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Journal articles on the topic 'Hamiltonian problems'

Author: Grafiati

Published: 10 March 2023

Last updated: 19 July 2025

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1

Bravyi, S., D. P. DiVincenzo, R. Oliveira, and B. M. Terhal. "The complexity of stoquastic local Hamiltonian problems." Quantum Information and Computation 8, no. 5 (2008): 361–85. http://dx.doi.org/10.26421/qic8.5-1.

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We study the complexity of the Local Hamiltonian Problem (denoted as LH-MIN) in the special case when a Hamiltonian obeys the condition that all off-diagonal matrix elements in the standard basis are real and non-positive. We will call such Hamiltonians, which are common in the natural world, stoquastic. An equivalent characterization of stoquastic Hamiltonians is that they have an entry-wise non-negative Gibbs density matrix for any temperature. We prove that LH-MIN for stoquastic Hamiltonians belongs to the complexity class \AM{}--- a probabilistic version of \NP{} with two rounds of communi

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2

Elyseeva, Julia. "The Oscillation Numbers and the Abramov Method of Spectral Counting for Linear Hamiltonian Systems." EPJ Web of Conferences 248 (2021): 01002. http://dx.doi.org/10.1051/epjconf/202124801002.

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In this paper we consider linear Hamiltonian differential systems which depend in general nonlinearly on the spectral parameter and with Dirichlet boundary conditions. For the Hamiltonian problems we do not assume any controllability and strict normality assumptions which guarantee that the classical eigenvalues of the problems are isolated. We also omit the Legendre condition for their Hamiltonians. We show that the Abramov method of spectral counting can be modified for the more general case of finite eigenvalues of the Hamiltonian problems and then the constructive ideas of the Abramov meth

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3

Pannell, William H. "The intersection between dual potential and sl(2) algebraic spectral problems." International Journal of Modern Physics A 35, no. 32 (2020): 2050208. http://dx.doi.org/10.1142/s0217751x20502085.

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The relation between certain Hamiltonians, known as dual, or partner Hamiltonians, under the transformation [Formula: see text] has long been used as a method of simplifying spectral problems in quantum mechanics. This paper seeks to examine this further by expressing such Hamiltonians in terms of the generators of sl(2) algebra, which provides another method of solving spectral problems. It appears that doing so greatly restricts the set of allowable potentials, with the only nontrivial potentials allowed being the Coulomb [Formula: see text] potential and the harmonic oscillator [Formula: se

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4

Iserles, A., J. M. Sanz-Serna, and M. P. Calvo. "Numerical Hamiltonian Problems." Mathematics of Computation 64, no. 211 (1995): 1346. http://dx.doi.org/10.2307/2153506.

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5

Masanes, Ll, G. Vidal, and J. I. Latorre. "Time--optimal Hamiltonian simulation and gate synthesis using homogeneous local unitaries." Quantum Information and Computation 2, no. 4 (2002): 285–96. http://dx.doi.org/10.26421/qic2.4-2.

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Motivated by experimental limitations commonly met in the design of solid state quantum computers, we study the problems of non--local Hamiltonian simulation and non--local gate synthesis when only {\em homogeneous} local unitaries are performed in order to tailor the available interaction. Homogeneous (i.e. identical for all subsystems) local manipulation implies a more refined classification of interaction Hamiltonians than the inhomogeneous case, as well as the loss of universality in Hamiltonian simulation. For the case of symmetric two--qubit interactions, we provide time--optimal protoco

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6

Sattath, Or, Siddhardh C. Morampudi, Chris R. Laumann, and Roderich Moessner. "When a local Hamiltonian must be frustration-free." Proceedings of the National Academy of Sciences 113, no. 23 (2016): 6433–37. http://dx.doi.org/10.1073/pnas.1519833113.

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A broad range of quantum optimization problems can be phrased as the question of whether a specific system has a ground state at zero energy, i.e., whether its Hamiltonian is frustration-free. Frustration-free Hamiltonians, in turn, play a central role for constructing and understanding new phases of matter in quantum many-body physics. Unfortunately, determining whether this is the case is known to be a complexity-theoretically intractable problem. This makes it highly desirable to search for efficient heuristics and algorithms to, at least, partially answer this question. Here we prove a gen

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7

Bassour, Mustapha. "Hamiltonian Polynomial Eigenvalue Problems." Journal of Applied Mathematics and Physics 08, no. 04 (2020): 609–19. http://dx.doi.org/10.4236/jamp.2020.84047.

