Methods and apparatus for mitigating imperfections in optical circuits

1. A method, comprising:

configuring a first plurality of beamsplitters in a network of interconnected beamsplitters of an optical circuit into a transmissive state, the optical circuit configured to perform a linear transformation of N input optical modes, N being a positive integer, the first plurality of beamsplitters being located along a beam path within the optical circuit and traversing a target location, the target location identifying an imperfection in the optical circuit; and

configuring a second plurality of beamsplitters in the network of interconnected beamsplitters of the optical circuit into a reflective state to reconfigure the optical circuit into a reconfigured optical circuit that circumvents the imperfection, the second plurality of beamsplitters being located along at least one edge of the optical circuit,

wherein the first plurality of beamsplitters and the second plurality of beamsplitters define a region of the optical circuit, the region includes the target location, and the reconfigured optical circuit is configured to perform a linear transformation on M input optical modes independent of the region, M being a positive integer less than N.

2. The method of claim 1 , wherein each beamsplitter in the network of interconnected beamsplitters includes a 2×2 reconfigurable beamsplitter.

3. The method of claim 1 , wherein the beam path is along a direction defined by a first end point of the optical circuit and a second end point of the optical circuit.

4. The method of claim 1 , wherein:

the beam path is along a direction defined by a first end point of the optical circuit and a second end point of the optical circuit, the beam path intersecting with a first edge of the optical circuit at a first intersection point and intersecting with a second edge of the optical circuit at a second intersection point, and

the second plurality of beamsplitters are located: (i) along the first edge of the optical circuit between the first intersection point and the first end point and (ii) along the second edge of the optical circuit between the second intersection point and the second end point.

5. The method of claim 1 , wherein M=N−1.

6. The method of claim 1 , wherein the target location is on a waveguide connecting a first beamsplitter and a second beamsplitter in the network of interconnected beamsplitters, and the beam path is along a direction defined by the first beamsplitter and the second beamsplitter, wherein the first and second beamsplitters are included in the first plurality of beamsplitters.

7. The method of claim 1 , wherein:

the target location is on a target beamsplitter in the network of interconnected beamsplitters, the target beamsplitter configured to receive a first input from a first beamsplitter and a second input from a second beamsplitter,

the beam path having a direction defined by the target beamsplitter and the first beamsplitter, wherein the first beamsplitter is included in the first plurality of beamsplitters, and the method further comprises:

configuring a third plurality of beamsplitters in the network of interconnected beamsplitters into the transmissive state, the third plurality of beamsplitters being located on a second beam path along a second direction defined by the target beamsplitter and the second beamsplitter, wherein the second beamsplitter is included in the third plurality of beamsplitters; and

configuring a fourth plurality of beamsplitters in the network of interconnected beamsplitters into the reflective state, the fourth plurality of beamsplitters being located along at least one edge of the optical circuit,

wherein the region is further defined by the third plurality of beamsplitters and the fourth plurality of beamsplitters.

8. The method of claim 1 , wherein the imperfection identified by the target location includes a defect of the optical circuit.

9. The method of claim 1 , wherein the imperfection identified by the target location includes an unresponsive optical component.

10. The method of claim 1 , wherein the reconfigured optical circuit is a first reconfigured optical circuit and the region is a first region, the method further comprising:

configuring a third plurality of beamsplitters in the network of interconnected beamsplitters of the optical circuit into a fixed setting to reconfigure the first reconfigured optical circuit into a second reconfigured optical circuit that defines a second region different from the first region, the second reconfigured optical circuit configured to perform a linear transformation of (N-n) input optical modes, n being a number of mitigated imperfections.

11. The method of claim 10 , wherein the imperfection is a first imperfection, and the second reconfigured optical circuit circumvents a second imperfection different from the first imperfection.

12. An apparatus, comprising:

N input ports, N being a positive integer; and

a network of interconnected beamsplitters in optical communication with the N input ports, the network of interconnected beamsplitters including:

a first plurality of beamsplitters located along a beam path traversing a target location and configured into a transmissive state, the target location identifying an imperfection in the network of interconnected beamsplitters;

a second plurality of beamsplitters located along at least one edge of the network of interconnected beamsplitters and configured into a reflective state, the first plurality of beamsplitters and the second plurality of beamsplitters defining a region of the network of interconnected beamsplitters, the region including the target location, and the first plurality of beamsplitters and the second plurality of beamsplitters circumventing the imperfection; and

a third plurality of beamsplitters that are reconfigurable and configured to perform a linear transformation on M input optical modes independent of the region, M being a positive integer less than N.

13. The apparatus of claim 12 , wherein the third plurality of beamsplitters does not include any beamsplitter from the first plurality of beamsplitters and the second plurality of beamsplitters.

14. The apparatus of claim 12 , wherein each beamsplitter in the network of interconnected beamsplitters includes a 2×2 reconfigurable beamsplitter.

15. The apparatus of claim 12 , wherein the beam path is along a direction defined by a first end point of the optical circuit and a second end point of the network of interconnected beamsplitters.

16. The apparatus of claim 12 , wherein:

the beam path is along a direction defined by a first end point of the network of interconnected beamsplitters and a second end point of the network of interconnected beamsplitters, the beam path intersecting with a first edge of the network of interconnected beamsplitters at a first intersection point and intersecting with a second edge of the network of interconnected beamsplitters at a second intersection point, and

the second plurality of beamsplitters are located: (i) along the first edge of the network of interconnected beamsplitters between the first intersection point and the first end point and (ii) along the second edge of the network of interconnected beamsplitters between the second intersection point and the second end point.

17. The apparatus of claim 12 , wherein M=N−1.

18. The apparatus of claim 12 , wherein the target location is on a waveguide connecting a first beamsplitter and a second beamsplitter in the network of interconnected beamsplitters, and the beam path is along a direction defined by the first beamsplitter and the second beamsplitter, wherein the first and second beamsplitters are included in the first plurality of beamsplitters.

19. An apparatus, comprising:

a plurality of input ports; and

a plurality of interconnected beamsplitters in optical communication with the plurality of input ports, the plurality of interconnected beamsplitters including:

a first plurality of beamsplitters located along a beam path traversing a target location and configured into a transmissive state, the target location identifying an imperfection in the plurality of interconnected beamsplitters;

a second plurality of beamsplitters located along at least one edge of the plurality of interconnected beamsplitters and configured into a reflective state, the first plurality of beamsplitters and the second plurality of beamsplitters defining a region of the plurality of interconnected beamsplitters, the region including the target location, and the first plurality of beamsplitters and the second plurality of beamsplitters circumventing the imperfection; and

a third plurality of beamsplitters configured to perform a linear transformation on a plurality of input optical modes independent of the region.

20. The apparatus of claim 19 , wherein the third plurality of beamsplitters does not include any beamsplitter from the first plurality of beamsplitters and the second plurality of beamsplitters.

21. The apparatus of claim 19 , wherein at least one beamsplitter from the plurality of interconnected beamsplitters includes a reconfigurable beamsplitter.

22. The apparatus of claim 19 , wherein at least one beamsplitter from the plurality of interconnected beamsplitters includes a 2×2 reconfigurable beamsplitter.

23. The apparatus of claim 19 , wherein one of:

the target location is on a waveguide connecting a first beamsplitter and a second beamsplitter in the plurality of interconnected beamsplitters, or

the beam path is along a direction defined by a first beamsplitter and a second beamsplitter connected by a waveguide containing the target location, wherein the first and second beamsplitters are included in the first plurality of beamsplitters.