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Evaluation of Fault-Tolerant Code Deformation
by
Andrew Cross
SAIC
Quantum error-correcting codes are an important tool for fighting noise in quantum computers. Topological quantum codes protect fragile quantum information by encoding it in the topology of a surface. A method called code deformation enables universal computation on the encoded data and involves changing that topology.
To reliably compute in the presence of noise, gate error rates need to be well below a constant accuracy threshold. High thresholds are desirable because they reduce accuracy requirements placed on quantum hardware. Raussendorf discovered that code deformation enables universal fault-tolerant quantum computation with thresholds near one percent [1]. The high threshold is achieved in a potentially realistic model where qubits interact with neighbors on a square two-dimensional grid.
Thresholds for this scheme are estimated by classically simulating quantum error correction [1, 2]. Thresholds for quantum computation are expected to be the same, but this has not been demonstrated. Our result is a conceptually simple method for fault-tolerantly deforming a planar code that retains a high accuracy threshold. The threshold for this method has been computed by direct simulation of code deformation within the stabilizer formalism.
This is joint work with Kevin Obenland. This work was supported by Science Applications International Corporation as internal research and development.
[1] Raussendorf and Harrington, Phys. Rev. Lett. 98, 190504 (2007).
[2] Fowler, Stephens, and Groszkowski, Phys. Rev. A 80, 052312 (2009).
Date received: November 29, 2010
Copyright © 2010 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbbr-25.