerezo ◽  
Alexander Poremba ◽  
Lukasz Cincio ◽  
Patrick J. Coles
Keyword(s):  
Phase Transitions ◽  
Quantum Computer ◽  
Quantum Phase Transitions ◽  
Upper Bounds ◽  
Low Rank ◽  
Matrix Elements ◽  
Lower And Upper Bounds ◽  
Classical Algorithm ◽  
Largest Eigenvalues ◽  
Quantum Fidelity

Computing quantum state fidelity will be important to verify and characterize states prepared on a quantum computer. In this work, we propose novel lower and upper bounds for the fidelity F(ρ,σ) based on the ``truncated fidelity'' F(ρm,σ), which is evaluated for a state ρm obtained by projecting ρ onto its m-largest eigenvalues. Our bounds can be refined, i.e., they tighten monotonically with m. To compute our bounds, we introduce a hybrid quantum-classical algorithm, called Variational Quantum Fidelity Estimation, that involves three steps: (1) variationally diagonalize ρ, (2) compute matrix elements of σ in the eigenbasis of ρ, and (3) combine these matrix elements to compute our bounds. Our algorithm is aimed at the case where σ is arbitrary and ρ is low rank, which we call low-rank fidelity estimation, and we prove that no classical algorithm can efficiently solve this problem under reasonable assumptions. Finally, we demonstrate that our bounds can detect quantum phase transitions and are often tighter than previously known computable bounds for realistic situations.

scholarly journals Nuclear Shell Model And Quantum Phase Transitions

2019 ◽  
Vol 26 ◽  
pp. 88
Author(s):  
S. Karampagia ◽  
V. Zelevinsky
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Shell Model ◽  
Quantum Phase Transitions ◽  
Mean Field ◽  
Nuclear Shell Model ◽  
Matrix Elements ◽  
Model Hamiltonian ◽  
Orbital Space ◽  
Nuclear Shell

The usual nuclear shell model defines nuclear properties through an effective mean-field plus a two-body interaction Hamiltonian in a finite orbital space. In this study we try to understand the correlation between the various parts of the shell model Hamiltonian and the nuclear observables and collectivity in nuclei. By varying specific groups of matrix elements we find signs of a phase transition in nuclei between a non-collective and a collective phase. In all cases studied the collective phase is attained when the single-particle transfer matrix elements are dominant in the shell model Hamiltonian, giving collective characteristics to nuclei.

scholarly journals Quantum fidelity susceptibility in excited state quantum phase transitions: application to the bending spectra of nonrigid molecules

2022 ◽  
Vol 12 (1) ◽  
Author(s):  
Jamil Khalouf-Rivera ◽  
Miguel Carvajal ◽  
Francisco Perez-Bernal
Keyword(s):  
Phase Transitions ◽  
Excited State ◽  
Molecular Species ◽  
Quantum Phase Transitions ◽  
Quantum Phase ◽  
The Other ◽  
Two Dimensional ◽  
Nonrigid Molecules ◽  
Bending Modes ◽  
Quantum Fidelity

We characterize excited state quantum phase transitions in the two dimensional limit of the vibron model with the quantum fidelity susceptibility, comparing the obtained results with the information provided by the participation ratio. As an application, we locate the eigenstate closest to the barrier to linearity and determine the linear or bent character of the different overtones for particular bending modes of six molecular species. We perform a fit and use the optimized eigenvalues and eigenstates in three cases and make use of recently published results for the other three cases.

scholarly journals On Instability Analysis of Linear Feedback Systems

Computation ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 16
Author(s):  
Mutti-Ur Rehman ◽  
Jehad Alzabut
Keyword(s):  
Differential Equation ◽  
System Theory ◽  
Numerical Simulation ◽  
Lower Bounds ◽  
Numerical Approximation ◽  
Upper Bounds ◽  
Low Rank ◽  
Linear Feedback ◽  
Feedback Systems ◽  
Lower And Upper Bounds

The numerical approximation of the μ -value is key towards the measurement of instability, stability analysis, robustness, and the performance of linear feedback systems in system theory. The MATLAB function mussv available in MATLAB Control Toolbox efficiently computes both lower and upper bounds of the μ -value. This article deals with the numerical approximations of the lower bounds of μ -values by means of low-rank ordinary differential equation (ODE)-based techniques. The numerical simulation shows that approximated lower bounds of μ -values are much tighter when compared to those obtained by the MATLAB function mussv.

scholarly journals Quantum fidelity for degenerate ground states in quantum phase transitions

2013 ◽  
Vol 88 (3) ◽  
Author(s):  
Yao Heng Su ◽  
Bing-Quan Hu ◽  
Sheng-Hao Li ◽  
Sam Young Cho
Keyword(s):  
Phase Transitions ◽  
Quantum Phase Transitions ◽  
Ground States ◽  
Quantum Phase ◽  
Quantum Fidelity

Quantum phase transitions

2004 ◽  
Vol 174 (8) ◽  
pp. 853 ◽  
Author(s):  
Sergei M. Stishov
Keyword(s):  
Phase Transitions ◽  
Quantum Phase Transitions ◽  
Quantum Phase

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

Energy of spherical fuzzy graphs

2020 ◽  
pp. 321-332
Author(s):  
S. Yahya Mohamed ◽  
A. Mohamed Ali
Keyword(s):  
Adjacency Matrix ◽  
Upper Bounds ◽  
Fuzzy Graph ◽  
Lower And Upper Bounds ◽  
Fuzzy Graphs

In this paper, the notion of energy extended to spherical fuzzy graph. The adjacency matrix of a spherical fuzzy graph is defined and we compute the energy of a spherical fuzzy graph as the sum of absolute values of eigenvalues of the adjacency matrix of the spherical fuzzy graph. Also, the lower and upper bounds for the energy of spherical fuzzy graphs are obtained.

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