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8

Zhao, Qi, and Xiao Yuan. "Exploiting anticommutation in Hamiltonian simulation." Quantum 5 (August 31, 2021): 534. http://dx.doi.org/10.22331/q-2021-08-31-534.

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Quantum computing can efficiently simulate Hamiltonian dynamics of many-body quantum physics, a task that is generally intractable with classical computers. The hardness lies at the ubiquitous anti-commutative relations of quantum operators, in corresponding with the notorious negative sign problem in classical simulation. Intuitively, Hamiltonians with more commutative terms are also easier to simulate on a quantum computer, and anti-commutative relations generally cause more errors, such as in the product formula method. Here, we theoretically explore the role of anti-commutative relation in

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9

Sanz-Serna, J. M. "Symplectic integrators for Hamiltonian problems: an overview." Acta Numerica 1 (January 1992): 243–86. http://dx.doi.org/10.1017/s0962492900002282.

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In the sciences, situations where dissipation is not significant may invariably be modelled by Hamiltonian systems of ordinary, or partial, differential equations. Symplectic integrators are numerical methods specifically aimed at advancing in time the solution of Hamiltonian systems. Roughly speaking, ‘symplecticness’ is a characteristic property possessed by the solutions of Hamiltonian problems. A numerical method is called symplectic if, when applied to Hamiltonian problems, it generates numerical solutions which inherit the property of symplecticness.

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10

Amodio, P., F. Iavernaro, and D. Trigiante. "Symmetric schemes and Hamiltonian perturbations of linear Hamiltonian problems." Numerical Linear Algebra with Applications 12, no. 2-3 (2005): 171–79. http://dx.doi.org/10.1002/nla.408.

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11

Lynch, Mark A. M. "Creating recreational Hamiltonian cycle problems." Mathematical Gazette 88, no. 512 (2004): 215–18. http://dx.doi.org/10.1017/s0025557200174935.

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In this paper graphs that contain unique Hamiltonian cycles are introduced. The graphs are of arbitrary size and dense in the sense that their average vertex degree is greater than half the number of vertices that make up the graph. The graphs can be used to generate challenging puzzles. The problem is particularly challenging when the graph is large and the ‘method’ of solution is unknown to the solver.

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12

Bohner, M. "Discrete linear Hamiltonian eigenvalue problems." Computers & Mathematics with Applications 36, no. 10-12 (1998): 179–92. http://dx.doi.org/10.1016/s0898-1221(98)80019-9.

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13

BERA, P. K., M. M. PANJA, and B. TALUKDAR. "ISOSPECTRAL INTERACTIONS FOR THREE-BODY PROBLEMS ON THE LINE." Modern Physics Letters A 11, no. 26 (1996): 2129–38. http://dx.doi.org/10.1142/s0217732396002113.

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The algebraic methods of supersymmetric quantum mechanics are used to construct isospectral Hamiltonians for the three-particle Calogero problem [F. Calogero, J. Math. Phys. 10, 2191 (1969)]. The similarity and points of contrast of the present study with the corresponding two-body problem are discussed. It is found that the family of isospectral interactions is determined essentially by the angular part of the potential in the basic Hamiltonian. A case study is presented to investigate the nature of the individual member in the family.

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14

Stogiannos, Evangelos, Christos Papalitsas, and Theodore Andronikos. "Experimental Analysis of Quantum Annealers and Hybrid Solvers Using Benchmark Optimization Problems." Mathematics 10, no. 8 (2022): 1294. http://dx.doi.org/10.3390/math10081294.

