Threshold error penalty for fault-tolerant quantum computation with nearest neighbor communication

The error threshold for fault-tolerant quantum computation with concatenated encoding of qubits is penalized by internal communication overhead. Many quantum computation proposals rely on nearest neighbor communication, which requires excess gate operations. For a qubit stripe with a width of L+1 physical qubits implementing L levels of concatenation, we find that the error threshold of 2.1×10^-5 without any communication burden is reduced to 1.2×10^-7 when gate errors are the dominant source of error. This ∼175× penalty in error threshold translates to an ∼13× penalty in the amplitude and timing of gate operation control pulses.