This device exhibits rich nonlinear properties and it is distinguished by a pinched hysteresis curve in the current-voltage (I/V) plane, which can be described by Kubo's response theory [3]. Since the experimental implementation of a memristor in a doped semiconductor by HP Labs in 2008 [4], memristors have garnered significant interest in several areas, including analog computing [5] and neuromorphic computing [6]. A notable application of memristors is the design of devices that mimic biological neural synapses [7] and neural networks [8]. Furthermore, memristor-enabled neuromorphic computing goes beyond the traditional von Neumann computing paradigm, avoiding the von Neumann bottleneck, which is one of the fundamental limitations of current classical computers [9, 10, 11]. Quantum computing [12] aims to revolutionize computation by exploiting exclusively quantum phenomena to surpass the capabilities of classical computers, as we can see from recent breakthroughs [13, 14, 15, 16, 17].

This article gives an overview and a perspective of recent theoretical proposals and their experimental implementations in the field of quantum machine learning. Without an aim to being exhaustive, the article reviews specific high-impact topics such as quantum reinforcement learning, quantum autoencoders, and quantum memristors, and their experimental realizations in the platforms of quantum photonics and superconducting circuits. The field of quantum machine learning could be among the first quantum technologies producing results that are beneficial for industry and, in turn, to society. Therefore, it is necessary to push forward initial quantum implementations of this technology, in Noisy Intermediate-Scale Quantum Computers, aiming for achieving fruitful calculations in machine learning that are better than with any other current or future computing paradigm.

At the heart of all artificial intelligence applications are mathematical models called neural networks. These models are inspired by the biological structure of the human brain, made of interconnected nodes. Just like our brain learns by constantly rearranging the connections between neurons, neural networks can be mathematically trained by tuning their internal structure until they become capable of human-level tasks: recognizing our face, interpreting medical images for diagnosis, even driving our cars. Having integrated devices capable of performing the computations involved in neural networks quickly and efficiently has thus become a major research focus, both academic and industrial. One of the major game changers in the field was the discovery of the memristor, made in 2008.

IKERBASQUE, Basque F oundation for Science, Mar ıa D ıaz de Haro 3, E-48013 Bilbao, Spain We propose a method to build quantum memristors in quantum photonic platforms. We firstly 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.