Qubit Complexity of Continuous Problems

The number of qubits used by a quantum algorithm will be a crucial computational resource for the foreseeable future. We show how to obtain the classical query complexity for continuous problems. We then establish a simple formula for a lower bound on the qubit complexity in terms of the classical query complexityComment: 6 pages, 2 figure

Non-Computability and Intractability: Does It Matter to Physics?

Should the impossibility results of theoretical computer science be of concern to physics

Construction of Globally Convergent Iteration Functions for the Solution of Polynomial Equations

Iteration functions for the approximation of zeros of a polynomial P are usually given as explicit functions of P and its derivatives. We introduce a class of iteration functions which are themselves constructed according to a certain algorithm given below. The construction of the iteration functions requires only simple polynomial manipulation which may be performed on a computer

Associated Polynomials and Uniform Methods for the Solution of Linear Problems

To every polynomial P of degree n we associate a sequence of n-1 polynomials of increasing degree which we call the associated polynomials of P. The associated polynomials depend in a particularly simple way on the coefficients of P. These polynomials have appeared in many guises in the literature, usually related to some particular application and most often going unrecognized. They have been called Horner polynomials and Laguerre polynomials. Often what occurs is not an associated polynomial itself but a number which is an associated polynomial evaluated at a zero of P. The properties of associated polynomials have never been investigated in themselves. We shall try to demonstrate that associated polynomials provide a useful unifying concept. Although many of the results of this paper are new, we shall also present known results in our framework

Variational Calculations of Energy and Fine Structure for the 2³P State of Helium

ERV accurate calculations of the energies of the 1s2 1S and 1s2s3S states of helium have been made recently. It is now possible to consider the contributions of relativistic and electrodynamic effects to the observed ionization energies in a meaningful way. These small effects must still be added to the large calculated nonrelativistic energy, however, before a comparison with experiment can be made. In the 3P states, the spin-dependent part of the theoretical electromagnetic interaction of the two electrons can be compared directly with observed fine-structure splittings. Recent improvements in the experimental accuracy of the fine-structure measurements, 45 particularly the direct observation of the splittings as radio-frequency transitions, have made such a comparison possible to an order of accuracy including higher order electrodynamic corrections to the usual fine structure formulas