Quantum Computation in a Ising Spin Chain Taking into Account Second Neighbor Couplings

Abstract

We consider the realization of a quantum computer in a chain of nuclear spins coupled by an Ising interaction. Quantum algorithms can be performed with the help of appropriate radio-frequency pulses. In addition to the standard nearest-neighbor Ising coupling, we also allow for a second neighbor coupling. It is shown, how to apply the 2πk method in this more general setting, where the additional coupling eventually allows to save a few pulses. We illustrate our results with two numerical simulations: the Shor prime factorization of the number 4 and the teleportation of a qubit along a chain of 3 qubits. In both cases, the optimal Rabi frequency (to suppress non-resonant effects) depends primarily on the strength of the second neighbor interaction.

Modular magnetic field on the z-direction on a chain of nuclear spin system and quantum Not and Controlled-Not gates

“…Furthermore, the approach relies in the universal character of Quantum Mechanics. In this model, the Ising interaction is considered among first and second neighbor spins which allows to implement ideally this type of computer up to 1000-qubits or more [13], [14]. Among other gates and algorithms [15], one qubit rotation and CNOT gates were study with this quantum computer model [16].…”

Simulation of static and random errors on Grover's search algorithm implemented in an Ising nuclear spin chain quantum computer with a few qubits

“…At the moment, there has not been a physical realization of this quantum computer. However, since the full Hamiltonian can be explicitly written for this system, several useful analytical and numerical studies have been made [16,17] where the results can be extrapolated to other solid state spins quantum computers. On the other hand, one important aspect of the simulation or implementation of a quantum algorithm is the effect that the noise can cause to the performance of this algorithm which may arise from error in the quantum parameters or from the interaction with the environment, or both.…”

“…The model of the system can be found in reference [15], and the explicit Hamiltonian for simulation of the Grover' search algorithm is given by [17] …”