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AIP conference proceedings

Computer Visualization of Many-Particle Quantum Dynamics

Al. Y. Ozhigov, Luigi Accardi, Guillaume Adenier, Christopher A. Fuchs, Gregg S. Jaeger, Andrei Yu. Khrennikov, Jan-Åke Larsson, Stig Stenholm

Published Jan 1, 2009• 0 citations
Publisher

Abstract

In this paper I show the importance of computer visualization in researching of many‐particle quantum dynamics. Such a visualization becomes an indispensable illustrative tool for understanding the behavior of dynamic swarm‐based quantum systems. It is also an important component of the corresponding simulation framework, and can simplify the studies of underlying algorithms for multi‐particle quantum systems.

DOI
10.1063/1.3109962

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In this paper I show the importance of computer visualization in researching of many‐particle quantum dynamics. Such a visualization becomes an indispensable illustrative tool for understanding the behavior of dynamic swarm‐based quantum systems. It is also an important component of the corresponding simulation framework, and can simplify the studies of underlying algorithms for multi‐particle quantum systems.
The simple algorithm for the simulation and visualization of non relativistic quantum dynamics is proposed that is based on a collective behavior of classical particles. Any quantum particle is represented as the swarm of its classical samples which interact by simple rules including emission and absorption of samples of tied photons. The quantum dynamics results from the collective behavior of such a swarm where the eigenstates are treated as the equilibrium states relatively to emission-absorption of photons. The entanglement is treated as a correlation between samples of the different swarms that is stored in the space-time part of the model inaccessible for a user. The amplitude is always grained. The Coulomb field between quantum particles is simulated, analogously to free flow of quantum package, by the point wise interaction between its samples and scalar photon samples which propagate by diffusion. It gives square root speedup in comparison to each-with-each method. This method obviously includes decoherence and admits the natural generalization on the QED of many particles with the linear computational cost.
A straightforward algorithm is proposed for simulating and visualizing nonrelativistic quantum dynamics in terms of the collective behavior of classical particles. In this approach, a quantum particle is treated as a swarm (collection) of its classical samples interacting with one another by simple rules involving the emission and absorption of associated photons. The quantum dynamics is regarded as resulting from the collective behavior of the swarm, and the eigenstates are treated as equilibrium states of the process of photon emission and absorption. Entanglement is seen as classical correlation between samples from distinct swarms; the information on this correlation is stored in a spatiotemporal section of the model inaccessible to the user. Amplitudes are invariably treated as consisting of amplitude quanta. A Coulomb field experienced by quantum particles is represented in a similar manner to the free spreading of a wave packet, by point interaction between the particle samples and the samples of scalar photons propagating by diffusion. This provides a square-root gam in computational speed against the direct method involving item-by-item examination. The approach presented covers decoherence and allows natural generalization to multiparticle quantum electrodynamics, the amount of memory required growing linearly.
My research has three main foci, one which is of interest to the fields of quantum information and quantum optics is to characterize the effects of coupling between quantum systems. Advances in technology made since the conception of quantum mechanics spurred the development of quantum technologies like quantum optics and quantum computing. These applications require a good understanding of the quantum systems that compose them, and the clever ways in which the information in these systems is stored and manipulated. By understanding the ways which quantum systems interact with their environment, their usefulness can be further utilized. The second is to develop methods of calculation which simplify the calculational and computational side of quantum dynamics. Understanding how quantum systems evolve in time is very important, but traditional methods of solving for the dynamics of quantum systems struggle to deal with time dependent parameters. Using results from the theory of Lie algebras, I will show how quantum dynamics problems can be made less computationally intensive by avoiding the partial differential equations typically associated with such problems and reducing the problem to a system of coupled ordinary differential equations. The third focus is to develop methods of visualizing properties of quantum systems. I think this is important as an educational tool and as a way to develop intuition about how quantum systems evolve considering how few opportunities there are to visualize quantum effects on a macroscopic scale. This problem is particularly challenging because quantum mechanics is non-deterministic, meaning that the only nontrivial definitive statements that can be made regarding quantum systems deal with probabilities. This coupled with the fact that many of the systems of interest depend on upwards of six variables and also evolve in time make creating useful visual representations challenging. Despite the challenges, I feel that useful insights can be gained from the visualizations, and will illustrate a few examples.
This paper introduces a novel non-linear multi-particle quantum dynamics model designed to explore the behavior and stability of complex systems. Traditional quantum mechanics models often assume single-particle dynamics, while this model leverages multi-particle quantum dynamics to investigate the intricate behavior and potential quantum effects within systems exhibiting non-linearity. The core mechanism involves a dynamic simulation framework built upon the principles of quantum field theory, aiming to predict system behavior and quantify quantum effects. This research contributes to the advancement of theoretical understanding and computational tools for analyzing complex quantum systems.
Quantum computing has emerged recently as a new computational paradigm. It considers quantum bits (qubits) instead of classical bits. However, quantum algorithms are often very difficult to understand. In this paper, we propose a tool for quantum software visualization. It presents visually the state of multiple-qubits and its evolution at runtime during the execution of a quantum program. This tool allows a unique representation of a quantum state, contrary to the usual vector notation. We show how the problem of visualizing a quantum state can be reduced to a set visualization problem, and our tool uses rainbow boxes to visualize the resulting sets. We also present the application of the proposed tool to quantum teleportation, an algorithm of high importance in cryptography. Finally, we discuss the limit of this approach and its perspectives, in particular for teaching quantum computing.
Simulation is a ubiquitous tool for understanding and predicting the behavior of complex systems, ranging from those in natural sciences to those in social studies. When it comes to quantum systems, however, conventional simulation methods encounter fundamental limitations imposed by quantum physics. To overcome this challenge, the concept of using quantum systems to simulate other quantum systems, namely, quantum simulation, has emerged as an indispensable paradigm. In this special issue, we explore the underlying concepts and theoretical frameworks that drive this rapidly developing field.