Entanglement Purification for Quantum Computation

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 $8\le d\le 32$. 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.