Abstract
A quantum memristor is a passive resistive circuit element with memory, engineered in a given quantum platform. It can be represented by a quantum system coupled to a dissipative environment, in which a system–bath coupling is mediated through a weak measurement scheme and classical feedback on the system. In quantum photonics, such a device can be designed from a beam splitter with tunable reflectivity, which is modified depending on the results of measurements in one of the outgoing beams. Here, we show that a similar implementation can be achieved with frequency-entangled optical fields and a frequency mixer that, working similarly to a beam splitter, produces state superpositions. We show that the characteristic hysteretic behavior of memristors can be reproduced when analyzing the response of the system with respect to the control, for different experimentally attainable states. Since memory effects in memristors can be exploited for classical and neuromorphic computation, the results presented in this work could be a building block for constructing quantum neural networks in quantum photonics, when scaling up.
Highlights
Memory circuit elements are poised to introduce a new paradigm in both classical and quantum computation [1,2,3,4,5]
We study a different implementation of a quantum memristor in a quantum photonics setup
The required non-Markovian dynamics is achieved by inserting a detector in one of the outcomes of the beam splitter and, via a feedback mechanism, changing the reflectivity of the beam splitter
Summary
Memory circuit elements are poised to introduce a new paradigm in both classical and quantum computation [1,2,3,4,5] Due to their dependence on previous dynamics, it seems fitting to exploit their passive storage capabilities for enhancement of information processing and for neuromorphic computing tasks. It describes a resistive element of an electric circuit that has memory, with a changing resistance whose instantaneous value depends on the history of signals that have crossed the device This information is codified in the internal variable of the memristor, μ, introducing a state-dependent Ohm’s law. Attempting to solve Equation (2) requires time integration over the past of the control signal This means that the current response given by the voltage-controlled memristor described in Equation (1) depends, through G (μ), on previous values of the control voltage, as well as on the present one. A memristor that undergoes a periodic control signal will display a hysteresis loop when plotting the response versus the control signal
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