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This paper studies the Hamiltonian cycle problem (HCP) and the traveling salesman problem (TSP) on D-Wave quantum systems. Motivated by the fact that most libraries present their benchmark instances in terms of adjacency matrices, we develop a novel matrix formulation for the HCP and TSP Hamiltonians, which enables the seamless and automatic integration of benchmark instances in quantum platforms. We also present a thorough mathematical analysis of the precise number of constraints required to express the HCP and TSP Hamiltonians. This analysis explains quantitatively why, almost always, runni

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15

ANDRIANOV, A. A., M. V. IOFFE, F. CANNATA, and J. P. DEDONDER. "SUSY QUANTUM MECHANICS WITH COMPLEX SUPERPOTENTIALS AND REAL ENERGY SPECTRA." International Journal of Modern Physics A 14, no. 17 (1999): 2675–88. http://dx.doi.org/10.1142/s0217751x99001342.

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We extend the standard intertwining relations used in supersymmetrical (SUSY) quantum mechanics which involve real superpotentials to complex superpotentials. This allows us to deal with a large class of non-Hermitian Hamiltonians and to study in general the isospectrality between complex potentials. In very specific cases we can construct in a natural way "quasicomplex" potentials which we define as complex potentials having a global property so as to lead to a Hamiltonian with real spectrum. We also obtained a class of complex transparent potentials whose Hamiltonian can be intertwined to a

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16

Udriste, Constantin, and Ionel Tevy. "Properties of Hamiltonian in free final multitime problems." Studia Universitatis Babes-Bolyai Matematica 66, no. 1 (2021): 223–40. http://dx.doi.org/10.24193/subbmath.2021.1.18.

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"In single-time autonomous optimal control problems, the Hamiltonian is constant on optimal evolution. In addition, if the final time is free, the optimal Hamiltonian vanishes on the hole interval of evolution. The purpose of this paper is to extend some of these results to the case of multitime optimal control. The original results include: anti-trace problem, weak and strong multitime maximum principles, multitime-invariant systems and change rate of Hamiltonian, the variational derivative of volume integral, necessary conditions for a free final multitime expressed with the Hamiltonian tens

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17

Wu, Xin, Ying Wang, Wei Sun, Fu-Yao Liu, and Wen-Biao Han. "Explicit Symplectic Methods in Black Hole Spacetimes." Astrophysical Journal 940, no. 2 (2022): 166. http://dx.doi.org/10.3847/1538-4357/ac9c5d.

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Abstract Many Hamiltonian problems in the solar system are separable into two analytically solvable parts, and thus serve as a great chance to develop and apply explicit symplectic integrators based on operator splitting and composing. However, such constructions are not in general available for curved spacetimes in general relativity and modified theories of gravity because these curved spacetimes correspond to nonseparable Hamiltonians without the two-part splits. Recently, several black hole spacetimes such as the Schwarzschild black hole were found to allow for the construction of explicit

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18

Fuqara, Anoud K., Amer D. Al-Oqali, and Khaled I. Nawafleh. "Hamilton-Jacobi Equation of Time Dependent Hamiltonians." Oriental Journal of Physical Sciences 5, no. 1-2 (2020): 09–15. http://dx.doi.org/10.13005/ojps05.01-02.04.

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In this work, we apply the geometric Hamilton-Jacobi theory to obtain solution of Hamiltonian systems in classical mechanics that are either compatible with two structures: the first structure plays a central role in the theory of time- dependent Hamiltonians, whilst the second is used to treat classical Hamiltonians including dissipation terms. It is proved that the generalization of problems from the calculus of variation methods in the nonstationary case can be obtained naturally in Hamilton-Jacobi formalism.

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19

Corli, Sebastiano, Lorenzo Moro, Davide E. Galli, and Enrico Prati. "Casting Rubik’s Group into a Unitary Representation for Reinforcement Learning." Journal of Physics: Conference Series 2533, no. 1 (2023): 012006. http://dx.doi.org/10.1088/1742-6596/2533/1/012006.

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Abstract Rubik’s Cube is one of the most famous combinatorial puzzles involving nearly 4.3 × 1019 possible configurations. However, only a single configuration matches the solved one. Its mathematical description is expressed by the Rubik’s group, whose elements define how its layers rotate. We develop a unitary representation of the Rubik’s group and a quantum formalism to describe the Cube based on its geometrical constraints. Using single particle quantum states, we describe the cubies as bosons for corners and fermions for edges. By introducing a set of four Ising-like Hamiltonians, we man

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20

Jiang, Tsin-Fu. "Solving Time-Dependent Schödinger Equation for Some PT-Symmetric Quantum Mechanical Problems." Atoms 12, no. 9 (2024): 46. http://dx.doi.org/10.3390/atoms12090046.

