Abstract: A method of generating an m-photon entangled state includes inputting photons into a plurality of sets of modes. Each set of modes is coupled to a different set of modes. The method includes detecting photons in the plurality of sets of modes. The method includes, in accordance with a determination, based on a number of photons detected, that more than m-photons remain in the plurality of sets of modes: performing a second detection operation that includes detecting photons in the plurality of sets of modes; determining, based at least in part on a number of photons detected, whether the photons remaining in the plurality of sets of modes after the second detection operation are in the m-photon entangled state; and in accordance with a determination that the photons remaining in the plurality of sets of modes are in the m-photon entangled state, outputting the remaining photons.

Abstract: Circuits for generating a pair of qudits in a maximally entangled state and methods of operating such circuits are disclosed. The circuits can be photonic circuits that use a combination of beam splitters, phase shifters, and detectors to produce an entangled pair of d-dimensional qudits from an input set of 4d photons. In a case where d equals 2, a pair of qubits in a Bell state can be generated.

Abstract: A method of generating an m-photon entangled state includes inputting photons into a plurality of sets of modes. Each set of modes is coupled to a different set of modes. The method includes detecting photons in the plurality of sets of modes. The method includes, in accordance with a determination, based on a number of photons detected, that more than m-photons remain in the plurality of sets of modes: performing a second detection operation that includes detecting photons in the plurality of sets of modes; determining, based at least in part on a number of photons detected, whether the photons remaining in the plurality of sets of modes after the second detection operation are in the m-photon entangled state; and in accordance with a determination that the photons remaining in the plurality of sets of modes are in the m-photon entangled state, outputting the remaining photons.

Abstract: An apparatus includes a plurality of first optical devices and a second optical device. Each first optical device includes a respective first pair of waveguides comprising a respective first waveguide and a respective second waveguide that are coupled together, a respective second pair of waveguides comprising a respective third waveguide and a respective fourth waveguide that are coupled together, and a first fusion gate that includes a detector. Each first fusion gate is configured to perform a fusion on the respective second waveguide and the respective third waveguide of a respective first optical device. The fusion produces a detection pattern for the respective first optical device. The apparatus further includes a multiplexer to select a respective first optical device of the plurality of first optical devices based at least in part on the detection pattern for the respective first optical device and output photons from the respective first optical device.

Abstract: Circuits for generating a pair of qudits in a maximally entangled state and methods of operating such circuits are disclosed. The circuits can be photonic circuits that use a combination of beam splitters, phase shifters, and detectors to produce an entangled pair of d-dimensional qudits from an input set of 4d photons. In a case where d equals 2, a pair of qubits in a Bell state can be generated.

Abstract: A method of generating an m photon entangled state includes inputting a photon into each of a first plurality of modes including first and second pairs of modes. The first plurality of modes is coupled with a second plurality of modes. Zero or more photons are detected in the second plurality of modes. The method includes, when more than m photons remain in the first plurality of modes: detecting zero or more photons in a third plurality of modes coupled with the first plurality of modes; determining, based on a number of photons detected, whether the photons remaining in the first plurality of modes are in the entangled state. The method includes, when the photons remaining in the first plurality of modes after the second detection operation are in the entangled state, outputting the photons remaining in the first plurality of modes.