A quantum memristor combines the memristive dynamics with the quantum behavior of the system. We analyze the idea of a quantum memristor based on ultracold ions trapped in a Paul trap. Corresponding input and output memristor signals are the ion electronic levels populations. We show that under certain conditions the output/input dependence is a hysteresis curve similar to classical memristive devices. This behavior becomes possible due to the partial decoherence provided by the feedback loop, which action depends on previous state of the system (memory). The feedback loop also introduces nonlinearity in the system. Ion-based quantum memristor possesses several advantages comparing to other platforms-photonic and superconducting circuits-due to the presence of a large number of electronic levels with different lifetimes as well as strong Coulomb coupling between ions in the trap. The implementation of the proposed ion-based quantum memristor will be a significant contribution to the novel direction of "quantum neural networks".
A quantum memristor combines the memristive dynamics with the quantum behavior of the system. We analyze the idea of a quantum memristor based on ultracold ions trapped in a Paul trap. Corresponding input and output memristor signals are the ion electronic levels populations. We show that under certain conditions the output/input dependence is a hysteresis curve similar to classical memristive devices. This behavior becomes possible due to the partial decoherence provided by the feedback loop, which action depends on previous state of the system (memory). The feedback loop also introduces nonlinearity in the system. Ion-based quantum memristor possesses several advantages comparing to other platforms-photonic and superconducting circuits-due to the presence of a large number of electronic levels with different lifetimes as well as strong Coulomb coupling between ions in the trap. The implementation of the proposed ion-based quantum memristor will be a significant contribution to the novel direction of "quantum neural networks".
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.
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.
Memristors are resistive elements retaining information of their past dynamics. They have garnered substantial interest due to their potential for representing a paradigm change in electronics, information processing and unconventional computing. Given the advent of quantum technologies, a design for a quantum memristor with superconducting circuits may be envisaged. Along these lines, we introduce such a quantum device whose memristive behavior arises from quasiparticle-induced tunneling when supercurrents are cancelled. For realistic parameters, we find that the relevant hysteretic behavior may be observed using current state-of-the-art measurements of the phase-driven tunneling current. Finally, we develop suitable methods to quantify memory retention in the system.
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.
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.
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.