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Using a high-precision code, we generate the eigenstates of a PT-symmetric Hamiltonian. We solve the time-dependent Schrödinger equation (TDSE) of the non-Hermitian system based on the eigenset. Since the formulation is relatively new and the observables are calculated differently than conventional quantum mechanics, we justify it with a paradigmatic case in Hermitian quantum mechanics. We present the harmonic generation spectra on some model PT-Hamiltonians driven by an electric pulse. We discuss the physical differences with the harmonic spectra of a pulse-driven atom.

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21

Kurzhanskii, A. B. "Hamiltonian Formalism in Team Control Problems." Differential Equations 55, no. 4 (2019): 532–40. http://dx.doi.org/10.1134/s0012266119040116.

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22

SANZ-SERNA, J. M., and M. P. CALVO. "SYMPLECTIC NUMERICAL METHODS FOR HAMILTONIAN PROBLEMS." International Journal of Modern Physics C 04, no. 02 (1993): 385–92. http://dx.doi.org/10.1142/s0129183193000410.

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We consider symplectic methods for the numerical integration of Hamiltonian problems, i.e. methods that preserve the Poincaré integral invariants. Examples of symplectic methods are given and numerical experiments are reported.

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23

Cubitt, Toby, and Ashley Montanaro. "Complexity Classification of Local Hamiltonian Problems." SIAM Journal on Computing 45, no. 2 (2016): 268–316. http://dx.doi.org/10.1137/140998287.

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24

Subbotina, Nina N. "Hamiltonian Systems in Dynamic Reconstruction Problems." IFAC-PapersOnLine 51, no. 32 (2018): 136–40. http://dx.doi.org/10.1016/j.ifacol.2018.11.368.

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25

Watkinson, L. R., A. S. Lawless, N. K. Nichols, and I. Roulstone. "Variational data assimilation for Hamiltonian problems." International Journal for Numerical Methods in Fluids 47, no. 10-11 (2005): 1361–67. http://dx.doi.org/10.1002/fld.844.

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26

BECKWITH, A. W. "AN OPEN QUESTION: ARE TOPOLOGICAL ARGUMENTS HELPFUL IN SETTING INITIAL CONDITIONS FOR TRANSPORT PROBLEMS IN CONDENSED MATTER PHYSICS?" Modern Physics Letters B 20, no. 05 (2006): 233–43. http://dx.doi.org/10.1142/s0217984906010585.

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The tunneling Hamiltonian is a proven method to treat particle tunneling between different states represented as wavefunctions in many-body physics. Our problem is how to apply a wave functionals formulation of tunneling Hamiltonians to a driven sine-Gordon system. We apply a generalization of the tunneling Hamiltonian to charge density wave (CDW) transport problems in which we consider tunneling between states that are wave functionals of a scalar quantum field ϕ. We present derived I–E curves that match Zenier curves used to fit data experimentally with wave functionals congruent with the fa

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27

Li, Xiao Chuan, and Jin Shuang Zhang. "Hamiltonian Duality Equation on Three-Dimensional Problems of Magnetoelectroelastic Solids." Applied Mechanics and Materials 268-270 (December 2012): 1099–104. http://dx.doi.org/10.4028/www.scientific.net/amm.268-270.1099.

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Hamiltonian system used in dynamics is introduced to formulate the three-dimensional problems of the transversely isotropic magnetoelectroelastic solids. The Hamiltonian dual equations in magnetoelectroelastic solids are developed directly from the modified Hellinger-Reissner variational principle derived from generalized Hellinger-Ressner variational principle with two classes of variables. These variables not only include such origin variables as displaces, electric potential and magnetic potential, but also include such their dual variables as lengthways stress, electric displacement and ma

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28

Amodio, Pierluigi, Luigi Brugnano, and Felice Iavernaro. "Continuous-Stage Runge–Kutta Approximation to Differential Problems." Axioms 11, no. 5 (2022): 192. http://dx.doi.org/10.3390/axioms11050192.

