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We propose a scalable way to construct a 3D cluster state for fault-toleranttopological one-way computation (TOWC) even if the entangling two-qubit gatessucceed with a small probability. It is shown that fault-tolerant TOWC can beperformed with the success probability of the two-qubit gate such as 0.5 (0.1)provided that the conditional error probability of the two-qubit gate is lessthan 0.040% (0.016%). Furthermore, the resource usage is considerablysuppressed compared to the conventional fault-tolerant schemes withprobabilistic two-qubit gates.

Fault-Tolerant Topological One-Way Quantum Computation with Probabilistic Two-Qubit Gates