  In certain approaches to quantum computing the operations between qubits are
non-deterministic and likely to fail. For example, a distributed quantum
processor would achieve scalability by networking together many small
components; operations between components should assumed to be failure prone.
In the logical limit of this architecture each component contains only one
qubit. Here we derive thresholds for fault tolerant quantum computation under
such extreme paradigms. We find that computation is supported for remarkably
high failure rates (exceeding 90%) providing that failures are heralded,
meanwhile the rate of unknown errors should not exceed 2 in 10^4 operations.
