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IEEE/ACM International Symposium on Nanoscale Architectures (NANOARCH)

Representation of Qubit States using 3D Memristance Spaces

Ioannis G. Karafyllidis, Georgios Ch. Sirakoulis, Panagiotis Dimitrakis

Published Jul 17, 2018• 4 citations
Publisher

Abstract

Development of quantum simulators is a major step towards the universal quantum computer. Quantum simulators are quantum systems that can perform specific quantum computations, or software packages that can reproduce most of the aspects of a general universal quantum computer on a general purpose classical computer. Development of quantum simulators using digital circuits, such as FPGAs is very difficult, mainly because the unit of quantum information, the qubit, has an infinite number of states, whereas the classical bit has only two. On the other hand, analog circuits comprising R, L and C elements have no internal state variables that can be used to reproduce and store qubit states. Here we take the first step towards the development of a new quantum simulator using memristors. The qubit state is mapped to a 3D space spanned by the memristances of three identical memristors. The qubit state evolution is reproduced by the input voltages applied to the memristors. We define the correspondence between the general qubit state rotation, i.e. the one-qubit quantum gates, and memristor input voltage variations and reproduce the rotations imposed by the action of quantum gates in the 3D memristance space. Our results show that, at least in principle, qubits and one-qubit quantum gates can be simulated by memristors.

DOI
10.1145/3232195.3232197

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Development of quantum simulators is a major step towards the universal quantum computer. Quantum simulators are quantum systems that can perform specific quantum computations, or software packages that can reproduce most of the aspects of a general universal quantum computer on a general purpose classical computer. Development of quantum simulators using digital circuits, such as FPGAs is very difficult, mainly because the unit of quantum information, the qubit, has an infinite number of states, whereas the classical bit has only two. On the other hand, analog circuits comprising R, L and C elements have no internal state variables that can be used to reproduce and store qubit states. Here we take the first step towards the development of a new quantum simulator using memristors. The qubit state is mapped to a 3D space spanned by the memristances of three identical memristors. The qubit state evolution is reproduced by the input voltages applied to the memristors. We define the correspondence between the general qubit state rotation, i.e. the one-qubit quantum gates, and memristor input voltage variations and reproduce the rotations imposed by the action of quantum gates in the 3D memristance space. Our results show that, at least in principle, qubits and one-qubit quantum gates can be simulated by memristors.
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.
Over the last years there has been significant progress in the development of quantum computers. It has been demonstrated that they can accelerate the solution of various problems exponentially compared to today's classical computers, harnessing the properties of superposition and entanglement, two resources that have no classical analog. Since quantum computer platforms that are currently available comprise only a few tenths of qubits, as well as the access to a fabricated quantum computer is time limited for the majority of researchers, the use of quantum simulators is essential in developing and testing new quantum algorithms. Taking inspiration from previous work on developing a novel quantum simulator based on memristor crossbar circuits, in this work, a framework that automates the circuit design of emulated quantum gates is presented. The proposed design framework deals with the generation and programming of memristor crossbar configuration that incorporates the desirable quantum circuit, leading to a technology agnostic design tool. To such a degree, various quantum gates can be efficiently emulated on memristor crossbar configurations for various types of memristive devices, aiming to assist and accelerate the fabrication process of a memristor based quantum simulator.
We propose the encoding of memristive quantum dynamics on a digital quantum computer. Using a set of auxiliary qubits, we simulate an effective non-Markovian environment inspired by a collisional model, reproducing memristive features between expectation values of different operators in a single qubit. We numerically test our proposal in an IBM quantum simulator with 32 qubits, obtaining a pinched hysteresis curve that characterizes our quantum memristor model. Furthermore, we extend our method to the case of two coupled quantum memristors, opening the door to the study of neuromorphic quantum computing in the current noisy devices.
Quantum computing and quantum computers are a major part of the second quantum revolution. Existing quantum algorithms can natively solve complex problems, such as the prime number factorization and searching of unstructured databases, in a fast and efficient way. The main obstacle towards building large and efficient quantum computers is decoherence, which produces errors that have to be continuously corrected using quantum error correcting codes. Beyond the realisation of quantum computing systems with actual quantum hardware, quantum algorithms have been developed based on quantum logic gates that can be described and utilised by classical computers and proper interfaces based on linear algebra operations. Furthermore, memristive grids have been proposed as novel nanoscale and low-power hardware accelerators for the time-consuming matrix-vector multiplication and tensor products. In this work, given that for quantum computations simulation, the matrix-vector multiplication is the dominant algebraic operation, we utilize the unprecedented characteristics of memristive grids to implement circuit-level quantum computations. Since all quantum computations can be mapped to quantum circuits, memristive grids can also be used as efficient quantum simulators, as classical/quantum interfaces and also as accelerators in mixed classical-quantum computing systems.
There is a growing interest in quantum computers and quantum algorithm development. It has been proved that ideal quantum computers, with zero error rates and large decoherence times, can solve problems that are intractable for today’s classical computers. Quantum computers use two resources, superposition and entanglement, that have no classical analog. Since quantum computer platforms that are currently available comprise only a few dozen of qubits, the use of quantum simulators is essential in developing and testing new quantum algorithms. We present a novel quantum simulator based on memristor crossbar circuits and use them to simulate well-known quantum algorithms, namely the Deutsch and Grover quantum algorithms. In quantum computing the dominant algebraic operations are matrix-vector multiplications. The execution time grows exponentially with the simulated number of qubits, causing an exponential slowdown in quantum algorithm execution using classical computers. In this work, we show that the inherent characteristics of memristor arrays can be used to overcome this problem and that memristor arrays can be used not only as independent quantum simulators but also as a part of a quantum computer stack where classical computers accelerators are connected. Our memristive crossbar circuits are re-configurable and can be programmed to simulate any quantum algorithm.
One of the major approaches to spike-based neuromorphic computing is using memristors as analog synapses.We propose unitary quantum gates that exhibit memristive behaviors, including Ohm's law, pinched hysteresis loop and synaptic plasticity.Hysteresis depending on the quantum phase and long-term plasticity that encodes the quantum state are observed.We also propose a three-layer neural network with the capability of universal quantum computing.Quantum state classification on the memristive neural network is demonstrated.These results pave the way towards quantum spiking neural network built on unitary processes.We obtain these results in numerical simulations and experiments on the superconducting quantum computer ibmq_vigo.