Academic paper: Certain properties and applications of shallow bosonic circuits

ORCA Computing’s Kamil Bradler and Hugo Wallner introduce a novel approach to solving optimization problems on a boson sampling device assisted by classical machine-learning techniques. By virtue of the parity function, they map all measurement patterns, which label the basis spanning an M-mode bosonic Hilbert space, to the Hilbert space of M qubits. As a result, the sampled probability function can be interpreted as a result of sampling a multiqubit circuit. The method is presented on several instances of a QUBO/Ising problem as well as portfolio optimization problems.

Among many demonstrated properties of the parity function is the ability to chart the entire qubit Hilbert space no matter how shallow the initial bosonic circuit is. In order to show this, boson sampling circuits are linked to a class of finite Young’s lattices (a special poset with the so-called Ferrers diagrams ordered by inclusion), Boolean lattices and the properties of Dyck/staircase paths on integer lattices. The results and methods can be applied to a large variety of photonic circuits, including the deep ones of essentially any geometry, but the main focus is on shallow circuits as they are less affected by photon loss and relatively easy to implement in the form of a time-bin interferometer.

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