Apparatus and methods for quantum computing and machine learning

1. An apparatus, comprising:

a plurality of processing layers coupled in series, each processing layer in the plurality of processing layers including:

a Gaussian unit configured to perform a linear transformation on an input signal including a plurality of optical modes, the Gaussian unit including:

a network of interconnected beamsplitters and phase shifters, a first portion of the network of interconnected beamsplitters and phase shifters being configured to form a first interferometer to apply one of a phase-less Gaussian transformation or a phase-sensitive Gaussian transformation to the plurality of optical modes, and a second portion of the network of interconnected beamsplitters and phase shifters being configured to form a second interferometer to apply a phase-less transformation to the plurality of optical modes; and

a plurality of squeezers operatively coupled to the network of interconnected beamsplitters and phase shifters, each squeezer from the plurality of squeezers configured to apply one of a position-only squeezing or squeezing along an arbitrary axis in a position-momentum plane to one optical mode from the plurality of optical modes, and

a plurality of nonlinear gates operatively coupled to the Gaussian unit and configured to apply an arbitrary nonlinear transformation to the plurality of optical modes; and

a controller operatively coupled to the plurality of processing layers and configured to change a setting of the plurality of processing layers based on an output signal from at least one processing layer from the plurality of processing layers, to vary the linear transformation and the arbitrary nonlinear transformation to switch the apparatus among a first mode to implement a classical neural network, a second mode to implement a quantum neural network, and a third mode to implement a hybrid neural network.

2. The apparatus of claim 1 , wherein the Gaussian unit further includes:

a plurality of displacers operatively coupled to the plurality of squeezers and the network of interconnected beamsplitters and phase shifters, each displacer from the plurality of displacers configured to apply one of a position-only displacement or a displacement along the arbitrary axis in the position-momentum plane to the one optical mode from the plurality of optical modes.

3. The apparatus of claim 1 , wherein:

the Gaussian unit further includes a plurality of displacers operatively coupled to the plurality of squeezers and the network of interconnected beamsplitters and phase shifters, each displacer from the plurality of displacers configured to apply a position-only displacement to one optical mode from the plurality of optical modes, and

the plurality of nonlinear gates being configured to apply the arbitrary nonlinear transformation between a first set of position eigenstates and a second set of position eigenstates of the plurality of optical modes.

4. The apparatus of claim 1 , wherein:

the Gaussian unit further includes a plurality of displacers operatively coupled to the plurality of squeezers and the network of interconnected beamsplitters and phase shifters, each displacer from the plurality of displacers configured to apply a displacement in position and momentum to one optical mode from the plurality of optical modes.

5. The apparatus of claim 1 , wherein:

the Gaussian unit further includes a plurality of displacers operatively coupled to the plurality of squeezers and the network of interconnected beamsplitters and phase shifters, each displacer from the plurality of displacers configured to apply a displacement in position and momentum to one optical mode from the plurality of optical modes.

6. The apparatus of claim 1 , wherein at least one of the Gaussian unit or the plurality of nonlinear gates is configured to create an entanglement or a superposition from the plurality of optical modes.

7. The apparatus of claim 1 , further comprising:

a light source configured to send the plurality of optical modes, the light source and the plurality of processing layers being fabricated in a substrate.

8. The apparatus of claim 1 , further comprising:

a feedback loop operatively coupled to an output interface of the plurality of processing layers, the feedback loop configured to send at least a portion of the output signal back from the plurality of processing layers to an input interface as a new input signal for the plurality of processing layers.

9. The apparatus of claim 8 , further comprising a detector operatively coupled to the plurality of processing layers and configured to measure a photon number of each optical mode from the plurality of optical modes in the output signal.

10. The apparatus of claim 1 , wherein the controller is operatively coupled to: (i) each beamsplitter and phase shifter in the network of interconnected beamsplitters and phase shifters; (ii) each squeezer from the plurality of squeezers; and (iii) each nonlinear gate from the plurality of nonlinear gates.

11. A method, comprising:

selecting, via a controller, an operational mode from a plurality of operational modes for a plurality of processing layers connected in series by adjusting a setting of the plurality of processing layers, the plurality of operational modes including a first operational mode to implement a classical neural network, a second operational mode to implement a quantum neural network, and a third operational mode to implement a hybrid neural network;

propagating an input signal through the plurality of processing layers, the input signal including a plurality of optical modes, the propagating of the input signal through the plurality of processing layers including at least one of:

performing a linear transformation on the plurality of optical modes using a Gaussian unit that includes:

a network of interconnected beamsplitters and phase shifters, a first portion of the network of interconnected beamsplitters and phase shifters being configured to form a first interferometer to apply one of a first phase-less transformation or a phase-sensitive Gaussian transformation to the plurality of optical modes, and a second portion of the network of interconnected beamsplitters and phase shifters being configured to form a second interferometer to apply a second phase-less transformation to the plurality of optical modes; and

a plurality of squeezers operatively coupled to the network of interconnected beamsplitters and phase shifters, each squeezer from the plurality of squeezers configured to apply one of a position-only squeezing or squeezing along an arbitrary axis in a position-momentum plane to one optical mode from the plurality of optical modes; or

performing an arbitrary nonlinear transformation on the plurality of optical modes using a plurality of nonlinear gates operatively coupled to the Gaussian unit; and

sending an output signal from the plurality of processing layers.

12. The method of claim 11 , wherein:

the performing the linear transformation on the plurality of optical modes includes

applying a position-only displacement to one or more optical modes from the plurality of optical modes using a plurality of displacers; and

the performing the arbitrary nonlinear transformation on the plurality of optical modes includes applying the arbitrary nonlinear transformation between a first set of position eigenstates and a second set of position eigenstates of the plurality of optical modes.

13. The method of claim 11 , wherein:

the performing the linear transformation on the plurality of optical modes includes

applying a displacement in position and momentum to one or more optical modes from the plurality of optical modes using a plurality of displacers.

14. The method of claim 11 , wherein:

the performing the linear transformation on the plurality of optical modes includes

applying a displacement in position and momentum to one or more optical modes from the plurality of optical modes using a plurality of displacers, and

the method further includes changing a phase setting of the plurality of processing layers based on the output signal from the plurality of processing layers.

15. The method of claim 11 , wherein:

at least one of the linear transformation or the arbitrary nonlinear transformation on the plurality of optical modes includes creating an entanglement or a superposition from the plurality of optical modes, and

the method further includes changing a phase setting of the plurality of processing layers based on the output signal from the plurality of processing layers.

16. The method of claim 11 , further comprising:

sending the input signal to the plurality of processing layers using a light source, the light source and the plurality of processing layers being fabricated in a substrate.

17. The method of claim 11 , further comprising:

sending at least a portion of the output signal from an output interface of the plurality of processing layers back to an input interface of the plurality of processing layers as a new input signal for the plurality of processing layers.

18. The method of claim 11 , further comprising:

measuring a photon number of each optical mode from the plurality of optical modes in the output signal.

19. The method of claim 11 ,

wherein the controller is operatively coupled to: (i) each beamsplitter and phase shifter from the network of interconnected beamsplitters and phase shifters; (ii) each squeezer from the plurality of squeezers; and (iii) each nonlinear gate from the plurality of nonlinear gates.