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/spl times/10/sup -5/ without any communication burden is reduced to 1.2/spl times/10/sup -7/ when gate errors are the dominant source of error. This /spl sim/175/spl times/ penalty in error threshold translates to an /spl sim/13/spl times/ penalty in the amplitude and timing of gate operation control pulses.