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arXiv:2402.03371 · Low Temperature Physics

The Zeno effect in a quantum computer

J. G. Esteve, Fernando Falceto

Published Jul 1, 2026• 0 citations
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Abstract

We present an approximate implementation of the quantum Zeno effect (QZE) in a quantum computer as an example of the relation between this effect and the bang-bang decoupling method in control theory. Although the true QZE cannot be strictly implemented on a quantum computer, where all the operations, except the final measurements, must be unitary, we can mimic it by coupling the system to a number of ancillas and replacing the projective measurements of the QZE by suitable unitary gates.

DOI
10.1063/10.0044349

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We present an approximate implementation of the quantum Zeno effect (QZE) in a quantum computer as an example of the relation between this effect and the bang-bang decoupling method in control theory. Although the true QZE cannot be strictly implemented on a quantum computer, where all the operations, except the final measurements, must be unitary, we can mimic it by coupling the system to a number of ancillas and replacing the projective measurements of the QZE by suitable unitary gates.
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We unify the quantum Zeno effect (QZE) and the ``bang-bang'' (BB) decoupling method for suppressing decoherence in open quantum systems: in both cases strong coupling to an external system or apparatus induces a dynamical superselection rule that partitions the open system's Hilbert space into quantum Zeno subspaces. Our unification makes use of von Neumann' s ergodic theorem and avoids making any of the symmetry assumptions usually made in discussions of BB. Thus we are able to generalize the BB to arbitrary fast and strong pulse sequences, requiring no symmetry, and to show the existence of two alternatives to a pulsed BB: continuous decoupling and pulsed measurements. Our unified treatment enables us to derive limits on the efficacy of the BB method: we explicitly show that the inverse QZE implies that the BB can in some cases accelerate, rather than inhibit, decoherence.
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:
Quantum repeaters pave the way for long-distance quantum communications and quantum Internet, and the idea of quantum repeaters is based on entanglement swapping which requires the implementation of controlled quantum gates. Frequently measuring a quantum system affects its dynamics which is known as the quantum Zeno effect (QZE). Beyond slowing down its evolution, QZE can be used to control the dynamics of a quantum system by introducing a carefully designed set of operations between measurements. Here, we propose an entanglement swapping protocol based on QZE, which achieves almost unit fidelity. Implementation of our protocol requires only simple frequent threshold measurements and single particle rotations. We extend the proposed entanglement swapping protocol to a series of repeater stations for constructing quantum Zeno repeaters which also achieve almost unit fidelity regardless of the number of repeaters. Requiring no controlled gates, our proposal reduces the quantum circuit complexity of quantum repeaters. Our work has potential to contribute to long distance quantum communications and quantum computing via quantum Zeno effect.
We analyze and compare three different strategies, all aimed at controlling and eventually halting decoherence. The first strategy hinges upon the quantum Zeno effect, the second makes use of frequent unitary interruptions (``bang-bang'' pulses and their generalization, quantum dynamical decoupling), and the third uses a strong, continuous coupling. Decoherence is shown to be suppressed only if the frequency NNN of the measurements or pulses is large enough or if the coupling KKK is sufficiently strong. Otherwise, if NNN or KKK is large, but not extremely large, all these control procedures accelerate decoherence. We investigate the problem in a general setting and then consider some practical examples, relevant for quantum computation.
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.