Thresholds and overheads for the toric code in the presence of bit (or phase) flip errors - Fern Watson

Quantum information is delicate, and as such must be protected from decoherence. Topological quantum error correcting codes are particularly robust to thermal noise, but still require active error correction. In this talk we will review one proposal for topological quantum error correction: Kitaevís 2 dimensional toric code. The toric code distance scales with lattice size, making a physically larger code more robust. However, in some ways a smaller code is desirable, because the experimental challenges in creating and manipulating such a state also scale with the number of qubits in the code. The overhead is a balance between these two requirements; in other words the minimum code size that will protect the state with a given accuracy, for a known error rate. We numerically investigate the overhead for the toric code and find it is logarithmic in both error rate and desired fidelity.