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Further compactifying linear optical unitaries
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DOI：10.1063/5.0053421.png)
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Abstract
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Quantum integrated photonics requires large-scale linear optical circuitry, and for many applications, it is desirable to have a universally programmable circuit, able to implement an arbitrary unitary transformation on a number of modes. This has been achieved using the Reck scheme, consisting of a network of Mach-Zehnder interferometers containing a variable phase shifter in one path as well as an external phase shifter after each Mach-Zehnder. It subsequently became apparent that with symmetric Mach-Zehnders containing a phase shifter in both paths, the external phase shifters are redundant, resulting in a more compact circuit. The rectangular Clements scheme improves on the Reck scheme in terms of circuit depth, but it has been thought that an external phase-shifter was necessary after each Mach-Zehnder. Here, we show that the Clements scheme can be realized using symmetric Mach-Zehnders, requiring only a small number of external phase-shifters that do not contribute to the depth of the circuit. This will result in a significant saving in the length of these devices, allowing more complex circuits to fit onto a photonic chip, and reducing the propagation losses associated with these circuits. We also discuss how similar savings can be made to alternative schemes, which have robustness to imbalanced beam-splitters.
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