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arXiv:2201.10309 · Physical Review Applied

Tripartite Entanglement in Quantum Memristors

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

Published Sep 1, 2022• 14 citations
arXivHTMLPDF

Abstract

We study the entanglement and memristive properties of three coupled quantum memristors. We consider quantum memristors based on conductance-asymmetric superconducting quantum interference device architectures that are coupled via inductors. The three quantum memristors are arranged in two different geometries: linear and triangular coupling configurations. We obtain a variety of correlation measures, including bipartite entanglement and tripartite negativity. For identical quantum memristors, we find that entanglement and memristivity follow the same behavior for the triangular case and the opposite one in the linear case. Finally, we study the multipartite correlations with the tripartite negativity and entanglement monogamy relations, showing that our system has genuine tripartite entanglement. Our results show that quantum correlations in multipartite memristive systems have a nontrivial role and can be used to design quantum memristor arrays for quantum neural networks and neuromorphic quantum computing architectures.

DOI
10.1103/physrevapplied.18.034004

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We study the entanglement and memristive properties of three coupled quantum memristors. We consider quantum memristors based on conductance-asymmetric superconducting quantum interference device architectures that are coupled via inductors. The three quantum memristors are arranged in two different geometries: linear and triangular coupling configurations. We obtain a variety of correlation measures, including bipartite entanglement and tripartite negativity. For identical quantum memristors, we find that entanglement and memristivity follow the same behavior for the triangular case and the opposite one in the linear case. Finally, we study the multipartite correlations with the tripartite negativity and entanglement monogamy relations, showing that our system has genuine tripartite entanglement. Our results show that quantum correlations in multipartite memristive systems have a nontrivial role and can be used to design quantum memristor arrays for quantum neural networks and neuromorphic quantum computing architectures.
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.
Memristive systems exhibit dynamics that depend on their past states, making them useful as memory units. Recently, quantum memristor models have been proposed, and notably, a photonic quantum memristor (PQM) has been experimentally proven. In this work, we explore and characterize various quantum properties that emerge from this specific model of PQM. First, we find that a single PQM displays memristive dynamics on its quantum coherence. Second, we analytically show that a network made of two independent PQMs can manifest memory effects on the dynamics of both entanglement and coherence of correlated photons traveling through the network, regardless of their distance, in the hypothesis of negligible external disturbances. Additionally, we build and run a circuit-model of the PQM on a real qubit-based quantum computer (IBM-Q), showing that (1) this system can effectively be used for nonlinear quantum computing under specific conditions and (2) digital quantum simulations can reproduce the dynamics of a memristive quantum system in a non-Markovian regime.
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.
Abstract Developing the field of neuromorphic quantum computing necessitates designing scalable quantum memory devices. Here, we propose a superconducting quantum memory device in the microwave regime, termed a microwave quantum memcapacitor. It comprises two linked resonators, the primary one is coupled to a Superconducting Quantum Interference Device, which allows for the modulation of the resonator properties through external magnetic flux. The auxiliary resonator, operated through weak measurements, provides feedback to the primary resonator, ensuring stable memory behavior. This device operates with a classical input in one cavity while reading the response in the other, serving as a fundamental building block toward arrays of microwave quantum memcapacitors. We observe that a bipartite setup can retain its memory behavior and gains entanglement and quantum correlations. Our findings pave the way for the experimental implementation of memcapacitive superconducting quantum devices and memory device arrays for neuromorphic quantum computing.