Related papers: A Algorithm for the Hamilton Circuit Problem
A bi-Hamiltonian formulation is proposed for triangular systems resulted by perturbations around solutions, from which infinitely many symmetries and conserved functionals of triangular systems can be explicitly constructed, provided that…
In this paper, we present experimental algorithms for solving the dualization problem. We present the results of extensive experimentation comparing the execution time of various algorithms.
Standandard Hamiltonian mechanics in its homogeneous formulation is applied to the study of discontinuities representing rapid changes of Hamiltonians. Different formulations of Hamiltonian mechanics are reviewed. An original representation…
A new non-associative algebra for the quantization of strongly interacting fields is proposed. The full set of quantum $(\pm)$associators for the product of three operators is offered. An algorithm for the calculation of some…
Plotting solution sets for particular equations may be complicated by the existence of turning points. Here we describe an algorithm which not only overcomes such problematic points, but does so in the most general of settings. Applications…
The Hamiltonian cycle problem in digraph is mapped into a matching cover bipartite graph. Based on this mapping, it is proved that determining existence a Hamiltonian cycle in graph is $O(n^3)$.
Before we proposed an algebraic technics for the Hamiltonian approach to the evolution systems of partial differential equations, including systems with constraints. Here we further develop this approach and present the defining system of…
We use the Riccati equation method with other ones to establish new oscillation and interval oscillation criteria for linear matrix Hamiltonian systems. We investigate the oscillation problem for linear matrix Hamiltonian systems in a new…
We study the efficiency of algorithms simulating a system evolving with Hamiltonian $H=\sum_{j=1}^m H_j$. We consider high order splitting methods that play a key role in quantum Hamiltonian simulation. We obtain upper bounds on the number…
An adiabatic quantum algorithm is essentially given by three elements: An initial Hamiltonian with known ground state, a problem Hamiltonian whose ground state corresponds to the solution of the given problem and an evolution schedule such…
We propose an algorithm for solving of the graph isomorphism problem. Also, we introduce the new class of graphs for which the graph isomorphism problem can be solved polynomially using the algorithm.
In this paper, we give a quantum algorithm which solves collision problem in an expected polynomial time. Especially, when the function is two-to-one, we present a quantum algorithm which can find a collision with certainty in a worst-case…
An observer-based Hamiltonian identification algorithm for quantum systems is proposed. For the 2-level case an exponential convergence result based on averaging arguments and some relevant transformations is provided. The convergence for…
Effective Hamiltonian methods are utilized to model the two-qubit cross-resonance gate for both the ideal two-qubit case and when higher levels are included. Analytic expressions are obtained in the qubit case and the higher-level model is…
The Riccati equation method is used to establish new oscillation criteria for linear matrix Hamiltonian systems. New approaches allow to extend and completed a result, obtained by S. Kumary and S. Umamaheswaram. The oscillation problem for…
We introduce a $2$-approximation algorithm for the minimum total covering number problem.
An algorithm is discussed for converting a class of recursive processes to a parallel system. It is argued that this algorithm can be superior to certain methods currently found in the literature for an important subset of problems. The…
In this paper we propose a special computational device which uses light rays for solving the Hamiltonian path problem on a directed graph. The device has a graph-like representation and the light is traversing it by following the routes…
Quantum algorithms are usually described as monolithic circuits, becoming large at modest input size. Near-term quantum architectures can only manage a small number of qubits. We develop an automated method to distribute quantum circuits…
We follow up on our previous works which presented a possible approach for deriving symplectic schemes for a certain class of highly oscillatory Hamiltonian systems. The approach considers the Hamilton-Jacobi form of the equations of…