Universal Fault-Tolerant Gates on Concatenated Stabilizer Codes

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...

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...

Fault-tolerant logical gates in quantum error-correcting codes∗

Recently, Bravyi and König have shown that there is a trade-off between fault-tolerantly implementable logical gates and geometric locality of stabilizer codes. They consider locality-preserving operations which are implemented by a constant-depth geometrically-local circuit and are thus fault-tolerant by construction. In particular, they shown that, for local stabilizer codes in D spatial dime...

On Universal and Fault-Tolerant Quantum Computing