Methods, systems, and apparatus for programmable quantum photonic processing

A method of performing quantum information processing, the method comprising:

• (A) coupling at least one optical mode into a plurality of input waveguides of a plurality of interconnected Mach-Zehnder interferometers fabricated in a semiconductor substrate so as to perform an arbitrary unitary optical transformation on the at least one optical mode;
• (B) detecting the at least one optical mode at a plurality of output waveguides of the plurality of interconnected Mach-Zehnder interferometers;
• (C) determining a density distribution of the at least one optical mode across the plurality of the output waveguides;
• and
• (D) adjusting a phase setting of at least one Mach-Zehnder interferometers in the plurality of interconnected Mach-Zehnder interferometers so as to change the density distribution of the at least one optical mode.

A photonic integrated circuit for performing quantum information processing, the photonic integrated circuit comprising:

• a semiconductor substrate;
• a plurality of interconnected Mach-Zehnder interferometers, fabricated in the semiconductor substrate, to perform at least one linear optical transformation on a plurality of optical modes coupled into the plurality of interconnected Mach-Zehnder interferometers, at least one Mach-Zehnder interferometer in the plurality of interconnected Mach-Zehnder interferometers comprising a heater operably coupled to an output arm of the at least one Mach-Zehnder interferometer;
• a plurality of detectors, in optical communication with the plurality of Mach-Zehnder interferometers, to measure the plurality of optical modes at a plurality of output waveguides of the plurality of interconnected Mach-Zehnder interferometers;
• control circuitry, operably coupled to the plurality of interconnected Mach-Zehnder interferometers and to the plurality of detectors, to determine a density distribution of the plurality of optical modes at the plurality of output waveguides and to adjust a temperature of the heater in the at least one Mach-Zehnder interferometer so as to change the density distribution of the plurality of optical modes at the plurality of output waveguides;
• and
• at least one feedback loop, in optical communication with the plurality of interconnected Mach-Zehnder interferometers, to guide at least one optical mode from at least one output waveguide in the plurality of output waveguides to an input of the plurality of interconnected Mach-Zehnder interferometers.