  What is the minimum number of extra qubits needed to perform a large
fault-tolerant quantum circuit? Working in a common model of fault-tolerance, I
show that in the asymptotic limit of large circuits, the ratio of physical
qubits to logical qubits can be a constant. The construction makes use of
quantum low-density parity check codes, and the asymptotic overhead of the
protocol is equal to that of the family of quantum error-correcting codes
underlying the fault-tolerant protocol.
