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Amplified and quantum based brain storm optimization algorithms for real power loss reduction
2021
International Journal of Applied Power Engineering (IJAPE)
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A node is arbitrarily chosen from the graph as the preliminary point to form a Hamiltonian cycle. ...
Monte Carlo simulation method is used, to measure the position for each idea from the quantum state to the traditional one. ...
Amplified and quantum based brain storm optimization algorithms for real power… (Kanagasabai Lenin)Step 6: new-fangled individuals are engendered Calculate the Hamiltonian cycle C and its extent Lt by ...
doi:10.11591/ijape.v10.i1.pp21-25
fatcat:wu4d6anjznhxlgj4gk7brfejty
Book Review: Critical point theory and submanifold geometry
1992
Bulletin of the American Mathematical Society
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Various new ideas, for example, the Mountain Pass Lemma and the Morse-Ekeland Index, are also described. ...
study of nonlinear Hamiltonian systems; while for Critical Point Theory the ideas described seem relatively unmotivated instead of coming from a coherent geometric picture of mechanics. ...
doi:10.1090/s0273-0979-1992-00255-0
fatcat:4uosigyfhrbzxd3qm6orriekma
Addressing hard classical problems with Adiabatically Assisted Variational Quantum Eigensolvers
[article]
2018
arXiv
pre-print
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The rational for this new algorithm is to circumvent the problem of facing very small gradients in the classical optimization piece of a VQE, while being able to run in current hardware efficient devices ...
We present a hybrid classical-quantum algorithm to solve optimization problems in current quantum computers, whose basic idea is to assist variational quantum eigensolvers (VQE) with adiabatic change of ...
This is rapidly corrected by the new optimization, which produces a new ground state for H(s i+1 ). The final ground state encodes the solution to the target problem. ...
arXiv:1806.02287v1
fatcat:qf6etcbxzzbglb34q5fvzhjhgy
Structure-preserving Runge-Kutta methods for stochastic Hamiltonian equations with additive noise
2013
Numerical Algorithms
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Here we extend these ideas to stochastic Hamiltonian problems with additive noise and show that there are classes of Runge-Kutta methods that are very effective in preserving the expectation of the Hamiltonian ...
Acknowledgements The authors would like to thank Luigi Brugnano and Grant Lythe for various discussions on issues related to this submission. ...
Burrage and Burrage [7] then propose a new formulation of a Runge-Kutta method that involves using s + 1 samples of a Wiener process per step. This idea is in line with the ideas of Brugnano et al. ...
doi:10.1007/s11075-013-9796-6
fatcat:pd6sgm2qqrc4laqwbl3c7cnsqy
Experimental Demonstrations of Native Implementation of Boolean Logic Hamiltonian in a Superconducting Quantum Annealer
[article]
2021
arXiv
pre-print
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As a superconducting integrated circuit, a problem Hamiltonian whose set of ground states is consistent with a given truth table is implemented for quantum annealing with no redundant qubits. ...
A proof-of-concept demonstration of a hybrid computing architecture for domain-specific quantum computing is described. ...
In cases where the problem Hamiltonian does not fit the fixed topology, we need to construct a new problem Hamiltonian satisfying two conditions: 1) interactions in the new problem Hamiltonian are consistent ...
arXiv:2106.08681v2
fatcat:rlalzlztzbg7potr5a52dy2lpe
A SPECIAL CASE OF LONGEST PATH PROBLEM
2019
Figshare
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We have that Hamiltonian Path can be reduced to a special case of Longest Path Problem. ...
Definition and claim Idea: Reduction from Hamiltonian path. ...
Try to think how many vertices should be added to a special instance G = (V, E) of longest path problem so that if there is a path of length at least |V| 4 in G then there is a Hamiltonian path in G. ...
doi:10.6084/m9.figshare.7750937.v1
fatcat:j264rmpl5nb2vdwvoao2yhmf7y
Gravity, time and varying constants
[article]
2018
arXiv
pre-print
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There are theories which implement the idea that the constants of nature may be "time dependent." These introduce new fields representing "evolving constants," in addition to physical fields. ...
We illustrate the idea in scalar field cosmology with spatial volume as a global clock, and compute the time dependence of the scalar mass and self-interaction coupling constants. ...
This involved a global choice of time, an expansion of a square root Hamiltonian, and a canonical transformation. Unlike other approaches, no new fields, couplings or actions were necessary. ...
arXiv:1807.09818v1
fatcat:oos77yzc75bwjig4j4ezj3jpzu
The Use of the Monte Carlo Hamiltonian
[article]
2003
arXiv
pre-print
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Here we discuss a recently proposed alternative Hamiltonian lattice formulation - the Monte Carlo Hamiltonian. ...
