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arXiv:2008.01070

Demonstrating Quantum Zeno Effect on IBM Quantum Experience

Subhashish Barik, Dhiman Kumar Kalita, Bikash K. Behera, Prasanta Kumar Panigrahi

Published Jan 1, 2019• 1 citation
arXivHTMLPDF

Abstract

Quantum Zeno Effect (QZE) has been one of the most interesting phenomena in quantum mechanics ever since its discovery in 1977 by Misra and Sudarshan [J. Math. Phys. \textbf{18}, 756 (1977)]. There have been many attempts for experimental realization of the same. Here, we present the first ever simulation of QZE on IBM quantum experience platform. We simulate a two-level system for Rabi-driven oscillation and then disturb the time evolution by intermediate repetitive measurements using quantum gates to increase the survival probability of the qubit in the initial state. The circuits are designed along with the added intermediate measurements and executed on IBM quantum simulator, and the outcomes are shown to be consistent with the predictions. The increasing survival probability with the number of intermediate measurements demonstrates QZE. Furthermore, some alternative explanations for the obtained results are provided which leads to some ambiguity in giving the exact reasoning for the observed outcomes.

DOI
10.13140/rg.2.2.27747.50725

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Quantum Zeno Effect (QZE) has been one of the most interesting phenomena in quantum mechanics ever since its discovery in 1977 by Misra and Sudarshan [J. Math. Phys. \textbf{18}, 756 (1977)]. There have been many attempts for experimental realization of the same. Here, we present the first ever simulation of QZE on IBM quantum experience platform. We simulate a two-level system for Rabi-driven oscillation and then disturb the time evolution by intermediate repetitive measurements using quantum gates to increase the survival probability of the qubit in the initial state. The circuits are designed along with the added intermediate measurements and executed on IBM quantum simulator, and the outcomes are shown to be consistent with the predictions. The increasing survival probability with the number of intermediate measurements demonstrates QZE. Furthermore, some alternative explanations for the obtained results are provided which leads to some ambiguity in giving the exact reasoning for the observed outcomes.
The quantum Zeno effect consists in the hindrance of the evolution of a quantum system that is very frequently monitored and found to be in its initial state at every single measurement. On the basis of the correct formula for the survival probability, i.e. the probability of finding the system in its initial state at every single measurement, we critically analyze a recent proposal and experimental test, that make use of an oscillating system. PACS: 03.65.Bz, 42.50.-p 1 The seminal formulation of the quantum Zeno effect, due to Misra and Sudarshan [1], deals with the probability of observing an unstable system in its initial state throughout a time interval ∆ = [0, t]. The purpose of this note is to point out that the quantum Zeno effect has not been experimentally observed, yet, in its original formulation. Indeed, we shall argue that the interesting proposal by Cook [2], that makes use of a two-level system undergoing Rabi oscillations, as well as the beautiful experiment performed by Itano et al. [3], investigate the probability of finding the
The quantum Zeno effect (QZE) introduced by Misra and Sudarshan consists in the ability of repeated measurements to inhibit or slow down unitary evolution. Its fundamental status in quantum mechanics has long been firmly established, but its much broader context, in-depth understanding and its applications are growing at a faster pace than ever before. Over the years, there have been several pivotal developments that have made the QZE and related effects the basic paradigms underlying the control of evolution in quantum systems:
The traditional approach to the quantum Zeno effect (QZE) and quantum anti-Zeno effect (QAZE) in open quantum systems (implicitly) assumes that the bath (environment) state returns to its original state after each instantaneous projective measurement on the system and thus ignores the cross-correlations of the bath operators between different Zeno intervals. However, this assumption is not generally true, especially for a bath with a considerably nonnegligible memory effect and for a system repeatedly projected into an initial general superposition state. We find that, in stark contrast to the result of a constant value found in the traditional approach, the scaled average decay rate in unit Zeno interval of the survival probability is generally time dependent or shows an oscillatory behavior. In the case of a strong bath correlation, the transition between the QZE and the QAZE depends sensitively on the number of measurements NNN. For a fixed NNN, a QZE region predicted by the traditional approach may in fact already be in the QAZE region. We illustrate our findings using an exactly solvable open qubit system model with a Lorentzian bath spectral density, which is directly related to realistic circuit cavity quantum electrodynamics systems. Thus the results and dynamics presented here can be verified with current superconducting circuit technology.
Reiterated or continuous measurement on a quantum system impedes the quantum object's evolution. This "quantum Zeno" effect (QZE), contemplated for decades, has been conventionally attributed to the reaction of the measuring device on the quantum object being measured, in the sense of the Heisenberg microscope. However, even reactionless "quantum non-demolition" measurements seem to qualify for that inhibition to take place and may constitute a "quantum Zeno paradox" (QZP). An experimental proof of QZE had been attempted in the past on clouds of ions confined in a Paul trap. In the meantime it has been shown, however, that the anticipated impediment of the quantum evolution by a sheer gain of information, i.e. by reactionless measurement cannot be, in principle, proven with an ensemble. Recently, experiments have been performed with the use of a single quantum system: an 172Yb+ ion, laser-driven on its E2 line S1/2 - D5/2, or an 171Yb+ ion, microwave-driven on its ground-state hyperfine resonance. The results of these experiments demonstrate that mere gain of information on the quantum system, while lacking dynamic action, modifies the system's evolution as it is predicted by quantum mechanics, based on the system's preparation. This seems plausible if we attribute reality to the results of the measurements. If, in contrast, reality is claimed for the prediction, two-fold discontinuity must be admitted: loss of coherence with potential measurements, and renormalization from the results of actual measurements.
Abstract We investigate the quantum Zeno effect (QZE) in spin 1/2, spin 1 and spin 3/2 open quantum systems undergoing Rabi oscillations, revealing unexplored features for the spin 1 and spin 3/2 systems. The systems interact with an environment designed to perform continuous measurements of an observable, driving the systems stochastically towards one of the eigenstates of the corresponding operator. The system-environment coupling constant represents the strength of the measurement. Stochastic quantum trajectories are generated by unravelling a Markovian Lindblad master equation using the quantum state diffusion formalism. These are regarded as a more appropriate representation of system behaviour than consideration of the averaged evolution since the latter can mask the effect of measurement. Complete positivity is maintained and thus the trajectories can be considered as physically meaningful. The QZE is investigated over a range of measurement strengths. Increasing the strength leads to greater system dwell in the vicinity of the eigenstates of the measured observable and lengthens the time taken by the system to return to that eigenstate, thus the QZE emerges. For very strong measurement, the Rabi oscillations resemble randomly occurring near-instantaneous jumps between eigenstates. The trajectories followed by the quantum system are heavily dependent on the measurement strength which other than slowing down and adding noise to the Rabi oscillations, changes the paths taken in spin phase space from a circular precession into elaborate figures-of-eight. For spin 1 and spin 3/2 systems, the measurement strength determines which eigenstates are explored and the QZE is stronger when the system dwells in the vicinity of certain eigenstates compared to others.