Anthony Hams

Fast algorithm for finding the eigenvalue distribution of very large matrices

A theoretical analysis is given of the equation of motion method, due to Alben et al. [Phys. Rev. B 12, 4090 (1975)], to compute the eigenvalue distribution (density of states) of very large matrices. The salient feature of this method is that for matrices of the kind encountered in quantum physics the memory and CPU requirements of this method scale linearly with the dimension of the matrix. We derive a rigorous estimate of the statistical error, supporting earlier observations that the computational efficiency of this approach increases with the matrix size. We use this method and an imaginary-time version of it to compute the energy and specific heat of three different, exactly solvable, spin-1/2 models, and compare with the exact results to study the dependence of the statistical errors on sample and matrix size.

Quantum Computer Emulator

Abstract We describe a Quantum Computer Emulator for a generic, general purpose Quantum Computer. This emulator consists of a simulator of the physical realization of the quantum computer and a graphical user interface to program and control the simulator. We illustrate the use of the quantum computer emulator through various implementations of the Deutsch–Jozsa and Grovers database search algorithm.

Feedback effect on Landau-Zener-Stückelberg transitions in magnetic systems

We examine the effect of the dynamics of the internal magnetic field on the staircase magnetization curves observed in large-spin molecular magnets. We show that the size of the magnetization steps depends sensitively on the intermolecular interactions, even if these are very small compared to the intramolecular couplings.

Quantum Statistical Mechanics on a Quantum Computer

We describe a simulation method for a quantum spin model of a generic, general purpose quantum computer. The use of this quantum computer simulator is illustrated through several implementations of Grover’s database search algorithm. Some preliminary results on the stability of quantum algorithms are presented.

Many-spin calculation of tunneling splittings in Mn12 magnetic molecules

We calculate the tunneling splittings in a Mn12 magnetic molecule taking into account its internal many-spin structure. We discuss the precision and reliability of these calculations and show that restricting the basis (limiting the number of excitations taken into account) may lead to significant error (orders of magnitude) in the resulting tunneling splittings for the lowest energy levels, so that an intuitive picture of different decoupled energy scales does not hold in this case.

Simulation of quantum computers

We describe a simulation approach to study the functioning of Quantum Computer hardware. The latter is modeled by a collection of interacting spin-1/2 objects. The time evolution of this spin system maps one-to-one to a quantum program carried out by the Quantum Computer. Our simulation software consists of code that solves the time-dependent Schrodinger equation for a sequence of time-dependent Hamiltonians and a graphical user interface to program and control the solver. We present results of simulations on a 4-qubit Quantum Computer executing Grover’s database search algorithm.