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arXiv:quant-ph/0409213 · Computer Physics Communications

Deterministic event-based simulation of quantum phenomena

Koen De Raedt, Hans A. De Raedt, Kristel F. L. Michielsen

Published Jun 14, 2005• 44 citations
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Abstract

We propose and analyse simple deterministic algorithms that can be used to construct machines that have primitive learning capabilities. We demonstrate that locally connected networks of these machines can be used to perform blind classification on an event-by-event basis, without storing the information of the individual events. We also demonstrate that properly designed networks of these machines exhibit behavior that is usually only attributed to quantum systems. We present networks that simulate quantum interference on an event-by-event basis. In particular we show that by using simple geometry and the learning capabilities of the machines it is possible to simulate single-photon interference in a Mach–Zehnder interferometer. The interference pattern generated by the network of deterministic learning machines is in perfect agreement with the quantum theoretical result for the single-photon Mach–Zehnder interferometer. To illustrate that networks of these machines are indeed capable of simulating quantum interference we simulate, event-by-event, a setup involving two chained Mach–Zehnder interferometers, and demonstrate that also in this case the simulation results agree with quantum theory.

DOI
10.1016/j.cpc.2005.04.012

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•Aug 24, 2015•0 citations
We propose and analyse simple deterministic algorithms that can be used to construct machines that have primitive learning capabilities. We demonstrate that locally connected networks of these machines can be used to perform blind classification on an event-by-event basis, without storing the information of the individual events. We also demonstrate that properly designed networks of these machines exhibit behavior that is usually only attributed to quantum systems. We present networks that simulate quantum interference on an event-by-event basis. In particular we show that by using simple geometry and the learning capabilities of the machines it is possible to simulate single-photon interference in a Mach–Zehnder interferometer. The interference pattern generated by the network of deterministic learning machines is in perfect agreement with the quantum theoretical result for the single-photon Mach–Zehnder interferometer. To illustrate that networks of these machines are indeed capable of simulating quantum interference we simulate, event-by-event, a setup involving two chained Mach–Zehnder interferometers, and demonstrate that also in this case the simulation results agree with quantum theory.
Event by event method is a simulation approach which is not based on the knowledge of the Schrodinger equation. This approach uses the classical wave theory and particle concept: we use particles, not waves. The data is obtained by counting the events that were detected by the detector, just as in real experiments. The particle is considered as a messenger (carries a message) that is processed by the deterministic learning machine. We demonstrated that the event-based deterministic learning machine simulation can produce the same interference patterns as those obtained in the experiment. The event-by-event method reproduces the results of quantum theory of the Mach-Zehnder interferometer, Mach-Zehnder interferometer with absorber, three beam interference, delayed choice and two-photon interference experiments.
Abstract. Franson-Type Bell experiments have been proposed to demonstrate the violation of local realism in quantum theory based on a violation of the Bell Clauser-Horne-Shimony-Holt inequality. We demonstrate that the original experiment constructed by Franson [1] as well as its modification by Cabello et al. [2] can be simulated on an event-by-event basis using causal, local, and event-based processes without solving the Schrödinger equation or using concepts such as wave fields or particle-wave duality. In our approach networks of locally connected processing units with a primitive learning capability are used which exhibit behaviour that is usually only attributed to quantum systems. There is a one-to-one correspondence between the components of the network and the physical devices in the experimental setup. Furthermore, only simple geometry is used to construct the simulation algorithm. In this sense, the simulation approach we propose satisfies