Limitations of quantum computing with Gaussian cluster states

TL;DR

This paper analyzes the fundamental limitations of Gaussian cluster states in measurement-based quantum computing, showing they cannot support long-range quantum information transport or processing, highlighting the need for non-Gaussian resources.

Contribution

It proves that Gaussian cluster states cannot carry logical quantum information beyond a limited region, even with non-Gaussian measurements, emphasizing the necessity of non-Gaussian resources for universal quantum computing.

Findings

Gaussian states cannot support long-distance quantum information transport.

Finite-width Gaussian cluster states cannot encode logical qubits.

Results imply non-Gaussian resources are essential for universal measurement-based quantum computing.

Abstract

We discuss the potential and limitations of Gaussian cluster states for measurement-based quantum computing. Using a framework of Gaussian projected entangled pair states (GPEPS), we show that no matter what Gaussian local measurements are performed on systems distributed on a general graph, transport and processing of quantum information is not possible beyond a certain influence region, except for exponentially suppressed corrections. We also demonstrate that even under arbitrary non-Gaussian local measurements, slabs of Gaussian cluster states of a finite width cannot carry logical quantum information, even if sophisticated encodings of qubits in continuous-variable (CV) systems are allowed for. This is proven by suitably contracting tensor networks representing infinite-dimensional quantum systems. The result can be seen as sharpening the requirements for quantum error correction and fault tolerance for Gaussian cluster states, and points towards the necessity of non-Gaussian resource states for measurement-based quantum computing. The results can equally be viewed as referring to Gaussian quantum repeater networks.