1536-125X (c) 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TNANO.2019.2941763, IEEE Transactions on Nanotechnology > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 1536-125X © 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications standards/publications/rights/index.html for more information. 1 Abstract—One of the most promising and powerful candidates for future computing is the notion of universal quantum computer. A vital advance towards this direction is the development of quantum simulators and their possible implementation either as standalone quantum systems or as compatible software for classical computers with pros and cons. On the other hand, memristive computing has been proposed recently as a tentative unconventional computing scheme promoting the idea of information storage and processing in the same nanoelectronic device. In this paper we present a memristive quantum computing simulator by coupling quantum simulation principles with memristor aspects and enabling us to tackle the existing difficulties on qubit representation in conventional computing systems. For doing so, we utilize the memristances of identical memristors to represent in 3D the qubit state while its corresponding evolution is defined by the memristors input voltages. In particular, we introduce an appropriate correspondence among the aforementioned memristor voltages and the general qubit state rotation, i.e. the one-qubit quantum gates, and as such we reproduce the rotations imposed by the action of quantum gates in the 3D memristance space. Moreover, we also define the action of the CNOT two-qubit gate and simulate entanglement between two qubits paving the way towards the establishment of a universal set for quantum computing. Our results show that, memristor circuits can simulate effectively quantum computations. Index Terms—Quantum simulators, Memristors, Qubits, Nanoelectronics. I. INTRODUCTION OWADAYS one of the major and utter importance research quests is the future computing challenge and how to advance the state of the art going beyond von Neumann classical computing architectures and beyond CMOS era. Quantum computing is presented as strong and promising candidate to respond to this challenge through the urgently requesting implementation of universal quantum computers. Such universal quantum computers originally proposed by Manin [1] and Feynman [2] and later advanced by Deutsch [3], use quantum-mechanical phenomena to perform computations by the utilization of the quantum properties of state superposition and entanglement; more important, these exact computations are intractable by classical computers [4]. As a result, when available, universal quantum computers will reduce the computational complexity of presently intractable problems and run quantum algorithms. This may lead to disruptive new technologies, such as the development of new Ioannis G. Karafyllidis and Georgios Ch. Sirakoulis are with the Department of Electrical and Computer Engineering, Democritus University of Thrace, 67100 Kimmeria, Xanthi, Greece (emails: ykar@ee.duth.gr, gsirak@ee.duth.gr) functionalized materials, artificial intelligence, handling of big data, discovery of new drugs and optimization of systems and processes, just to name a few [5]. Till this moment, i.e. when universal quantum computers will be fully available for the masses, the development of quantum simulators [6, 7] seems a sine qua non condition. The quantum simulators proposed so far can be categorized as follows: (i) a small number of controllable quantum systems using photonic devices [8], superconducting circuits [9], molecular nanomagnets [10], and ion trapping [11] developed to perform quantum computations with, however, a restricted number of quantum bits (qubits), and (ii) software-based quantum simulators that execute quantum algorithms with several qubits on classical computers [12-15]. As a possible alternative, the digital implementation of quantum simulators through suitable digital circuitry, like FPGAs devices, could be also considered. Nevertheless, an inherent disadvantage of such an implementation arrives from the fact that qubits can assume practically an infinite number of non-basis states, in contrast to the two states of classical bits. Many-qubit quantum computations use multi-dimensional Hilbert spaces which demand large matrices, which in turn causes exponential slowdown [2]. As another tentative counterpart, an analog, i.e. analog electronic circuits comprising passive elements, implementation of quantum simulators can potentially represent the infinite qubit states; however, such an approach lacks state variables, which should be internal, that will both retain the qubit state for long computation times and determine the evolution of qubit states by the action of quantum gates during computations. In order to overcome the aforementioned difficulties, we propose the usage of novel nanoelectronics devices, namely memristors, for representing qubit states and, moreover, to simulate adequately the quantum gate functions when evolving qubit states during quantum computing. Memristor, theoretically conceived by Leon Chua in 1971 [16] and later re- introduced by the Hewlett Packard Labs invention in 2008 [17] demonstrate many promising features, such as analog nature, non-volatility, plasticity together with low power consumption, high density, and excellent scalability. All these properties characterize memristors as an emerging trend in today electronics with plentiful applications in a vast number of applications in various scientific fields [18-23]. While the recent research is also focusing on the concept of quantum Panagiotis Dimitrakis is with the Institute of Nanoscience and Nanotechnology, NCSR “Demokritos”, 15 310 Aghia Paraskevi, Athens, Greece (email: p.dimitrakis@inn.demokritos.gr) Memristive Quantum Computing Simulator Ioannis G. Karafyllidis * , Georgios Ch. Sirakoulis, Member, IEEE, and Panagiotis Dimitrakis, Senior Member, IEEE N