Generating Fault-Tolerant Cluster States from Crystal Structures

TL;DR

This paper introduces a novel method for constructing fault-tolerant cluster states from crystal structures using combinatorial tiling theory, enhancing the robustness of measurement-based quantum computing.

Contribution

It presents a systematic approach to generate new fault-tolerant cluster states from crystal structures, including a self-dual state with low connectivity, and benchmarks their performance under noise.

Findings

Identified promising fault-tolerant cluster states with noise resilience

Developed a framework that bypasses traditional data-ancilla distinctions

Demonstrated performance variability depending on noise models

Abstract

Measurement-based quantum computing (MBQC) is a promising alternative to traditional circuit-based quantum computing predicated on the construction and measurement of cluster states. Recent work has demonstrated that MBQC provides a more general framework for fault-tolerance that extends beyond foliated quantum error-correcting codes. We systematically expand on that paradigm, and use combinatorial tiling theory to study and construct new examples of fault-tolerant cluster states derived from crystal structures. Included among these is a robust self-dual cluster state requiring only degree-3 connectivity. We benchmark several of these cluster states in the presence of circuit-level noise, and find a variety of promising candidates whose performance depends on the specifics of the noise model. By eschewing the distinction between data and ancilla, this malleable framework lays a foundation for the development of creative and competitive fault-tolerance schemes beyond conventional error-correcting codes.