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arXiv:2107.05306 · Physical Review A

Entangled quantum memristors

Shubham Kumar, F. A. Cárdenas-López, Narendra N. Hegade, Xi Chen, F. Albarrán-Arriagada, E. Solano, G. Alvarado Barrios

Published Dec 6, 2021• 17 citations
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Abstract

We propose the interaction of two quantum memristors via capacitive and inductive coupling in feasible superconducting circuit architectures. In this composed system the input gets correlated in time, which changes the dynamic response of each quantum memristor in terms of its pinched hysteresis curve and nontrivial entanglement. In this sense, the concurrence and memristive dynamics follow an inverse behavior, showing maximal values of entanglement when the hysteresis curve is minimal and vice versa. Moreover, the direction followed in time by the hysteresis curve is reversed whenever the quantum memristor entanglement is maximal. The study of composed quantum memristors paves the way for developing neuromorphic quantum computers and native quantum neural networks, on the path towards quantum advantage with current noisy intermediate-scale quantum era technologies.

DOI
10.1103/physreva.104.062605

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We propose the interaction of two quantum memristors via capacitive and inductive coupling in feasible superconducting circuit architectures. In this composed system the input gets correlated in time, which changes the dynamic response of each quantum memristor in terms of its pinched hysteresis curve and nontrivial entanglement. In this sense, the concurrence and memristive dynamics follow an inverse behavior, showing maximal values of entanglement when the hysteresis curve is minimal and vice versa. Moreover, the direction followed in time by the hysteresis curve is reversed whenever the quantum memristor entanglement is maximal. The study of composed quantum memristors paves the way for developing neuromorphic quantum computers and native quantum neural networks, on the path towards quantum advantage with current noisy intermediate-scale quantum era technologies.
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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.
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.
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.
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.