Quantum computation in a Ising spin chain taking into account second neighbor couplings

TL;DR

This paper explores implementing quantum algorithms in a nuclear spin chain with both nearest and second neighbor Ising couplings, showing how to optimize pulse sequences and Rabi frequency considering the additional interactions.

Contribution

It extends the 2πk method to include second neighbor couplings, demonstrating potential pulse savings and analyzing effects on quantum algorithm implementations.

Findings

Second neighbor coupling influences optimal Rabi frequency.

The 2πk method adapts to more complex spin interactions.

Numerical simulations validate the approach with Shor's algorithm and teleportation.

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 2\pi k 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.