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In recent years, the efficient numerical solution of Hamiltonian problems has led to the definition of a class of energy-conserving Runge–Kutta methods named Hamiltonian Boundary Value Methods (HBVMs). Such methods admit an interesting interpretation in terms of continuous-stage Runge–Kutta methods. In this review paper, we recall this aspect and extend it to higher-order differential problems.

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29

Zhang, Hairui, and Yongxin Yuan. "Generalized inverse eigenvalue problems for Hermitian and J-Hamiltonian/skew-Hamiltonian matrices." Applied Mathematics and Computation 361 (November 2019): 609–16. http://dx.doi.org/10.1016/j.amc.2019.06.004.

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30

Petrongolo, Carlo. "Two Quantum Triatomic Hamiltonians: Applications to Non-Adiabatic Effects in NO2 Spectroscopy and in Kr + OH(A2Σ+) Electronic Quenching". Symmetry 17, № 3 (2025): 346. https://doi.org/10.3390/sym17030346.

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This review discusses two triatomic Hamiltonians and their applications to some non-adiabatic spectroscopic and collision problems. Carter and Handy in 1984 presented the first Hamiltonian in bond lengths–bond angle coordinates, that is here applied for studying the NO2 spectroscopy: vibronic states, internal dynamics, and interaction with the radiation due to the X˜2A′(A1)−A˜2A′(B2) conical intersection. The second Hamiltonian was reported by Tennyson and Sutcliffe in 1983 in Jacobi coordinates and is here employed in the study of the Kr + OH(A2Σ+) electronic quenching due to conical intersec

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31

SHIFMAN, M. A. "NEW FINDINGS IN QUANTUM MECHANICS (PARTIAL ALGEBRAIZATION OF THE SPECTRAL PROBLEM)." International Journal of Modern Physics A 04, no. 12 (1989): 2897–952. http://dx.doi.org/10.1142/s0217751x89001151.

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We discuss a new class of spectral problems discovered recently which occupies an intermediate position between the exactly-solvable problems (like the famous harmonic oscillator) and all others. The problems belonging to this class are distinguished by the fact that an (arbitrary) part of the eigenvalues and eigenfunctions can be found algebraically, but not the whole spectrum. The reason explaining the existence of the quasi-exactly-solvable problems is a hidden dynamical symmetry present in the Hamiltonian. For one-dimensional motion, this hidden symmetry is SU(2). The simplest one-dimensio

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32

Paulraja, P., and Kumar Sampath. "On hamiltonian decompositions of tensor products of graphs." Applicable Analysis and Discrete Mathematics 13, no. 1 (2019): 178–202. http://dx.doi.org/10.2298/aadm170803003p.

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Finding a hamiltonian decomposition of G is one of the challenging problems in graph theory. We do not know for what classes of graphs G and H, their tensor product G x H is hamiltonian decomposable. In this paper, we have proved that, if G is a hamiltonian decomposable circulant graph with certain properties and H is a hamiltonian decomposable multigraph, then G x H is hamiltonian decomposable. In particular, tensor products of certain sparse hamiltonian decomposable circulant graphs are hamiltonian decomposable.

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33

Zhang, Lina, Xin Wu, and Enwei Liang. "Adjustment of Force–Gradient Operator in Symplectic Methods." Mathematics 9, no. 21 (2021): 2718. http://dx.doi.org/10.3390/math9212718.

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Many force–gradient explicit symplectic integration algorithms have been designed for the Hamiltonian H=T(p)+V(q) with kinetic energy T(p)=p2/2 in the existing references. When a force–gradient operator is appropriately adjusted as a new operator, it is still suitable for a class of Hamiltonian problems H=K(p,q)+V(q) with integrable part K(p,q)=∑i=1n∑j=1naijpipj+∑i=1nbipi, where aij=aij(q) and bi=bi(q) are functions of coordinates q. The newly adjusted operator is not a force–gradient operator but is similar to the momentum-version operator associated to the potential V. The newly extended (or

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34

Chen, Shou-Ting, and Wen-Xiu Ma. "Higher-Order Matrix Spectral Problems and Their Integrable Hamiltonian Hierarchies." Mathematics 11, no. 8 (2023): 1794. http://dx.doi.org/10.3390/math11081794.

