Universal fault-tolerant quantum computing with stabilizer codes

Fault-tolerant quantum computing with color codes

We have just completed a thorough, multi-year study of fault-tolerant quantum computation with color codes. These codes are amazing—one way to think about them is as a family of codes which generalize the Steane code not by concatenation but by lattice embedding [1]. Our study of fault-tolerant computing with these codes is complete with analytic bounds, numerical simulations, multiple noise mo...

Universal Fault-Tolerant Gates on Concatenated Stabilizer Codes

It is an oft-cited fact that no quantum code can support a set of fault-tolerant logical gates that is both universal and transversal. This no-go theorem is generally responsible for the interest in alternative universality constructions including magic state distillation. Widely overlooked, however, is the possibility of nontransversal, yet still fault-tolerant, gates that work directly on sma...

On Universal and Fault-Tolerant Quantum Computing

Using concatenated quantum codes for universal fault-tolerant quantum gates.

We propose a method for universal fault-tolerant quantum computation using concatenated quantum error correcting codes. The concatenation scheme exploits the transversal properties of two different codes, combining them to provide a means to protect against low-weight arbitrary errors. We give the required properties of the error correcting codes to ensure universal fault tolerance and discuss ...

Scheme for fault-tolerant holonomic computation on stabilizer codes

Ognyan Oreshkov, Todd A. Brun, and Daniel A. Lidar Grup de Física Teòrica, Universitat Autònoma de Barcelona, Bellaterra, Barcelona 08193, Spain Department of Physics, University of Southern California, Los Angeles, California 90089, USA Center for Quantum Information Science & Technology, University of Southern California, Los Angeles, California 90089, USA Communication Science Institute, Uni...