Topological quantum error correction using a data bus

A method for implementing a merge operation by performing an arbitrary length fault tolerant parity check in surface code quantum computing comprising:

• a) preparing a first and a second logical qubit each in the form of square patch of qubits in a joint quantum state corresponding to a surface code with distance d, the square patches of qubits each having a side-length of (d+1) qubits, the qubits of the square patches being classified as either data qubits or syndrome qubits,
• b) preparing a chain of N data bus qubits with N>=2 in a joint GHZ-state, wherein the chain of data qubits connects the first and second logical qubit in that each of the logical qubits contains one or more data qubits that is adjacent to a qubit of the data bus,
• c) for each data qubit of the first and second logical qubit adjacent to a data bus qubit, performing a transversal CNOT operation between that data qubit and the qubit of the data bus to which it is adjacent,
• d) measuring all qubits of the data bus,
• e) repeating steps b)-d) d times, and
• f) obtaining an error corrected measurement result by a majority vote over the individual measurement results of step d).