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.
We present a scalable solid-state system in which the superconducting charge qubits are coupled with a nanomechanical resonator (NAMR) to achieve highly entangled cluster states, which are responsible for one-way quantum computing via single-qubit measurements. Since the NAMR can play the essential role of the data bus, the long-range interactions among the qubits can occur. Therefore, without using the interacting picture we can directly obtain the long-range Ising-like unitary operator ${U}_{z}(\ensuremath{\lambda})=\mathrm{exp}[i\ensuremath{\lambda}{S}_{z}^{2}]$ with
Sz the collective spin operator in
z direction and $\ensuremath{\lambda}$ a parameter, which is insensitive to the thermal state of the NAMR. Based on this unitary operator, a set of highly entangled cluster states can be produced by efficient one-step generation. Moreover, the robustness of the highly entangled cluster states with respect to unavoidable parameter variations is also demonstrated.
We propose the use of collective states of matter as a resource for the deterministic generation of quantum states of light, which are fundamental for quantum information technologies. Our minimal model consists of three emitters coupled to a half-waveguide, i.e., a one-dimensional waveguide terminated by a mirror. Photon-mediated interactions between the emitters result in the emergence of bright and dark states. The dark states form a decoherence-free subspace, protected from dissipation. Local driving of the emitters and control of their resonance frequencies allows us to perform arbitrary quantum gates within the decoherence-free subspace. Coupling to bright states facilitates photon emission, thereby enabling the realization of quantum gates between light and matter. We demonstrate that sequential application of these gates leads to the generation of photonic entangled states, such as Greenberger-Horne-Zeilinger and one- and two-dimensional cluster states.