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LOv-Calculus: A Graphical Language for Linear Optical Quantum Circuits
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We introduce the LOv-calculus, a graphical language for reasoning about linear optical quantum circuits with so-called vacuum state auxiliary inputs. We present the axiomatics of the language and prove its soundness and completeness: two LOv-circuits represent the same quantum process if and only if one can be transformed into the other with the rules of the LOv-calculus. We give a confluent and terminating rewrite system to rewrite any polarisation-preserving LOv-circuit into a unique triangular normal form, inspired by the universal decomposition of Reck et al. (1994) for linear optical quantum circuits.
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Resource-efficient crosstalk mitigation for the high-fidelity operation of photonic integrated circuits with induced phase shifters
Crosstalk in photonic circuits is better modeled by adding parasitic phase shifters on bare waveguides, and a circuit can cancel all such crosstalk exactly if and only if a certain pruned graph is acyclic.
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