Kick and fix: the roots of quantum control

Abstract

When two operators $A$ and $B$ do not commute, the calculation of the exponential operator $e^{A+B}$ is a difficult and crucial problem. The applications are vast and diversified: to name but a few examples, quantum evolutions, product formulas, quantum control, Zeno effect. The latter are of great interest in quantum applications and quantum technologies. We present here a historical survey of results and techniques, and discuss differences and similarities. We also highlight the link with the strong coupling regime, via the adiabatic theorem, and contend that the "pulsed" and "continuous" formulations differ only in the order by which two limits are taken, and are but two faces of the same coin.

arXiv comment6 pages

References in corpus (17)

• Dynamical suppression of decoherence in two-state quantum systems
• Quantum Zeno subspaces
• Quantum Zeno dynamics: mathematical and physical aspects
• Unification of Dynamical Decoupling and the Quantum Zeno Effect
• From the quantum Zeno to the inverse quantum Zeno effect
• Decoherence-Free Subspaces and Subsystems
• Control of decoherence: analysis and comparison of three different strategies
• Quantum Zeno Dynamics
• A Brief History of the GKLS Equation
• Coherent quantum dynamics in steady-state manifolds of strongly dissipative systems
• Quantum Computing in Plato's Cave
• Quantum Zeno Dynamics from General Quantum Operations
• Berry phase from a quantum Zeno effect
• Generalized Adiabatic Theorem and Strong-Coupling Limits
• Quantum Zeno effect and dynamics
• Noise suppression via generalized-Markovian processes
• The geometry of the quantum Zeno effect

Cited by in corpus (3)

• Quantum simulation of non-Markovianity using the quantum Zeno effect
• Generalized Product Formulas and Quantum Control
• Stability and convergence of dynamical decoupling with finite amplitude control