We experimentally demonstrate a simple scheme for generating a four-photon entangled cluster state with fidelity over 0.860+/-0.015. We show that the fidelity is high enough to guarantee that the produced state is distinguished from Greenberger-Horne-Zeilinger, W, and Dicke types of genuine four-qubit entanglement. We also demonstrate basic operations of one-way quantum computing using the produced state and show that the output state fidelities surpass classical bounds, which indicates that the entanglement in the produced state essentially contributes to the quantum operation.

We propose a family of surface codes with general lattice structures, where the error tolerances against bit and phase errors can be controlled asymmetrically by changing the underlying lattice geometries. The surface codes on various lattices are found to be efficient in the sense that their threshold values universally approach the quantum Gilbert-Varshamov bound. We find that the error tolerance of the surface codes depends on the connectivity of the underlying lattices; the error chains on a lattice of lower connectivity are easier to correct. On the other hand, the loss tolerance of the surface codes exhibits an opposite behavior; the logical information on a lattice of higher connectivity has more robustness against qubit loss. As a result, we come upon a fundamental trade-off between error and loss tolerances in the family of surface codes with different lattice geometries. We also provide the physical aspects of the present results from the viewpoint of statistical physics, which leads to an equality that captures well both the error and loss tolerances of these surface codes.

We propose a scalable way to construct a 3D cluster state for fault-tolerant topological one-way computation (TOWC) even if the entangling two-qubit gates succeed with a small probability. It is shown that fault-tolerant TOWC can be performed with the success probability of the two-qubit gate such as 0.5 (0.1) provided that the unheralded error probability of the two-qubit gate is less than 0.040% (0.016%). Furthermore, the resource usage is considerably suppressed compared to the conventional fault-tolerant schemes with probabilistic two-qubit gates.

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