Source-linked AI summary
Fault-tolerant conversion between the Steane and Reed-Muller quantum codes
Jonas T. Anderson, Guillaume Duclos-Cianci, David Poulin
TL;DR
Universal fault-tolerant computation requires more than the Clifford gates available in Steane’s code, while Reed-Muller codes provide complementary non-Clifford gates. The paper presents direct fault-tolerant code conversion, interprets the codes as different gauges of one subsystem code, and extends the scheme across the quantum Reed-Muller family.
Problem
No quantum code admits a universal set of transversal gates, and Steane’s fault-tolerant Clifford gates are not universal without additional techniques.
Method
The paper directly converts encoded information between Steane’s 7-qubit and 15-qubit Reed-Muller codes by modifying the code during computation, using freedom in stabilizer completion and a subsystem-code interpretation.
Results
The scheme fault-tolerantly converts between a family of quantum error-correcting codes and combines their transversal gate sets into an overcomplete universal gate set.
Takeaways & Limitations
Different quantum Reed-Muller codes correspond to one subsystem code with different gauge fixings, while Steane’s code supplies Clifford gates and higher codes supply increasingly complex transversal gates.
Takeaways & Limitations
The proposal to improve Reed-Muller magic-state distillation is left for future work without a detailed study.
Abstract
from arXiv · showhide
Steane's 7-qubit quantum error-correcting code admits a set of fault-tolerant gates that generate the Clifford group, which in itself is not universal for quantum computation. The 15-qubit Reed-Muller code also does not admit a universal fault-tolerant gate set but possesses fault-tolerant T and control-control-Z gates. Combined with the Clifford group, either of these two gates generate a universal set. Here, we combine these two features by demonstrating how to fault-tolerantly convert between these two codes, providing a new method to realize universal fault-tolerant quantum computation. One interpretation of our result is that both codes correspond to the same subsystem code in different gauges. Our scheme extends to the entire family of quantum Reed-Muller codes.