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arXiv:2404.04255 · Physical review. B./Physical review. B

Zeno physics of the Ising chain with symmetry-breaking boundary dephasing

Umar Javed, Riccardo J. Valencia-Tortora, Jamir Marino, Vadim Oganesyan, Michael Kolodrubetz

Published Jan 28, 2025• 6 citations
arXivHTMLPDF

Abstract

In few-qubit systems, the quantum Zeno effect arises when measurement occurs sufficiently frequently that the spins are unable to relax between measurements. This can compete with Hamiltonian terms, resulting in interesting relaxation processes which depend nonmonotonically on the ratio of measurement rate to coherent oscillations. While Zeno physics for a single qubit is well understood, an interesting open question is how the Zeno effect is modified by coupling the measured spin to a nontrivial bulk. In this work, we study the effect of coupling a one-dimensional transverse field Ising to a Zeno spin which lives at the boundary. We find that sharp singularities occur in the boundary relaxation dynamics, which can be tied to the emergence or destruction of edge modes that can be found analytically. Finally, we provide numerical indications that the dynamical singularities are stable in the presence of integrability-breaking interactions.

DOI
10.1103/physrevb.111.014316

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In few-qubit systems, the quantum Zeno effect arises when measurement occurs sufficiently frequently that the spins are unable to relax between measurements. This can compete with Hamiltonian terms, resulting in interesting relaxation processes which depend nonmonotonically on the ratio of measurement rate to coherent oscillations. While Zeno physics for a single qubit is well understood, an interesting open question is how the Zeno effect is modified by coupling the measured spin to a nontrivial bulk. In this work, we study the effect of coupling a one-dimensional transverse field Ising to a Zeno spin which lives at the boundary. We find that sharp singularities occur in the boundary relaxation dynamics, which can be tied to the emergence or destruction of edge modes that can be found analytically. Finally, we provide numerical indications that the dynamical singularities are stable in the presence of integrability-breaking interactions.
It is well known that by repeatedly measuring a quantum system it is possible to completely freeze its dynamics into a well defined state, a signature of the quantum Zeno effect. Here we show that for a many-body system evolving under competing unitary evolution and variable-strength measurements the onset of the Zeno effect takes the form of a sharp phase transition. Using the Quantum Ising chain with continuous monitoring of the transverse magnetization as paradigmatic example we show that for weak measurements the entanglement produced by the unitary dynamics remains protected, and actually enhanced by the monitoring, while only above a certain threshold the system is sharply brought into an uncorrelated Zeno state. We show that this transition is invisible to the average dynamics, but encoded in the rare fluctuations of the stochastic measurement process, which we show to be perfectly captured by a non-Hermitian Hamiltonian which takes the form of a Quantum Ising model in an imaginary valued transverse field. We provide analytical results based on the fermionization of the non-Hermitian Hamiltonian in supports of our exact numerical calculations.
We theoretically study the open quantum system dynamics (in the Trotterized limit) of integrable quantum circuits in the presence of on-site dephasing noise with a spin-1/2 ``impurity'' interacting at the edge. Using a combination of Bethe ansatz (BA) and exact diagonalization (ED), we study the dynamics of both the bulk and the impurity for the XXX (Heisenberg) and the XX qubit chains with and without bulk noise. In the absence of noise, we show that the impurity exhibits two distinct phases: the bound-mode phase, where the impurity undergoes persistent oscillations, and the Kondo phase, where it decays with Kondo time tK{t}_{K}tK​. Turning on the bulk dephasing noise, we find for the two models that in the long-time limit in both regimes, the quantum Zeno effect takes place where the dynamics of the impurity magnetization slows down as the noise strength $\ensuremath{\gamma}$ increases. In contrast, the impurity magnetization in the bound-mode regime shows the opposite effect, decaying faster as the noise strength increases at short times $(t\ensuremath{\ll}1/\ensuremath{\gamma})$. We show that the Zeno effect slows down the impurity dynamics in the long-time limit, driven by the transition in bulk dynamics from ballistic (KPZ) universality class in the XX (XXX) chain to diffusive dynamics in the presence of noise.
We study the quantum Zeno effect (QZE) in two many-body systems, namely the one-dimensional transverse-field Ising model and the Lipkin-Meshkov-Glick (LMG) model, coupled to a central qubit. Our result shows that in order to observe QZE in the Ising model, the frequency of the projective measurement should be of comparable order to that of the system sizes. The same criterion also holds in the symmetry broken phase of the LMG model while in the model's polarized phase, the QZE can be easily observed.
We show how the quantum Zeno effect can be exploited to control quantum many-body dynamics for quantum information and computation purposes. In particular, we consider a one dimensional array of three level systems interacting via a nearest-neighbour interaction. By encoding the qubit on two levels and using simple projective frequent measurements yielding the quantum Zeno effect, we demonstrate how to implement a well defined quantum register, quantum state transfer on demand, universal two-qubit gates and two-qubit parity measurements. Thus, we argue that the main ingredients for universal quantum computation can be achieved in a spin chain with an always-on and constant many-body Hamiltonian. We also show some possible modifications of the initially assumed dynamics in order to create maximally entangled qubit pairs and single qubit gates.
We examine the critical system parameters which affect the quantum Zeno–anti-Zeno transition in a spin–boson system by applying the notion of correlated Zeno subspaces beyond the qubit system to its decayed part represented by a collective reservoir of oscillators. We also examine the effect of coherent control via a periodic sequence of dynamical decoupling pulses prior to projective measurement. Our results show that depending on the system bias and measurement time interval of the spin–boson model, coherent control via periodic dynamical decoupling pulses eliminates the Zeno–anti-Zeno transition behavior. We extend the calculations to examine the entanglement dynamics of two initially entangled qubits coupled to independent reservoirs with varying configuration and subjected to frequent measurements. In a multipartite system, in which one or more qubit–reservoir system can undergo the Zeno–anti-Zeno transition, we show that the effects of measurements made in a one qubit–reservoir subsystem can reverberate noticeably throughout a whole array of N pairs of qubit–reservoir subsystems.
The Zeno and anti-Zeno effects are features of measurement-driven quantum evolution where frequent measurement inhibits or accelerates the decay of a quantum state. Either type of evolution can emerge depending on the system-environment interaction and measurement method. In this experiment, we use a superconducting qubit to map out both types of Zeno effect in the presence of structured noise baths and variable measurement rates. We observe both the suppression and acceleration of qubit decay as repeated measurements are used to modulate the qubit spectrum causing the qubit to sample different portions of the bath. We compare the Zeno effects arising from dispersive energy measurements and purely dephasing "quasimeasurements," showing energy measurements are not necessary to accelerate or suppress the decay process.