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

TL;DR

This paper investigates how static and random errors affect Grover's search algorithm implemented on a small nuclear spin chain quantum computer, analyzing fidelity decay under different noise conditions and error suppression techniques.

Contribution

It provides a comparative analysis of fidelity decay patterns for static and random noise in a nuclear spin chain quantum computer implementing Grover's algorithm.

Findings

Fidelity decays exponentially or Gaussian depending on noise type and error suppression.

Static and random errors impact the algorithm's performance differently.

Error suppression methods can mitigate fidelity loss.

Abstract

We consider Grover's search algorithm on a model quantum computer implemented on a chain of four or five nuclear spins with first and second neighbour Ising interactions. Noise is introduced into the system in terms of random fluctuations of the external fields. By averaging over many repetitions of the algorithm, the output state becomes effectively a mixed state. We study its overlap with the nominal output state of the algorithm, which is called fidelity. We find either an exponential or a Gaussian decay for the fidelity as a function of the strength of the noise, depending on the type of noise (static or random) and whether error supression is applied (the 2pi k-method) or not.