Quantum advantage and noise reduction in distributed quantum computing

TL;DR

This paper explores how distributed quantum computing can reduce noise and maintain quantum advantages in algorithms like Grover, Simon, and Deutsch-Jozsa, despite some complexity and probabilistic trade-offs.

Contribution

It demonstrates that distributed quantum algorithms can preserve exponential or quantum advantages with manageable complexity increases and probabilistic outcomes.

Findings

Distributed Grover search shows noise reduction benefits.

Distributed Simon algorithm retains exponential advantage with increased complexity.

Distributed Deutsch-Jozsa remains probabilistic but still outperforms classical methods.

Abstract

Distributed quantum computing can give substantial noise reduction due to shallower circuits. An experiment illustrates the advantages in the case of Grover search. This motivates studying the quantum advantage of the distributed version of the Simon and Deutsch-Jozsa algorithm. We show that the distributed Simon algorithm retains the exponential advantage, but the complexity deteriorates from O(n) to O(n^2), where n = log2(N). The distributed Deutsch-Jozsa deteriorates to being probabilistic but retains a quantum advantage over classical random sampling.