scholarly journals Variational quantum solver employing the PDS energy functional

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 473
Author(s):  
Bo Peng ◽  
Karol Kowalski
Keyword(s):  
Quantum Algorithms ◽  
Energy Functional ◽  
Strongly Correlated ◽  
Local Minima ◽  
New Class ◽  
Moment Expansion ◽  
Energy Gradient ◽  
Model Hamiltonian ◽  
New Energy ◽  
Quantum Approach

Recently a new class of quantum algorithms that are based on the quantum computation of the connected moment expansion has been reported to find the ground and excited state energies. In particular, the Peeters-Devreese-Soldatov (PDS) formulation is found variational and bearing the potential for further combining with the existing variational quantum infrastructure. Here we find that the PDS formulation can be considered as a new energy functional of which the PDS energy gradient can be employed in a conventional variational quantum solver. In comparison with the usual variational quantum eigensolver (VQE) and the original static PDS approach, this new variational quantum solver offers an effective approach to navigate the dynamics to be free from getting trapped in the local minima that refer to different states, and achieve high accuracy at finding the ground state and its energy through the rotation of the trial wave function of modest quality, thus improves the accuracy and efficiency of the quantum simulation. We demonstrate the performance of the proposed variational quantum solver for toy models, H2 molecule, and strongly correlated planar H4 system in some challenging situations. In all the case studies, the proposed variational quantum approach outperforms the usual VQE and static PDS calculations even at the lowest order. We also discuss the limitations of the proposed approach and its preliminary execution for model Hamiltonian on the NISQ device.

A Combined Spin-Flip and IP/EA Approach for Handling Spin and Spatial Degeneracies: Application to Double Exchange Systems

2018 ◽  
Author(s):  
Shannon Houck ◽  
Nicholas Mayhall
Keyword(s):  
Single Molecule ◽  
Double Exchange ◽  
Computational Effort ◽  
Strongly Correlated ◽  
Single Molecule Magnets ◽  
New Approach ◽  
Spin Flip ◽  
Model Hamiltonian ◽  
Simultaneous Existence ◽  
Exchange Parameters

<div>Many multiconfigurational systems, such as single-molecule magnets, are difficult to study using traditional computational methods due to the simultaneous existence of both spin and spatial degeneracies. In this work, a new approach termed n-spin-flip Ionization Potential/Electron Affinity (<i>n</i>SF-IP or <i>n</i>SF-EA) is introduced which combines the spin-flip method of Anna Krylov with particle-number changing IP/EA methods. We demonstrate the efficacy of the approach by applying it to the strongly-correlated N<sub>2</sub><sup>+</sup> as well as several double exchange systems. We also demonstrate that when these systems are well-described by a double exchange model Hamiltonian, only 1SF-IP/EA is required to extract the double exchange parameters and accurately predict energies for the low-spin states. This significantly reduces the computational effort for studying such systems. The effects of including additional excitations (using a RAS-<i>n</i>SF-IP/EA scheme) are also examined, with particular emphasis on hole and particle excitations.</div>

A Combined Spin-Flip and IP/EA Approach for Handling Spin and Spatial Degeneracies: Application to Double Exchange Systems

2018 ◽  
Author(s):  
Shannon Houck ◽  
Nicholas Mayhall
Keyword(s):  
Single Molecule ◽  
Double Exchange ◽  
Computational Effort ◽  
Strongly Correlated ◽  
Single Molecule Magnets ◽  
New Approach ◽  
Spin Flip ◽  
Model Hamiltonian ◽  
Simultaneous Existence ◽  
Exchange Parameters

<div>Many multiconfigurational systems, such as single-molecule magnets, are difficult to study using traditional computational methods due to the simultaneous existence of both spin and spatial degeneracies. In this work, a new approach termed n-spin-flip Ionization Potential/Electron Affinity (<i>n</i>SF-IP or <i>n</i>SF-EA) is introduced which combines the spin-flip method of Anna Krylov with particle-number changing IP/EA methods. We demonstrate the efficacy of the approach by applying it to the strongly-correlated N<sub>2</sub><sup>+</sup> as well as several double exchange systems. We also demonstrate that when these systems are well-described by a double exchange model Hamiltonian, only 1SF-IP/EA is required to extract the double exchange parameters and accurately predict energies for the low-spin states. This significantly reduces the computational effort for studying such systems. The effects of including additional excitations (using a RAS-<i>n</i>SF-IP/EA scheme) are also examined, with particular emphasis on hole and particle excitations.</div>

scholarly journals Regularity of the m-symphonic map

2021 ◽  
Vol 2 (2) ◽  
Author(s):  
Masashi Misawa ◽  
Nobumitsu Nakauchi
Keyword(s):  
Critical Points ◽  
Conformal Invariance ◽  
Hölder Continuity ◽  
Energy Functional ◽  
Higher Dimension ◽  
Holder Continuity ◽  
New Energy ◽  
Symphonic Map

