Logical error rate scaling of the toric code

What is it about?

Quantum computing relies on the ability to maintain quantum systems in perfect superpositions for an arbitrarily long time but interactions with the environment that destroy this superposition are unavoidable so it is necessary to devise ways to protect the information. In this work we study a model for quantum error correction: the toric code, and determine the probability of it successfully protecting the information for a given set of input parameters.

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Why is it important?

A key metric for the performance of quantum error correcting codes is the resource overhead: the minimum resources required to achieve a desired error correction performance. We determine a method for quantifying this using the logical error rate scaling to find the minimum system size required. The techniques developed are applicable to other scenarios, and should be of interest to experimentalists interested in realising quantum error correcting codes.