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Quantum computing with nearest neighbor interactions and error rates over 1%
David S. Wang, Austin G. Fowler, Lloyd C. L. Hollenberg
TL;DR
Existing QEC schemes tolerating error rates above 1% assume deterministic interactions between arbitrarily distant qubits, while such nonlocal interactions are particularly challenging to engineer. The procedure estimates pairwise syndrome-change connection probabilities and uses their negative logarithms as distances for minimum-weight perfect matching, while avoiding explicit qubit initialization. The threshold is 1.1%; the balanced error model yields 1.2%, and the ion trap error model yields 1.4%.
Problem
Existing QEC schemes tolerating error rates above 1% assume deterministic interactions between arbitrarily distant qubits, while such nonlocal interactions are particularly challenging to engineer.
Source: p. 1Method
The procedure estimates pairwise syndrome-change connection probabilities and uses their negative logarithms as distances for minimum-weight perfect matching, while avoiding explicit qubit initialization.
Source: pp. 1–2Results
The threshold is 1.1%; the balanced error model yields 1.2%, and the ion trap error model yields 1.4%.
Source: pp. 3–4Takeaways & Limitations
The study raises the geometrically constrained threshold above 1% for the first time while maintaining computational efficiency.
Source: p. 4Further improvement may come from accounting for correlations between X and Z errors, which the paper leaves for future work.
Source: p. 4
Abstract
from arXiv · showhide
Large-scale quantum computation will only be achieved if experimentally implementable quantum error correction procedures are devised that can tolerate experimentally achievable error rates. We describe a quantum error correction procedure that requires only a 2-D square lattice of qubits that can interact with their nearest neighbors, yet can tolerate quantum gate error rates over 1%. The precise maximum tolerable error rate depends on the error model, and we calculate values in the range 1.1--1.4% for various physically reasonable models. Even the lowest value represents the highest threshold error rate calculated to date in a geometrically constrained setting, and a 50% improvement over the previous record.