AbstractWe introduce a new energy functional of conformal invariance and consider its critical points, named the m-symphonic map. We study a Hölder continuity of m-symphonic maps from domains of $$\mathbb {R}^m$$ R m into the spheres in the higher dimension $$m \ge 4$$ m ≥ 4 .

scholarly journals An Image Segmentation Method Based on Improved Regularized Level Set Model

2018 ◽  
Vol 8 (12) ◽  
pp. 2393 ◽  
Author(s):  
Lin Sun ◽  
Xinchao Meng ◽  
Jiucheng Xu ◽  
Shiguang Zhang
Keyword(s):  
Image Segmentation ◽  
Level Set ◽  
Energy Functional ◽  
External Energy ◽  
Regularization Term ◽  
Level Set Function ◽  
New Energy ◽  
Segmentation Approach ◽  
Set Function ◽  
Distance Regularization

When the level set algorithm is used to segment an image, the level set function must be initialized periodically to ensure that it remains a signed distance function (SDF). To avoid this defect, an improved regularized level set method-based image segmentation approach is presented. First, a new potential function is defined and introduced to reconstruct a new distance regularization term to solve this issue of periodically initializing the level set function. Second, by combining the distance regularization term with the internal and external energy terms, a new energy functional is developed. Then, the process of the new energy functional evolution is derived by using the calculus of variations and the steepest descent approach, and a partial differential equation is designed. Finally, an improved regularized level set-based image segmentation (IRLS-IS) method is proposed. Numerical experimental results demonstrate that the IRLS-IS method is not only effective and robust to segment noise and intensity-inhomogeneous images but can also analyze complex medical images well.

scholarly journals Progress in calculating the potential energy surface of H 3 +

2012 ◽  
Vol 370 (1978) ◽  
pp. 5001-5013 ◽  
Author(s):  
Ludwik Adamowicz ◽  
Michele Pavanello
Keyword(s):  
Potential Energy ◽  
Potential Energy Surface ◽  
Energy Surface ◽  
Molecular Geometry ◽  
Computational Procedure ◽  
Energy Functional ◽  
Basis Functions ◽  
Vibrational States ◽  
Energy Gradient ◽  
Explicitly Correlated

The most accurate electronic structure calculations are performed using wave function expansions in terms of basis functions explicitly dependent on the inter-electron distances. In our recent work, we use such basis functions to calculate a highly accurate potential energy surface (PES) for the H ion. The functions are explicitly correlated Gaussians, which include inter-electron distances in the exponent. Key to obtaining the high accuracy in the calculations has been the use of the analytical energy gradient determined with respect to the Gaussian exponential parameters in the minimization of the Rayleigh–Ritz variational energy functional. The effective elimination of linear dependences between the basis functions and the automatic adjustment of the positions of the Gaussian centres to the changing molecular geometry of the system are the keys to the success of the computational procedure. After adiabatic and relativistic corrections are added to the PES and with an effective accounting of the non-adiabatic effects in the calculation of the rotational/vibrational states, the experimental H rovibrational spectrum is reproduced at the 0.1 cm −1 accuracy level up to 16 600 cm −1 above the ground state.

scholarly journals On pendent drops in a capillary tube

1983 ◽  
Vol 28 (3) ◽  
pp. 343-354 ◽  
Author(s):  
G. Huisken
Keyword(s):  
Capillary Tube ◽  
Energy Functional ◽  
Reasonable Assumption ◽  
Local Minima ◽  
Pendent Drop

The energy functional for a pendent drop in a capillary tube is neither convex nor bounded from below. We obtain local minima of the energy by making the physically reasonable assumption that the gravitation or the prescribed volume of the drop is small.

scholarly journals Topological Information Data Analysis: Poincare-Shannon Machine and Statistical Physic of Finite Heterogeneous Systems

2018 ◽  
Author(s):  
Pierre Baudot ◽  
Monica Tapia ◽  
Jean-Marc Goaillard
Keyword(s):  
Statistical Physic ◽  
Free Energy ◽  
Statistical Tests ◽  
Arbitrary Dimension ◽  
Minimum Free Energy ◽  
Energy Functional ◽  
Information Storage ◽  
Local Minima ◽  
Energy Principle ◽  
Data Set

