Entanglement purification for quantum computation -: art. no. 067901

We show that thresholds for fault-tolerant quantum computation are solely determined by the quality of single-system operations if one allows for d-dimensional systems with 8 less than or equal to d less than or equal to 32. Each system serves to store one logical qubit and additional auxiliary dimensions are used to create and purify entanglement between systems. Physical, possibly probabilistic two-system operations with error rates up to 2/3 are still tolerable to realize deterministic high-quality two-qubit gates on the logical qubits. The achievable error rate is of the same order of magnitude as of the single-system operations. We investigate possible implementations of our scheme for several physical setups.