We consider the evolution of an arbitrary quantum dynamical semigroup of a finite-dimensional quantum system under frequent kicks, where each kick is a generic quantum operation. We develop a generalization of the Baker-Campbell-Hausdorff formula allowing to reformulate such pulsed dynamics as a continuous one. This reveals an adiabatic evolution. We obtain a general type of quantum Zeno dynamics, which unifies all known manifestations in the literature as well as describing new types.
 M. Müller, S. Diehl, G. Pupillo, and P. Zoller, Engineered Open Systems and Quantum Simulations with Atoms and Ions, in Advances in Atomic, Molecular, and Optical Physics, edited by P. Berman, E. Arimondo, and C. Lin (Elsevier, Amsterdam, 2012), Vol. 61, pp. 1–80.
 A. Messiah, Quantum Mechanics (Dover, New York, 2017).
 P. Krantz, M. Kjaergaard, F. Yan, T. P. Orlando, S. Gustavsson, and W. D. Oliver, A Quantum Engineer's Guide to Superconducting Qubits, Appl. Phys. Rev. 6, 021318 (2019).
 P. Facchi, S. Tasaki, S. Pascazio, H. Nakazato, A. Tokuse, and D. A. Lidar, Control of Decoherence: Analysis and Comparison of Three Different Strategies, Phys. Rev. A 71, 022302 (2005).
 P. Facchi and S. Pascazio, Quantum Zeno Dynamics: Mathematical and Physical Aspects, J. Phys. A: Math. Theor. 41, 493001 (2008).
 O. Oreshkov and J. Calsamiglia, Adiabatic Markovian Dynamics, Phys. Rev. Lett. 105, 050503 (2010).
 P. Zanardi and L. Campos Venuti, Coherent Quantum Dynamics in Steady-State Manifolds of Strongly Dissipative Systems, Phys. Rev. Lett. 113, 240406 (2014).
 E. W. Streed, J. Mun, M. Boyd, G. K. Campbell, P. Medley, W. Ketterle, and D. E. Pritchard, Continuous and Pulsed Quantum Zeno Effect, Phys. Rev. Lett. 97, 260402 (2006).
 F. Schäfer, I. Herrera, S. Cherukattil, C. Lovecchio, F. S. Cataliotti, F. Caruso, and A. Smerzi, Experimental Realization of Quantum Zeno Dynamics, Nat. Commun. 5, 3194 (2014).
 F. Ticozzi, L. Zuccato, P. D. Johnson, and L. Viola, Alternating Projections Methods for Discrete-Time Stabilization of Quantum States, IEEE Trans. Autom. Control 63, 819 (2018).
 K. Macieszczak, M. Guţă, I. Lesanovsky, and J. P. Garrahan, Towards a Theory of Metastability in Open Quantum Dynamics, Phys. Rev. Lett. 116, 240404 (2016).
 G. A. Paz-Silva, A. T. Rezakhani, J. M. Dominy, and D. A. Lidar, Zeno Effect for Quantum Computation and Control, Phys. Rev. Lett. 108, 080501 (2012).
 J. M. Dominy, G. A. Paz-Silva, A. T. Rezakhani, and D. A. Lidar, Analysis of the Quantum Zeno Effect for Quantum Control and Computation, J. Phys. A: Math. Theor. 46, 075306 (2013).
 M. M. Wolf, ``Quantum Channels & Operations: Guided Tour,'' URL: https://www-m5.ma.tum.de/foswiki/pub/M5/Allgemeines/MichaelWolf/QChannelLecture.pdf.
 D. Burgarth, P. Facchi, M. Fraas, and R. Hillier, A Quantum Environment Leading to Non-Exponential Decay with Zeno Region Which Cannot be Dynamically Decoupled, arXiv:1904.03627 [quant-ph].
 B. M. Terhal and D. P. DiVincenzo, Problem of Equilibration and the Computation of Correlation Functions on a Quantum Computer, Phys. Rev. A 61, 022301 (2000).
 D. Pérez-García, M. M. Wolf, D. Petz, and M. B. Ruskai, Contractivity of Positive and Trace-Preserving Maps under $L_p$ Norms, J. Math. Phys. 47, 083506 (2006).
 G. H. Golub and C. F. Van Loan, Matrix Computations, 4th ed. (Johns Hopkins University Press, Baltimore, 2013).
 Daniel Burgarth, Paolo Facchi, Hiromichi Nakazato, Saverio Pascazio, and Kazuya Yuasa, "Eternal adiabaticity in quantum evolution", Physical Review A 103 3, 032214 (2021).
 Lester Ingber, "Forecasting with Importance-Sampling and Path-Integrals: Applications to COVID-19", SSRN Electronic Journal (2020).
 Norbert Barankai and Zoltán Zimborás, "Generalized quantum Zeno dynamics and ergodic means", arXiv:1811.02509.
 Daniel Burgarth, Paolo Facchi, Giovanni Gramegna, and Saverio Pascazio, "Generalized product formulas and quantum control", Journal of Physics A Mathematical General 52 43, 435301 (2019).
 Tim Möbus and Michael M. Wolf, "Quantum Zeno effect generalized", Journal of Mathematical Physics 60 5, 052201 (2019).
 Simon Becker, Nilanjana Datta, and Robert Salzmann, "Quantum Zeno effect for open quantum systems", arXiv:2010.04121.
 Paolo Facchi and Saverio Pascazio, "Kick and fix: the roots of quantum control", arXiv:1902.01591.
The above citations are from Crossref's cited-by service (last updated successfully 2021-04-21 22:57:12) and SAO/NASA ADS (last updated successfully 2021-04-21 22:57:13). The list may be incomplete as not all publishers provide suitable and complete citation data.
This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.