Methods and apparatus for decomposition to account for imperfect beamsplitters

1. A method, comprising:

identifying at least one imperfection associated with an N-mode interferometer that includes at least one beamsplitter, N being a positive integer value, by:

for each beamsplitter from the at least one beamsplitter:

causing that beamsplitter to be set to a cross state,

causing each remaining beamsplitter from the plurality of beamsplitters to be set to a bar state,

causing light to be incident at an input port of that beamsplitter, and

causing a light intensity to be measured at each output port of that beamsplitter; and

calculating the at least one imperfection based on the measured light intensities;

identifying, via a processor and based on a representation of the N-mode interferometer and a representation of the at least one imperfection, (1) a plurality of two mode interferometers, and (2) a plurality of phases, the plurality of two-mode interferometers and the plurality of phases configured to apply a unitary transformation to an input signal; and

sending a signal to cause at least one of storage or display of a representation of the plurality of two-mode interferometers and a representation of the plurality of phases.

2. The method of claim 1 , wherein the N-mode interferometer is a linear optical interferometer.

3. The method of claim 1 , wherein the at least one imperfection includes a splitting ratio that is different from a desired splitting ratio.

4. The method of claim 1 , further comprising implementing the plurality of two-mode interferometers using a plurality of optical components.

5. The method of claim 1 , wherein the at least one imperfection is a plurality of imperfections, the method further comprising identifying the plurality of imperfections by:

calculating a plurality of expected light intensities for the N-mode interferometer based on a first plurality of estimated splitting ratios;

causing light to be incident at an input port of the N-mode interferometer, the N-mode interferometer configured to implement a fixed unitary operator;

causing a light intensity to be measured at each output port of the N-mode interferometer, to produce a plurality of measured light intensities;

comparing the plurality of measured light intensities to the plurality of expected light intensities; and

iteratively estimating additional pluralities of splitting ratios and associated expected light intensities, based on the comparing, to identify a plurality of splitting ratios having associated expected light intensities that are closest to the measured light intensities, the plurality of imperfections including the plurality of splitting ratios having associated expected light intensities that are closest to the plurality of measured light intensities.

6. The method of claim 1 , wherein the identifying the plurality of two-mode interferometers includes performing a decomposition of the unitary transformation.

7. The method of claim 1 , wherein the identifying the plurality of two-mode interferometers includes performing a decomposition of the unitary transformation, the decomposition based on a measured reflectivity value of a beamsplitter from the at least one beamsplitter included in the N-mode interferometer.

8. The method of claim 1 , wherein the identifying the plurality of two-mode interferometers includes sequentially nulling elements of a matrix of the unitary transformation to produce a diagonal matrix and inverting the diagonal matrix.

9. The method of claim 1 , wherein the plurality of two-mode interferometers is configured to implement the unitary transformation with balanced optical losses.

10. The method of claim 1 , wherein each two-mode interferometer from the plurality of two-mode interferometers is an imperfect Mach-Zehnder interferometer.

11. The method of claim 1 , further comprising receiving, at the processor and prior to the identifying the plurality of two-mode interferometers and the plurality of phases, a signal representing a user selection of the unitary transformation.

12. A system, comprising:

a processor; and

a memory storing instructions to cause the processor to:

identify at least one imperfection associated with a linear optical interferometer that includes at least one beamsplitter, by:

for each beamsplitter from the at least one beamsplitter:

causing that beamsplitter to be set to a cross state,

causing each remaining beamsplitter from the plurality of beamsplitters to be set to a bar state,

causing light to be incident at an input port of that beamsplitter, and

causing a light intensity to be measured at each output port of that beamsplitter; and

calculating the at least one imperfection based on the measured light intensities;

identify a plurality of two-mode interferometers based on a representation of the linear optical interferometer and a representation of at least one splitting ratio;

identify a plurality of phases based on the representation of the linear optical interferometer and the representation of the at least one splitting ratio; and

send a signal at least one of: (1) to a chip for implementation of the plurality of two-mode interferometers; or (2) to cause display, via a graphical user interface, of a representation of the plurality of two-mode interferometers and a representation of the plurality of phases, the plurality of two-mode interferometers and the plurality of phases configured to apply a unitary transformation to an input signal.

13. The system of claim 12 , wherein the instructions to cause the processor to identify the plurality of two-mode interferometers include instructions to perform a decomposition of the unitary transformation.

14. The system of claim 12 , wherein the instructions to cause the processor to identify the plurality of two-mode interferometers include instructions to perform a decomposition of the unitary transformation, the decomposition based on a measured reflectivity value of a beamsplitter from the at least one beamsplitter included in the linear optical interferometer.

15. The system of claim 12 , wherein the instructions to cause the processor to identify the plurality of two-mode interferometers include instructions to (1) sequentially null elements of the unitary transformation to produce a diagonal matrix, and (2) invert the diagonal matrix.

16. The system of claim 12 , wherein each two-mode interferometer from the plurality of two-mode interferometers is an imperfect Mach-Zehnder interferometer.

17. The system of claim 12 , wherein the memory further stores instructions to cause the processor to identify a plurality of imperfections by:

calculating a plurality of expected light intensities for the linear optical interferometer based on a first plurality of estimated splitting ratios;

causing light to be incident at an input port of the linear optical interferometer;

causing a light intensity to be measured at each output port of the linear optical interferometer, to produce a plurality of measured light intensities;

comparing the plurality of measured light intensities to the plurality of expected light intensities; and

iteratively estimating additional pluralities of splitting ratios and associated expected light intensities, based on the comparison, to identify a plurality of splitting ratios having associated expected light intensities that are closest to the measured light intensities, the plurality of imperfections including the plurality of splitting ratios having associated expected light intensities that are closest to the measured light intensities.

18. The system of claim 12 , wherein the memory further stores instructions to cause the processor to receive a signal representing a user selection of the unitary transformation.