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arXiv:1709.07808 · APL Photonics

Invited Article: Quantum memristors in quantum photonics

M. Sanz, L. Lamata, E. Solano

Published Jun 20, 2018• 57 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1063/1.5036596

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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.
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.
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.
Technology based on memristors, resistors with memory whose resistance depends on the history of the crossing charges, has lately enhanced the classical paradigm of computation with neuromorphic architectures. However, in contrast to the known quantized models of passive circuit elements, such as inductors, capacitors or resistors, the design and realization of a quantum memristor is still missing. Here, we introduce the concept of a quantum memristor as a quantum dissipative device, whose decoherence mechanism is controlled by a continuous-measurement feedback scheme, which accounts for the memory. Indeed, we provide numerical simulations showing that memory effects actually persist in the quantum regime. Our quantization method, specifically designed for superconducting circuits, may be extended to other quantum platforms, allowing for memristor-type constructions in different quantum technologies. The proposed quantum memristor is then a building block for neuromorphic quantum computation and quantum simulations of non-Markovian systems.
We propose a quantum beam splitter (QBS) with tunable reflection and transmission coefficients. More importantly, our device based on a Hermitian parity-time (PT\mathcal{PT}PT) symmetric system enables the generation and manipulation of asymmetric quantum coherence of the output photons. For the interference of two weak coherent-state inputs, our QBS can produce anti-bunched photons from one output port and bunched photons from the other, showcasing high parity asymmetry and strong coherence control capabilities. Beyond the Hong-Ou-Mandel effect, perfect photon blockade with vanishing g(2)(0)g^{(2)}(0)g(2)(0) is achievable in two-photon interference. These striking effects of the QBS fundamentally arise from the parity-symmetry-breaking interaction and the quantum interference between the photon scattering channels. Our results could inspire novel applications and the development of innovative photonic devices for the manipulation of weak quantum light.
We theoretically demonstrate that a photonic crystal microcavity coupled to waveguides works as an optical beam splitter. Numerical simulations illustrate that spatially separated two output modes have a relative phase close to $\ensuremath{\pi}/2$ and tunable transmission coefficients. The general transformation of this beam splitter gives a single-qubit rotation operator about the xxx axis. Using such beam splitters, we show single-photon interference via the Mach-Zehnder interferometer and two-photon entanglement via Hong-Ou-Mandel effect. This system may have great applications in constructing interferometers and integrated circuits for optical quantum information processing with solid-state materials.