Loss tolerance in one-way quantum computation via counterfactual error correction.

We introduce a scheme for fault tolerantly dealing with losses (or other "leakage" errors) in cluster state computation that can tolerate up to 50% qubit loss. This is achieved passively using an adaptive strategy of measurement--no coherent measurements or coherent correction is required. Since the scheme relies on inferring information about what would have been the outcome of a measurement had one been able to carry it out, we call this counterfactual error correction.