This paper establishes methods that quantify the structure of statistical interactions within a given data set using the characterization of information theory in cohomology by finite methods, and provides their expression in terms of statistical physic and machine learning. Following [1&ndash;3], we show directly that k multivariate mutual-informations (Ik) are k-coboundaries. The k-cocycles are given by&nbsp;Ik = 0, which generalize statistical independence to arbitrary dimension k. The topological approach allows to investigate Shannon&rsquo;s information in the multivariate case without the assumptions of independent identically distributed variables. We develop the computationally tractable subcase of simplicial information cohomology represented by entropy Hk and information&nbsp;Ik landscapes. The I1 component defines a self-internal energy functional Uk, and (&minus;1)k Ik,k&ge;2 components define the contribution to a free energy functional Gk of the k-body interactions. The set of information paths in simplicial structures is in bijection with the symmetric group and random processes, provides a topological expression of the 2nd law and points toward a discrete Noether theorem (1st law). The local minima of free-energy, related to conditional information negativity and the non-Shannonian cone of Yeung [4], characterize a minimum free energy complex. This complex formalizes the minimum free-energy principle in topology, provides a definition of a complex system, and characterizes a multiplicity of local minima that quantifies the diversity observed in biology. Finite data size effects and estimation bias severely constrain the effective computation of the information topology on data, and we provide simple statistical tests for the undersampling bias and for the k-dependences following [5]. We give an example of application of these methods to genetic expression and cell-type classification. The maximal positive&nbsp;Ik identifies the variables that co-vary the most in the population, whereas the minimal negative&nbsp;Ik identifies clusters and the variables that differentiate-segregate the most. The methods unravel biologically relevant I10 with a sample size of 41. It establishes generic methods to quantify the epigenetic information storage and a unified epigenetic unsupervised learning formalism.

scholarly journals Encoding strongly-correlated many-boson wavefunctions on a photonic quantum computer: application to the attractive Bose-Hubbard model

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 572
Author(s):  
Saad Yalouz ◽  
Bruno Senjean ◽  
Filippo Miatto ◽  
Vedran Dunjko
Keyword(s):  
Hubbard Model ◽  
Quantum Computer ◽  
Quantum Algorithms ◽  
Experimental System ◽  
Quantum Circuit ◽  
Continuous Variable ◽  
Computer Application ◽  
Strongly Correlated ◽  
Many Body ◽  
Boson Systems

Variational quantum algorithms (VQA) are considered as some of the most promising methods to determine the properties of complex strongly correlated quantum many-body systems, especially from the perspective of devices available in the near term. In this context, the development of efficient quantum circuit ansatze to encode a many-body wavefunction is one of the keys for the success of a VQA. Great efforts have been invested to study the potential of current quantum devices to encode the eigenstates of fermionic systems, but little is known about the encoding of bosonic systems. In this work, we investigate the encoding of the ground state of the (simple but rich) attractive Bose-Hubbard model using a Continuous-Variable (CV) photonic-based quantum circuit. We introduce two different ansatz architectures and demonstrate that the proposed continuous variable quantum circuits can efficiently encode (with a fidelity higher than 99%) the strongly correlated many-boson wavefunction with just a few layers, in all many-body regimes and for different number of bosons and initial states. Beyond the study of the suitability of the ansatz to approximate the ground states of many-boson systems, we also perform initial evaluations of the use of the ansatz in a variational quantum eigensolver algorithm to find it through energy minimization. To this end we also introduce a scheme to measure the Hamiltonian energy in an experimental system, and study the effect of sampling noise.

EFFICIENT ACTIVE CONTOUR MODEL FOR MULTIPHASE SEGMENTATION WITH APPLICATION TO BRAIN MR IMAGES

2013 ◽  
Vol 27 (01) ◽  
pp. 1355001 ◽  
Author(s):  
YUNYUN YANG ◽  
YI ZHAO ◽  
BOYING WU
Keyword(s):  
Active Contour ◽  
Active Contour Model ◽  
Energy Functional ◽  
Energy Model ◽  
Mr Images ◽  
Split Bregman Method ◽  
Split Bregman ◽  
Contour Model ◽  
New Energy ◽  
Brain Mr Images

In this paper, we propose an efficient active contour model for multiphase image segmentation in a variational level set formulation. By incorporating the globally convex segmentation idea and the split Bregman method into the multiphase formulation of the local and global intensity fitting energy model, our new model improved the original local and global intensity fitting energy model in the following aspects. First, we propose a new energy functional using the globally convex segmentation method to guarantee fast convergence. Second, we incorporate information from the edge into the energy functional by using a non-negative edge detector function to detect boundaries more easily. Third, instead of a constant value to control the influence of the local and global intensity fitting terms, we use a weight function varying with the locations of the image to balance the weights between the local and the global fitting terms dynamically. Lastly, the special structure of our energy functional enables us to apply the split Bregman method to minimize the energy much more efficiently. We have applied our model to synthetic images and real brain MR images with promising results. Experimental results demonstrate the efficiency and superiority of our model.

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