Decoder graphs for a cluster state built from the srs tiling in both phenomenological (left) and circuit-level (right) error models. Vertices represent local correlations used to correct errors, while edges represent linear-probability faults. In the phenomenological setting, the absence of correlated errors yields robust error-correction. In the circuit-level setting, construction of the cluster state itself yields a complicated network of correlated errors (red edges). Balancing the robustness of a cluster state with the complexity of its construction is key to tailoring measurement-based error-correction to different noise profiles.
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. doi 10.22331/q-2020-07-13-295
Newman, Michael; Andreta de Castro, Leonardo; Brown, Kenneth R,
