Figure 1

Schematic for the entangler. Two qubus beams are coupled to the two single photons as indicated. The XPM phases $\theta$ and two phase shifters $-\theta$ are applied to the qubus beams. The quantum nondemolition (QND) module and the classical feedforward are used to make this operation deterministic. This operation entangles the polarization modes of two single photons.Reuse & Permissions

Figure 2

The generation of a cluster state string with entanglers. (1) Use of entanglers and Hadamard operations to generate a cluster state string. (2) Use of four entanglers and Hadamard operations to create a star cluster state. (3) Use of one entangler and a Hadamard operation to add one photon to the already created cluster state.Reuse & Permissions

Figure 3

Schematic for generating a type-I box. (1) One entangler plus three Hadamard operations are performed on photons 2 and 4 in order to connect two links 1–4, 3–4. Then, a box cluster state could be generated by only three entangler operations without an ancilla photon. (2) The generalization of adding a box structure to an already generated cluster state.Reuse & Permissions

Figure 4

Schematic for generating a type-II box. Two entanglers are used to add two single photons to the already generated cluster state. Then, one CZ gate is performed on photons $q$ and $s$ for creating two links s–r, s–p. A total of four entanglers with one ancilla photon are required to add a type-II box to an already created cluster state or between two already created cluster states.Reuse & Permissions

Figure 5

The generation of a $5\times 5$ cluster state from a string and two types of box structures. A nine-photon cluster string and four entanglers are used to create four type-I box cluster states, and then two type-I boxes are added by six entanglers. Next, two type-II boxes are generated by four entanglers and two CZ gates. After that, with two entanglers, two independent photons will be added to the eight-box cluster state. At the last step, six CZ gates are applied to complete the connection of entanglement bonds. There is a total of 40 necessary entanglers. The number of entanglers is equal to that of the bonds of the cluster state.Reuse & Permissions