Expanded photonic bell state generators

1. An optical circuit comprising:

a number 2m of input waveguides, wherein m is an integer greater than 4;

a number m of output waveguides;

a set of m directional couplers, each directional coupler coupled between a different pair of the input waveguides, wherein each directional coupler has a first output mode coupled to one of the m output waveguides and a second output mode;

a mode-coupler network having a set of m input modes coupled to the second output modes of the m directional couplers and a set of m output modes, wherein the mode-coupler network is configured such that a photon entering the mode-coupler network on any one of the m input modes of the mode-coupler network has an equal probability of exiting on any one of the m output modes of the mode-coupler network;

a set of m photon detectors, each photon detector coupled to one of the m output modes of the mode-coupler network and configured to generate a detection signal indicating whether a photon is detected;

a photon source circuit configured to provide photons non-deterministically to at least a subset of the 2m input waveguides and to generate a photon pattern signal indicating which of the 2m input waveguides receive photons in a given time bin; and

control logic coupled to the m photon detectors and to the photon source circuit, the control logic being configured to determine, based at least in part on the detection signals generated by the m photon detectors and the photon pattern signal received from the photon source circuit, whether a Bell state is carried on four of the m output waveguides.

2. The optical circuit of claim 1 further comprising:

a set of 2m blocking switches, each blocking switch disposed on one of the 2m input waveguides upstream of the directional couplers,

wherein the control logic is further configured to control the 2m blocking switches so that, for a given time bin, photons pass through not more than four of the 2m input waveguides.

3. The optical circuit of claim 2 wherein a probability of producing the Bell state depends on which four of the m directional couplers receive photons and wherein the control logic is further configured such that in the event that more than four photons are provided by the photon source circuit, respective states of the 2m blocking switches are determined based at least in part on the probability of producing the Bell state for each possible selection of four photons.

4. The optical circuit of claim 1 wherein the control logic is further configured to determine, based on the photon pattern signal, which four of the m output waveguides carry the Bell state.

5. The optical circuit of claim 1 wherein m is equal to 2q, wherein q is an integer greater than or equal to 3.

6. The optical circuit of claim 5 wherein the mode-coupler network implements an m-mode Hadamard transfer matrix.

7. The optical circuit of claim 1 wherein the photon source circuit includes a set of at least m non-deterministic single photon sources, each non-deterministic single photon source being coupled to a different one of the input waveguides.

8. The optical circuit of claim 1 further comprising:

a set of four multiplexer circuits, each multiplexer circuit having a number m/4 of mux input waveguides and a mux output waveguide, each multiplexer circuit being configured to selectably optically couple one of the m/4 mux input waveguides to the mux output waveguide; and

a number m/2 of 2×2 muxes, each 2×2 mux having two inputs and two outputs, each input of each 2×2 mux being coupled to a different one of the m output waveguides, and each output of each 2×2 mux being coupled to one mux input waveguide of each of two different ones of the multiplexer circuits.

9. The optical circuit of claim 8 wherein the control logic is further configured to control the 2×2 muxes to optically couple the four of the m output waveguides on which the Bell state is carried to the four multiplexer circuits such that each one of the four of the m output waveguides is optically coupled to a different one of the multiplexer circuits.

10. An optical circuit comprising:

an expanded Bell state generator having a number 2m of input waveguides and a number m of output waveguides, wherein m is an integer greater than 4, the expanded Bell state generator being configured to receive four photons on any four of the 2m input waveguides and to produce a Bell state carried on four of the m output waveguides;

a set of four multiplexer circuits, each multiplexer circuit having a number m/4 of input waveguides and an output waveguide, each multiplexer circuit being configured to selectably optically couple one of the m/4 input waveguides to the output waveguide;

a number m/2 of 2×2 muxes, each 2×2 mux having two inputs and two outputs, each input of each 2×2 mux being coupled to a different one of them output waveguides of the expanded Bell state generator circuit, and each output of each 2×2 mux being coupled to one input waveguide of each of two different ones of the multiplexer circuits; and

control logic configured to control the 2×2 muxes to optically couple the four of the m output waveguides on which the Bell state is carried to the four multiplexer circuits such that each one of the four of the m output waveguides on which the Bell state is carried is optically coupled to a different one of the multiplexer circuits.

11. The optical circuit of claim 10 wherein the number m/2 of 2×2 muxes are arranged into groups of four 2×2 muxes and wherein, within each group of 2×2 muxes:

the two outputs of a first one of the 2×2 muxes are a first output coupled to a first one of the input waveguides of a first one of the four multiplexer circuits and a second output coupled to a first input waveguide of a second one of the four multiplexer circuits;

the two outputs of a first one of the 2×2 muxes are a first output coupled to a first one of the input waveguides of a first one (1) of the four multiplexer circuits and a second output coupled to a first one of the input waveguides of a second one (2) of the four multiplexer circuits;

the two outputs of a second one of the 2×2 muxes are a first output coupled to a second one of the input waveguides of the second one (2) of the four multiplexer circuits and a second output coupled to a first one of the input waveguides of a third one (3) of the four multiplexer circuits;

the two outputs of a third one of the 2×2 muxes are a first output coupled to a second one of the input waveguides of the third one (3) of the four multiplexer circuits and a second output coupled to a one of the input waveguides of a fourth one (4) of the four multiplexer circuits; and

the two outputs of a fourth one of the 2×2 muxes are a first output coupled to a second one of the input waveguides of the fourth one of the four multiplexer circuits and a second output coupled to a second one of the input waveguides of the first one of the four multiplexer circuits.