The variational quantum eigensolver (VQE) typically optimizes parameters in a circuit to prepare eigenstates for system. Its application many problems may involve group of Hamiltonians, e.g., Hamiltonian molecule is function the nuclear configurations. In this paper we incorporate derivatives into VQE and develop some hybrid quantum-classical algorithms, which explore both wave-function spaces ...

According to Arnol’d and Sevryuk, a Hamiltonian vector field XH is said to be weakly reversible if φ∗XH = −XH for some germ φ of real analytic transformation with φ(0) = 0, while XH is reversible if additionally φ is an involution, i.e., φ = Id. One also says that α1, . . . , αn are non-resonant, if k · α ≡ k1α1 + · · · + knαn = 0 (3) for all integers kj with k = (k1, . . . , kn) = 0. The main ...

We prove a conjecture by N.N. Nekhoroshev about the long{time stability of elliptic equilibria of Hamiltonian systems, without any Diophantine condition on the frequencies. Higher order terms of the Hamiltonian are used to provide convexity. The singularity of the action{angle coordinates at the origin is overcome by working in cartesian coordinates.

A cycle double cover (CDC) of an undirected graph is a collection of the graph’s cycles such that every edge of the graph belongs to exactly two cycles. We describe a constructive method for generating all the cubic graphs that have a 6-CDC (a CDC in which every cycle has length 6). We also prove that all such graphs have a Hamiltonian cycle.

A method for the calculation of the temperature dependence of dielectric and piezoelectric responses, based on the use of a first-principles effective Hamiltonian, is described. Results are presented for the ferroelectric perovskite PbTiO 3. While the method includes only the soft-mode contributions to the responses, it is argued to give a good description of the divergences or near-divergences...

Barnette conjectured that each planar, bipartite, cubic, and 3-connected graph is hamiltonian. We prove that this conjecture is equivalent to the statement that there is a constant c > 0 such that each graph G of this class contains a path on at least c|V (G)| vertices.

A comparison of the eigenvalues of the Dirac and Laplace operator on the two-dimensional torus. Abstract We compare the eigenvalues of the Dirac and Laplace operator on a two-dimensional torus with respect to the trivial spin structure. In particular, we compute their variation up to order 4 upon deformation of the flat metric, study the corresponding Hamiltonian and discuss several families of...

In my previous paper [2] with I. M. Singer, B. Wong and Stephen Yau, I gave a lower estimate of the gap of the first 2 eigenvalues of the Schrödinger operator in case the potential is convex. In this note we note that the estimate can be improved if we assume the potential is strongly convex. In particular if the Hessian of the potential is bounded from below by a positive constant, the gap has...