We address properties of the MC Hamiltonian, like a finite temperature window, and scaling properties. ...
The problem with such procedure is that a cut-off in Fock space particle number and in high momentum is uncontrolled. A much better idea is the renormalisation group idea by Kadanoff and Wilson. ...
arXiv:hep-lat/0301012v1
fatcat:u7dxg4y5znez5d3tgynhor7txi
A Direct Shooting Method is Equivalent to an Indirect Method
[article]
2020
arXiv
pre-print
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A mathematical explanation is provided for the successes and failures of such patched nonlinear programming methods. ...
We also show that a theoretical equivalence does not necessarily translate to practical equivalence if the parameterized optimal control problem is simply patched to a nonlinear programming solver. ...
Recently, these ideas have reemerged as a new field for designing and analyzing optimization algorithms [2, 15, 16, 17, 18] . ...
arXiv:2003.02418v2
fatcat:xlznfyeybjdkjh5yrq3cijqppq
Numerical Solution of ODEs and the Columbus' Egg: Three Simple Ideas for Three Difficult Problems
[article]
2010
arXiv
pre-print
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Often, the insistence in following a path already traced in the continuous setting, has caused waste of time and efforts, whereas new specific tools have solved the problems both more easily and elegantly ...
problems, are often insufficient to handle the discrete case, and new specific tools are needed. ...
The new idea was to design methods working for finite values of h, at least for dissipative problems. This led to the already mentioned definition of A-stability. ...
arXiv:1008.4789v4
fatcat:ugw7olxtcvcyrkw2gtm5ddcth4
Experimental Demonstrations of Native Imple-mentation of Boolean Logic Hamiltonian in a Superconducting Quantum Annealer
2021
IEEE Transactions on Quantum Engineering
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Inomata for his dedicated support in the experiments, and Y. Araga and K. Kikuchi for their heartfelt cooperation. ...
In cases where the problem Hamiltonian does not fit the fixed topology, we need to construct a new problem Hamiltonian satisfying two conditions: 1) interactions in the new problem Hamiltonian are consistent ...
The first problem is that performing quantum annealing on the original and the new problem Hamiltonian can have drastically different efficiencies. ...
doi:10.1109/tqe.2021.3106776
fatcat:7nrhjg2yvfdljdmavnekjx23zu
Page 1930 of Mathematical Reviews Vol. , Issue 97C
[page]
1997
Mathematical Reviews
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Summary: “We present a new system for image processing based on the topological theory of manifolds. ...
These new concepts and algorithm are promising in binary image extraction. In this paper, the color classification for a color geographic map image is considered.” ...
The Density Matrix Renormalization Group
[chapter]
2013
Springer Series in Solid-State Sciences
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From its original formulation in a condensed matter context, it has been adapted to study problems in various fields, such as nuclear physics and quantum chemistry, becoming one of the dominant numerical ...
In this chapter, we shall cover many technical aspects of the DMRG, from a "traditional", or "conventional" perspective, describing the theoretical fundamentation, as well as the details of the algorithm ...
with m largest eigenvalues to build the new blocks for the next step (d) (a) (b) (c) (d) • Build all the operator matrices for a single-site Hamiltonian, and the operators involved in the interactions ...
doi:10.1007/978-3-642-35106-8_2
fatcat:xou5bl4hhngkbboio4zjfmn35u
Unitary transformations depending on a small parameter
2011
Proceedings of the Royal Society A
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The original Hamiltonian is converted into a solvable one by a transformation obtained through a Magnus expansion. This ensures unitarity at every order in a small parameter. ...
We formulate a unitary perturbation theory for quantum mechanics inspired by the Lie-Deprit formulation of canonical transformations. ...
Then the idea is to look for a unitary transformation T (e) (or 'canonical transformation' in the language of matrix mechanics) such that the new Hamiltonian K = T † HT is diagonal. ...
doi:10.1098/rspa.2011.0388
fatcat:kle3x7lubfauhgi6xm32lasjja
Page 3236 of Mathematical Reviews Vol. , Issue 93f
[page]
1993
Mathematical Reviews
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This paper provides a new reduction theorem for a special class of Poisson manifolds called bi-Hamiltonian manifolds. They are manifolds equipped with a pair of compatible Poisson brackets. ...
Ideas like this show great promise for also understanding the sense in which modulation equations are Hamiltonian (see, for example, a paper by N. Ercolani et al. [Duke Math. ...
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