  Assuming an array that consists of two parallel lines of qubits and that
permits only nearest neighbor interactions, we construct physical and logical
circuitry to enable universal fault tolerant quantum computation under the
[[7,1,3]] quantum code. A rigorous lower bound to the fault tolerant threshold
for this array is determined in a number of physical settings. Adversarial
memory errors, two-qubit gate errors, and readout errors are included in our
analysis. In the setting where the physical memory failure rate is equal to
one-tenth of the physical gate error rate, the physical readout error rate is
equal to the physical gate error rate, and the duration of physical readout is
ten times the duration of a physical gate, we obtain a lower bound to the
asymptotic threshold of 1.96x10^-6.
