We propose a method to build quantum memristors in quantum photonic platforms. We first design an effective beam splitter, which is tunable in real time, by means of a Mach-Zehnder-type array with two equal 50:50 beam splitters and a tunable retarder, which allows us to control its reflectivity. Then, we show that this tunable beam splitter, when equipped with weak measurements and classical feedback, behaves as a quantum memristor. Indeed, in order to prove its quantumness, we show how to codify quantum information in the coherent beams. Moreover, we estimate the memory capability of the quantum memristor. Finally, we show the feasibility of the proposed setup in integrated quantum photonics.
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