Quantum control for the Zeno effect with noise
arXiv:2402.13325 · doi:10.1103/PhysRevA.109.062414
Abstract
The quantum Zeno effect is a distinctive phenomenon in quantum mechanics, describing the nontrivial effect of frequent projective measurements on hindering the evolution of a quantum system. However, when subjected to environmental noise, the quantum system may dissipate, and the quantum Zeno effect no longer works. This research starts from the physical mechanism for the decay of the quantum Zeno effect in the presence of noise and investigates the effect of coherent quantum controls on mitigating the decrease of the survival probability that the system stays in the initial state induced by the noise. We derive the decay rate of the survival probability with and without coherent quantum controls in general, and show that when the frequency of the projective measurements is large but finite, proper coherent controls by sufficiently strong Hamiltonians can be designed to decrease the decay rate of the survival probability. A two-level quantum system suffering from typical unitary and nonunitary noise is then considered to demonstrate the effect of the proposed coherent quantum control scheme in protecting the quantum Zeno effect against the noise. The decay rate of the survival probability is obtained in the presence of noise, and the control Hamiltonian is further optimized analytically to minimize the decay rate by a variational approach. The evolution paths of the quantum system with the optimal coherent controls are illustrated numerically for different scenarios to explicitly show how the coherent control scheme works in lowering the decay of survival probability.
22 pages, 11 figures. Typos corrected, close to the published version
References in corpus (44)
- Circuit Quantum Electrodynamics
- Trapped-Ion Quantum Computing: Progress and Challenges
- Open Quantum Systems. An Introduction
- Semiconductor Spin Qubits
- Quantum Zeno subspaces
- Quantum Zeno dynamics: mathematical and physical aspects
- Unification of Dynamical Decoupling and the Quantum Zeno Effect
- Quantum Zeno effect by general measurements
- Towards a theory of metastability in open quantum dynamics
- Control of decoherence: analysis and comparison of three different strategies
- Constrained dynamics via the Zeno effect in quantum simulation: Implementing non-Abelian lattice gauge theories with cold atoms
- Experimental realization of quantum zeno dynamics
- Continuous and Pulsed Quantum Zeno Effect
- Universality of Uhrig dynamical decoupling for suppressing qubit pure dephasing and relaxation
- Confined quantum Zeno dynamics of a watched atomic arrow
- Quantum Zeno and Anti-Zeno Effect without Rotating Wave Approximation
- A Brief History of the GKLS Equation
- Zeno effect for quantum computation and control
- Freezing a Coherent Field Growth in a Cavity by Quantum Zeno Effect
- Theory of Initialization-Free Decoherence-Free Subspaces and Subsystems
- Relaxation and Zeno effect in qubit measurements
- Phase space tweezers for tailoring cavity fields by quantum Zeno dynamics
- Fundamentals of Quantum Mechanics in Liouville Space
- Quantum Zeno effect appears in stages
- Quantum Zeno effect in the strong measurement regime of circuit quantum electrodynamics
- Quantum Zeno Dynamics from General Quantum Operations
- Constrained Optimization via Quantum Zeno Dynamics
- Stochastic Quantum Zeno by Large Deviation Theory
- Generalized Adiabatic Theorem and Strong-Coupling Limits
- Product formula related to quantum Zeno dynamics
- Effective quantum Zeno dynamics in dissipative quantum systems
- Quantum Zeno and Anti-Zeno probes of noise correlations in photon polarisation
- Full spectrum of the Liouvillian of open dissipative quantum systems in the Zeno limit
- Criterion for quantum Zeno and anti-Zeno effects
- Quantum Error Correction in the Zeno Regime
- Quantum simulation of non-Markovianity using the quantum Zeno effect
- Quantum Zeno effect with partial measurement and noisy dynamics
- Quantum Zeno stabilization in weak continuous measurement of two qubits
- Zeno product formula revisited
- Unification of Random Dynamical Decoupling and the Quantum Zeno Effect
- Qubit control using quantum Zeno effect: Action principle approach
- Error prevention scheme with two pairs of qubits
- Note on a Product Formula Related to Quantum Zeno Dynamics
- Generalized Product Formulas and Quantum Control