Optically Generated 2-Dimensional Photonic Cluster State from Coupled Quantum Dots

We propose a method to generate a two-dimensional cluster state of polarization encoded photonic qubits from two coupled quantum dot emitters. We combine the proposal for generating one-dimensional cluster state strings from a single dot, with a new proposal for an induced conditional phase gate between the two quantum dots. The entanglement between the two dots translates to entanglement between the two photonic cluster state strings. Further interpair coupling of the quantum dots using cavities and waveguides can lead to a two-dimensional cluster sheet, the importance of which stems from the fact that it is a universal resource for quantum computation. Analysis of errors indicates that our proposal is feasible with current technology. Crucially, the emitted photons need not have identical frequencies, and so there are no constraints on the resonance energies for the quantum dots.

Figure 1

Diagrams depicting the generation of the cluster state using the standard diagrammatic representations of such states. The spins are depicted as filled circles, the initial electronic state is $|\uparrow ⟩|\uparrow ⟩$. At step (a) both spins precess under $R_y(\pi /2)$, at (b) the CZ gate is applied, at (c) a pulse excitation followed by trion decay produces photons (open circles). These procedures are then repeated, leading to the states of (d)–(h). Note that to recover the standard form of cluster states one must use a mapping where the logical qubit $|1⟩$ state is equivalent to the photonic state $-|L⟩$ [5].

Figure 2

A quantum circuit which is logically equivalent to the idealized evolution of the two QDs. The CZ gates correspond to the interdot coupling, the CNOT gates to photon emission, and the $R_y$ to precession by $\pi /2$ around a magnetic field in the $y$ direction.