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arXiv:2112.13476 · Scientific Reports

Proposal for a Lorenz qubit

Michael R. Geller

Published Aug 29, 2023• 5 citations
arXivHTMLPDF

Abstract

Nonlinear qubit master equations have recently been shown to exhibit rich dynamical phenomena such as period doubling, Hopf bifurcation, and strange attractors usually associated with classical nonlinear systems. Here we investigate nonlinear qubit models that support tunable Lorenz attractors. A Lorenz qubit could be realized experimentally by combining qubit torsion, generated by real or simulated mean field dynamics, with linear amplification and dissipation. This would extend engineered Lorenz systems to the quantum regime, allowing for their direct experimental study and possible application to quantum information processing.

DOI
10.1038/s41598-023-40893-0

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Nonlinear qubit master equations have recently been shown to exhibit rich dynamical phenomena such as period doubling, Hopf bifurcation, and strange attractors usually associated with classical nonlinear systems. Here we investigate nonlinear qubit models that support tunable Lorenz attractors. A Lorenz qubit could be realized experimentally by combining qubit torsion, generated by real or simulated mean field dynamics, with linear amplification and dissipation. This would extend engineered Lorenz systems to the quantum regime, allowing for their direct experimental study and possible application to quantum information processing.
Starting from the work of Lorenz, it has been realized that the dynamics of many various dissipative systems converges to so-called strange attractors. These objects are characterized by fractal dimensions and chaotic unstable dynamics of individual trajectories. They appear in nature in very different contexts, including applications to turbulence and weather forecast, molecular dynamics, chaotic chemical reactions, multimode solid state lasers and complex dynamics in ecological systems and physiology. The efficient numerical simulation of such dissipative systems can therefore lead to many important practical applications. Here we study a simple deterministic model where dynamics converges to a strange attractor, and show that it can be efficiently simulated on a quantum computer. Even if the dynamics on the attractor is unstable, dissipative and irreversible, a realistic quantum computer can simulate it in a reversible way, and, already with 70 qubits, will provide access to new informations unaccessible for modern supercomputers.
Simulating nonlinear classical dynamics on a quantum computer is an inherently challenging task due to the linear operator formulation of quantum mechanics. In this work, we provide a systematic approach to alleviate this difficulty by developing an explicit quantum algorithm that implements the time evolution of a second-order time-discretized version of the Lorenz model. The Lorenz model is a celebrated system of nonlinear ordinary differential equations that has been extensively studied in the contexts of climate science, fluid dynamics, and chaos theory. Our algorithm possesses a recursive structure and requires only a linear number of copies of the initial state with respect to the number of integration time-steps. This provides a significant improvement over previous approaches, while preserving the characteristic quantum speed-up in terms of the dimensionality of the underlying differential equations system, which similar time-marching quantum algorithms have previously demonstrated. Notably, by classically implementing the proposed algorithm, we showcase that it accurately captures the structural characteristics of the Lorenz system, reproducing both regular attractors-limit cycles-and the chaotic attractor within the chosen parameter regime.
We study the complex nonlinear dynamics of the two-photon Dicke model in the semiclassical limit by considering cavity and qubit dissipation. In addition to the normal and super-radiant phases, another phase that contains abundant chaos-related phenomena is found under balanced rotating and counter-rotating couplings. In particular, chaos may manifest itself through period-doubling bifurcation, intermittent chaos, or quasi-periodic oscillation, depending on the value of qubit frequency. Transition mechanisms that exist in these three distinct routes are investigated through the system's long-time evolution and bifurcation diagram. Additionally, we provide a comprehensive phase diagram detailing both the existence of stable fixed points and the aforementioned chaos-related dynamics.
This paper explores the application of adaptive dynamics within nonlinear quantum systems to achieve complex and realistic quantum system behavior. Traditional analytical approaches often struggle to capture the intricate dynamics of these systems, particularly when dealing with non-linear interactions. We propose a novel framework leveraging quantum entanglement and nonlinear effects to simulate and model such systems more effectively. The core of this approach lies in mimicking the behavior of quantum systems through dynamically adjusted parameters, allowing for a more nuanced and robust representation of quantum phenomena. This research aims to provide a new method for quantum system modeling, offering a departure from conventional approaches and potentially unlocking novel functionalities in quantum technologies.
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Many proposals for quantum devices are based on qubits that are physically realized by the spin magnetic moment of some quantum object. In this case, one of the most often adopted strategies for manipulating qubits is that of using external magnetic fields. However, selectively applying a field just to one qubit may be a practically unattainable goal, as it is, for instance, in most solid-state based setups. In this work, we present a proposal for using nonlinear excitations of solitonic type to accomplish the above task. Our scheme entails the generation of a dynamical soliton in a classical spin-chain which is locally coupled with one qubit: as the soliton runs through, the qubit behaves, due to its interaction with the chain, as if it were subject to a magnetic field with a time dependence that follows from the soliton's features. We here present results for the time evolution of the qubit density-matrix induced by the overall dynamics of the above scheme.