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Photonics for Quantum (PfQ)

Nonlinearity of photonic quantum memristors in high-frequency regime

Iris Agresti, Philip John Walther

Published Jul 19, 2022• 0 citations
Publisher

Abstract

Over the last decades, the combination of quantum computing and machine learning has opened many possibilities, for example enhancing machine learning algorithms through quantum platforms. However, one of the current challenges consists in combining the linear unitary evolution of closed quantum systems with the nonlinearity required by neural networks, which are currently the most widely used and versatile machine learning algorithms. This issue can now be addressed by a novel photonic tool, the quantum memristor,1 which displays a nonlinear behavior, while preserving quantum coherence, through a weak controlled interaction of its input state with the environment. Here, we show how its operation can be extended to deal with higher frequency modulations of the input and, possibly, with a simplification in its scheme. This method can prove useful for the future implementation of memristor-based quantum neural networks.

DOI
10.1117/12.2631512

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•Jan 1, 2020•5 citations
Over the last decades, the combination of quantum computing and machine learning has opened many possibilities, for example enhancing machine learning algorithms through quantum platforms. However, one of the current challenges consists in combining the linear unitary evolution of closed quantum systems with the nonlinearity required by neural networks, which are currently the most widely used and versatile machine learning algorithms. This issue can now be addressed by a novel photonic tool, the quantum memristor,1 which displays a nonlinear behavior, while preserving quantum coherence, through a weak controlled interaction of its input state with the environment. Here, we show how its operation can be extended to deal with higher frequency modulations of the input and, possibly, with a simplification in its scheme. This method can prove useful for the future implementation of memristor-based quantum neural networks.
Machine learning has recently developed novel approaches, mimicking the synapses of the human brain to achieve similarly efficient learning strategies. Such a method retains the universality of standard ones, while attempting to circumvent their excessive requirements, which hinder their scalability. In this landscape, quantum (or quantum inspired) algorithms may bring enhancement. However, high-performing neural networks invariably display nonlinear behaviors, which poses a challenge to quantum platforms, given the intrinsically linear evolution of closed systems. We propose a strategy to enhance the nonlinearity achievable in this context, without resorting to entangling gates and report the first neuromorphic architecture based on a photonic quantum memristor. In detail, we show how the memristive feedback loop enhances the nonlinearity and hence the performance of the tested algorithms. We test our model on several tasks, widely recognized to benchmark the performance of (quantum) neuromorphic models. We highlight the essential role of the quantum memristive element and demonstrate the possibility of using it as a building block in more sophisticated networks.
Quantum computer technology harnesses the features of quantum physics for revolutionizing information processing and computing. As such, quantum computers use physical quantum gates that process information unitarily, even though the final computing steps might be measurement-based or non-unitary. The applications of quantum computers cover diverse areas, reaching from well-known quantum algorithms to quantum machine learning and quantum neural networks. The last of these is of particular interest by belonging to the promising field of artificial intelligence. However, quantum neural networks are technologically challenging as the underlying computation requires non-unitary operations for mimicking the behavior of neurons. A landmark development for classical neural networks was the realization of memory-resistors, or "memristors". These are passive circuit elements that keep a memory of their past states in the form of a resistive hysteresis and thus provide access to nonlinear gate operations. The quest for realising a quantum memristor led to a few proposals, all of which face limited technological practicality. Here we introduce and experimentally demonstrate a novel quantum-optical memristor that is based on integrated photonics and acts on single photons. We characterize its memristive behavior and underline the practical potential of our device by numerically simulating instances of quantum reservoir computing, where we predict an advantage in the use of our quantum memristor over classical architectures. Given recent progress in the realization of photonic circuits for neural networks applications, our device could become a building block of immediate and near-term quantum neuromorphic architectures.
Abstract Memristive devices are a class of physical systems with history-dependent dynamics characterized by signature hysteresis loops in their input–output relations. In the past few decades, memristive devices have attracted enormous interest in electronics. This is because memristive dynamics is very pervasive in nanoscale devices, and has potentially groundbreaking applications ranging from energy-efficient memories to physical neural networks and neuromorphic computing platforms. Recently, the concept of a quantum memristor was introduced by a few proposals, all of which face limited technological practicality. Here we propose and experimentally demonstrate a novel quantum-optical memristor (based on integrated photonics) that acts on single-photon states. We fully characterize the memristive dynamics of our device and tomographically reconstruct its quantum output state. Finally, we propose a possible application of our device in the framework of quantum machine learning through a scheme of quantum reservoir computing, which we apply to classical and quantum learning tasks. Our simulations show promising results, and may break new ground towards the use of quantum memristors in quantum neuromorphic architectures.
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.
Quantum memristors represent a promising interface between quantum and neuromorphic computing, combining the nonlinear, memory-dependent behavior of classical memristors with the properties of quantum states. An optical quantum memristor can be realized with a vacuum-one-photon qubit entering a tunable beam splitter whose reflectivity is adapted according to the mean number of photons in the device. In this work, we report on the experimental implementation of a bulk quantum-optical memristor, working with single-rail coherent superposition states in the Fock basis, generated via a resonantly excited quantum dot single-photon source. We demonstrate that the coherence of the input state is preserved by the quantum memristor. Moreover, our modular platform allows investigating the nonlinear behavior arising from a cascade of two quantum memristors, a building block for larger networks of such devices toward the realization of complex neuromorphic quantum architectures.
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.