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Starting from a kind of higher-order matrix spectral problems, we generate integrable Hamiltonian hierarchies through the zero-curvature formulation. To guarantee the Liouville integrability of the obtained hierarchies, the trace identity is used to establish their Hamiltonian structures. Illuminating examples of coupled nonlinear Schrödinger equations and coupled modified Korteweg–de Vries equations are worked out.

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35

Fu, Jingli, Lijun Zhang, Shan Cao, Chun Xiang, and Weijia Zao. "A Symplectic Algorithm for Constrained Hamiltonian Systems." Axioms 11, no. 5 (2022): 217. http://dx.doi.org/10.3390/axioms11050217.

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In this paper, a symplectic algorithm is utilized to investigate constrained Hamiltonian systems. However, the symplectic method cannot be applied directly to the constrained Hamiltonian equations due to the non-canonicity. We firstly discuss the canonicalization method of the constrained Hamiltonian systems. The symplectic method is used to constrain Hamiltonian systems on the basis of the canonicalization, and then the numerical simulation of the system is carried out. An example is presented to illustrate the application of the results. By using the symplectic method of constrained Hamilton

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36

WOCJAN, PAWEL, and THOMAS BETH. "THE 2-LOCAL HAMILTONIAN PROBLEM ENCOMPASSES NP." International Journal of Quantum Information 01, no. 03 (2003): 349–57. http://dx.doi.org/10.1142/s021974990300022x.

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We show that the NP-complete problems max cut and independent set can be formulated as the 2-local Hamiltonian problem as defined by Kitaev. The 5-local Hamiltonian problem was the first problem to be shown to be complete for the quantum complexity class QMA — the quantum analog of NP. Subsequently, it was shown that 3-locality is already sufficient for QMA-completeness. It is still not known whether the 2-local Hamiltonian problem is QMA-complete. Therefore it is interesting to determine what problems can be reduced to the 2-local Hamiltonian problem. Kitaev showed that 3-SAT can be formulate

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37

Mielke, Alexander. "Weak-convergence methods for Hamiltonian multiscale problems." Discrete & Continuous Dynamical Systems - A 20, no. 1 (2008): 53–79. http://dx.doi.org/10.3934/dcds.2008.20.53.

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38

Chan, R. P. K., and A. Murua. "Extrapolation of symplectic methods for Hamiltonian problems." Applied Numerical Mathematics 34, no. 2-3 (2000): 189–205. http://dx.doi.org/10.1016/s0168-9274(99)00127-0.

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39

Buttà, Paolo, and Silvia Noschese. "Structured maximal perturbations for Hamiltonian eigenvalue problems." Journal of Computational and Applied Mathematics 272 (December 2014): 304–12. http://dx.doi.org/10.1016/j.cam.2013.04.031.

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40

VIGO-AGUIAR, JESÚS, T. E. SIMOS, and A. TOCINO. "AN ADAPTED SYMPLECTIC INTEGRATOR FOR HAMILTONIAN PROBLEMS." International Journal of Modern Physics C 12, no. 02 (2001): 225–34. http://dx.doi.org/10.1142/s0129183101001626.

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In this paper, a new procedure for deriving efficient symplectic integrators for Hamiltonian problems is introduced. This procedure is based on the combination of the trigonometric fitting technique and symplecticness conditions. Based on this procedure, a simple modified Runge–Kutta–Nyström second algebraic order trigonometrically fitted method is developed. We present explicity the symplecticity conditions for the new modified Runge–Kutta–Nyström method. Numerical results indicate that the new method is much more efficient than the "classical" symplectic Runge–Kutta–Nyström second algebraic

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41

Baryshnikov, Yu M. "Hamiltonian form of non-holonomic variational problems." Russian Mathematical Surveys 45, no. 1 (1990): 198–99. http://dx.doi.org/10.1070/rm1990v045n01abeh002307.

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42

Castrillón, López, and Masqué Muñoz. "Hamiltonian structure of gauge-invariant variational problems." Advances in Theoretical and Mathematical Physics 16, no. 1 (2012): 39–63. http://dx.doi.org/10.4310/atmp.2012.v16.n1.a2.

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43

Faibusovich, L. E. "Collective Hamiltonian method in optimal control problems." Cybernetics 25, no. 2 (1989): 230–37. http://dx.doi.org/10.1007/bf01070131.

