We describe an integrated waveguide device that creates entanglement between a sequence of periodically spaced (in time) photons in a single input and output mode. The device consists of a polarization maintaining integrated waveguide chip containing a number of delay lines, integrated multimode interferometers with the potential for rapid switching, a polarization controller and off chip computer logic and timing. The device is capable of creating a diverse array of outputs such as linear cluster states and ring cluster states in a single output mode.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. An apparatus for sequentially entangling photons in two dimensions, comprising: a waveguide chip having integrated optical components and interconnecting optical waveguide disposed therein, wherein said optical components further comprise an input port connected to said optical waveguide for inputting said photons into said waveguide chip; a polarization controller connected to said input port for rotating the polarization of said input port; a plurality of delay lines for synchronizing said photons in time; a plurality of multimode interferometers for selectably routing said photons through any of said interconnecting optical waveguide; a controller for switching the input mode of any of said plurality of multimode interferometers so as to route said photons into and out of a selected interferometer's input and output ports; a clock source for synchronizing said controller with the arrival of said photons; a plurality of entangling gates having bypass and entangling inputs and bypass and entangling outputs for selectively entangling said photons; and an output port for routing said entangled photons out of said waveguide chip. 2. The apparatus of claim 1, wherein said polarization controller rotates the polarization of said photons to a plus state. 3. The apparatus of claim 1, wherein each of said plurality of multimode interferometers is comprised of multimode optical waveguide material. 4. The apparatus of claim 1, wherein a first of said plurality of said delay lines has a length chosen to provide a delay equal to the period of the periodic sequence of said photons. 5. The apparatus of claim 1, wherein a first of said plurality of multimode interferometers synchronizes photons by routing a photon through a first output into said first of said plurality of delay lines and routing a next photon through a second output which bypasses said first of said plurality of delay lines. 6. The apparatus of claim 1, wherein a second of said plurality of multimode interferometers, has as a first of two inputs, the output of said first delay line. 7. The apparatus of claim 1, wherein said second and a third of said plurality of said multimode interferometers are arranged in parallel, wherein said third multimode interferometer has as an input the non-delayed output of said first multimode interferometer, and wherein said second and said third multimode interferometers each have a first output connected to a bypass input and a second output connected to an entangling input of a first of said entangling gates. 8. The apparatus of claim 7, wherein a fourth and a fifth of said plurality of said multimode interferometers are arranged in parallel, said fourth and fifth multimode interferometers each having a first input connected to an entangling output of said first entangling gate and a second input connected to a bypass output of said first entangling gate; said fourth and fifth multimode interferometers each having a first output connected to an input of a sixth of said plurality of said multimode interferometers; and said fourth multimode interferometer having a second output connected to an input of a second of said plurality of delay lines. 9. The apparatus of claim 8, wherein said second of said plurality of said delay lines has an output connected to a second of said two inputs of said second multimode interferometer. 10. The apparatus of claim 9, wherein said sixth of said plurality of said multimode interferometers has a first output connected to an input of a third of said plurality of delay lines; and a second output connected to an input of a seventh of said plurality of multimode interferometers. 11. The apparatus of claim 10, wherein said seventh of said plurality of multimode interferometers has a first output connected to a second input of a second of said plurality of entangling gates; and a second output connected to a second input of an eighth of said plurality of multimode interferometers. 12. The apparatus of claim 11, wherein said second of said plurality of entangling gates has a first input connected to an output of said third of said plurality of delay lines; a first output connected to an input of a fourth of said plurality of delay lines; and a second output connected to a first input of said eighth of said multimode interferometers. 13. The apparatus of claim 12, wherein said fourth of said plurality of multimode interferometers has an output connected to a first input of a ninth of said plurality of multimode interferometers. 14. The apparatus of claim 13, wherein said ninth of said plurality of multimode interferometers has a second input connected to an output of said eighth of said plurality of multimode interferometers; and an output connected to said output port.