  The field of quantum computation currently lacks a formal proof of
experimental feasibility. Qubits are fragile and sophisticated quantum error
correction is required to achieve reliable quantum computation. The surface
code is a promising quantum error correction code, requiring only a physically
reasonable 2-D lattice of qubits with nearest neighbor interactions. However,
existing proofs that reliable quantum computation is possible using this code
assume the ability to measure four-body operators and, despite making this
difficult to realize assumption, require that the error rate of these operator
measurements is less than 10^-9, an unphysically low target. High error rates
have been proved tolerable only when assuming tunable interactions of strength
and error rate independent of distance, which is also unphysical. In this work,
given a 2-D lattice of qubits with only nearest neighbor two-qubit gates, and
single-qubit measurement, initialization, and unitary gates, all of which have
error rate p, we prove that arbitrarily reliable quantum computation is
possible provided p<7.4x10^-4, a target that many experiments have already
achieved. This closes a long-standing open problem, formally proving the
experimental feasibility of quantum computation under physically reasonable
assumptions.
