Topological Quantum Error Correction with Optimal Encoding Rate

Quantum computation has overcome major difficulties and has become a field of solid research. On the theoretical side, several models of quantum computation are already proposed like the quantum network model using a set of universal logic gates. Quantum error correction and fault tolerant quantum computation have been proved to be well established theoretically. On the experimental side, test-ground experiments have been conducted with a small number of quantum logic gates based on several proposals for realizing qubits. These constitute proof-of-principle experimental realizations showing that theory meets experiment. Yet, it still faces a major challenge in order to built a real quantum computer: for a scalable quantum computer to be ever built, we have to battle decoherence and systematic errors in an efficient way [1], [2]. In fact, the network model corrects errors combinatorially and this requires a very low initial error rate, known as the threshold, in order to stabilize a quantum computation [3], [4], [5], [6]. There exists a very clever proposal of fault-tolerant quantum computation based on quantum topological ideas [7], [8]. The idea is to design the quantum operations so as to have a physically built-in mechanism for error correction, without resorting to external corrections every time an error occurs [9]. The key point here is that quantum topology is a global resource that is robust