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44

SZPAK, B., J. DUDEK, M. G. PORQUET, K. RYBAK, H. MOLIQUE, and B. FORNAL. "NUCLEAR MEAN-FIELD HAMILTONIANS AND FACTORS LIMITING THEIR SPECTROSCOPIC PREDICTIVE POWER: ILLUSTRATIONS." International Journal of Modern Physics E 19, no. 04 (2010): 665–71. http://dx.doi.org/10.1142/s0218301310015072.

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Determination of the mean-field Hamiltonian parameters can be seen as gathering information about all the single-particle states out of a very partial information on only a few experimentally known levels. This is exactly what the inverse problem in applied mathematics is about. We illustrate some of the related concepts in view of a preparation of the fully statistically significant parameter adjustment procedures. For this purpose we construct the exactly soluble inverse problems associated with the realistic and phenomenologically powerful nuclear Woods-Saxon Hamiltonian and we analyse a fe

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45

Novo, Leonardo, and Dominic Berry. "Improved Hamiltonian simulation via a truncated Taylor series and corrections." Quantum Information and Computation 17, no. 7&8 (2017): 623–35. http://dx.doi.org/10.26421/qic17.7-8-5.

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We describe an improved version of the quantum algorithm for Hamiltonian simulation based on the implementation of a truncated Taylor series of the evolution operator. The idea is to add an extra step to the previously known algorithm which implements an operator that corrects the weightings of the Taylor series. This way, the desired accuracy is achieved with an improvement in the overall complexity of the algorithm. This quantum simulation method is applicable to a wide range of Hamiltonians of interest, including to quantum chemistry problems.

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46

Qian, Jiang, and Roger C. E. Tan. "On some inverse eigenvalue problems for Hermitian and generalized Hamiltonian/skew-Hamiltonian matrices." Journal of Computational and Applied Mathematics 250 (October 2013): 28–38. http://dx.doi.org/10.1016/j.cam.2013.02.023.

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47

Evangelisti, S., J. P. Daudey, and J. P. Malrieu. "Qualitative intruder-state problems in effective Hamiltonian theory and their solution through intermediate Hamiltonians." Physical Review A 35, no. 12 (1987): 4930–41. http://dx.doi.org/10.1103/physreva.35.4930.

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48

Meissner, Leszek, and JarosłaW Gryniaków. "Effective Hamiltonian and Intermediate Hamiltonian Formulations of the Fock-Space Coupled-Cluster Method." Collection of Czechoslovak Chemical Communications 68, no. 1 (2003): 105–38. http://dx.doi.org/10.1135/cccc20030105.

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Various aspects of the effective Hamiltonian and intermediate Hamiltonian formulations are discussed in the context of the Fock-space coupled-cluster method. Problems that occur when single-reference methods of solving the Schrödinger equation need to be generalized to the multireference (MR) cases are pointed out. These problems make the generalization nontrivial, especially in the case of the most powerful coupled-cluster (CC) method. It is shown how some specific features of one of the basic MR-CC schemes, the Fock-space CC method, can be used to obtain a simple, yet very effective version

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49

Myo, Myo Hla. "A Study on Travelling Salesperson Problems." Bago University Research Journal Vol.9, No.1, no. 2019 (2019): 171–82. https://doi.org/10.5281/zenodo.3920547.

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In this paper, graph, simple graph, directed graph, simple path, cycle, simple cycle are presented. After that Euler’s cycle, Hamiltonian cycle are studied and travelling salesperson problems are solved.

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50

McLachlan, Robert I., and Christian Offen. "Hamiltonian Boundary Value Problems, Conformal Symplectic Symmetries, and Conjugate Loci." New Zealand Journal of Mathematics 48 (December 31, 2018): 83–99. http://dx.doi.org/10.53733/34.

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In this paper we continue our study of bifurcations of solutions of boundary-value problems for symplectic maps arising as Hamiltonian diffeomorphisms. These have been shown to be connected to catastrophe theory via generating functions and ordinary and reversal phase space symmetries have been considered. Here we present a convenient, coordinate free framework to analyse separated Lagrangian boundary value problems which include classical Dirichlet, Neumann and Robin boundary value problems. The framework is then used to prove the existence of obstructions arising from conformal symplectic sy

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