Introduction to Quantum Control and Dynamics

By D. D’Alessandro. 2007

1,041 citations recorded by the source corpus.

QUANTUM MECHANICS States and Operators Observables and Measurement Dynamics of Quantum Systems MODELING OF QUANTUM CONTROL SYSTEMS: EXAMPLES Quantum Theory of Interaction of Particles and Fields Approximations and Modeling: Molecular Systems Spin Dynamics and Control Mathematical Structure of Quantum Control Systems CONTROLLABILITY Lie Algebras and Lie Groups Controllability Test: The Dynamical Lie Algebra Notions of Controllability for the State Pure State Controllability Equivalent State Controllability Equality of Orbits OBSERVABILITY AND STATE DETERMINATION Quantum State Tomography Observability Observability and Methods for State Reconstruction LIE GROUP DECOMPOSITIONS AND CONTROL Decompositions of SU(2) and Control of Two Level Systems Decomposition in Planar Rotations Cartan Decompositions Levi Decomposition Examples of Application of Decompositions to Control OPTIMAL CONTROL OF QUANTUM SYSTEMS Formulation of the Optimal Control Problem The Necessary Conditions of Optimality Example: Optimal Control of a Two Level Quantum System Time Optimal Control of Quantum Systems Numerical Methods for Optimal Control of Quantum Systems MORE TOOLS FOR QUANTUM CONTROL Selective Population Transfer via Frequency Tuning Time Dependent Perturbation Theory Adiabatic Control STIRAP Lyapunov Control of Quantum Systems ANALYSIS OF QUANTUM EVOLUTIONS: ENTANGLEMENT, ENTANGLEMENT MEASURES, AND DYNAMICS Entanglement of Quantum Systems Dynamics of Entanglement Local Equivalence of States APPLICATIONS OF QUANTUM CONTROL AND DYNAMICS Nuclear Magnetic Resonance Experiments Molecular Systems Control Atomic Systems Control: Implementations of Quantum Information Processing with Ion Traps APPENDIX A: POSITIVE AND COMPLETELY POSITIVE MAPS, QUANTUM OPERATIONS, AND GENERALIZED MEASUREMENT THEORY Positive and Completely Positive Maps Quantum Operations and Operator Sum Representation Generalized Measurement Theory APPENDIX B: LAGRANGIAN AND HAMILTONIAN FORMALISM IN CLASSICAL ELECTRODYNAMICS Lagrangian Mechanics Extension of Lagrangian Mechanics to Systems with Infinite Degrees of Freedom Lagrangian and Hamiltonian Mechanics for a System of Interacting Particles and Field APPENDIX C: CARTAN SEMISIMPLICITY CRITERION AND CALCULATION OF THE LEVI DECOMPOSITION The Adjoint Representation Cartan Semisimplicity Criterion Quotient Lie Algebras Calculation of the Levi Subalgebra in the Levi Decomposition Algorithm for the Levi Decomposition APPENDIX D: PROOF OF THE CONTROLLABILITY TEST OF THEOREM 3.2.1 APPENDIX E: THE BAKER-CAMPBELL-HAUSDORFF FORMULA AND SOME EXPONENTIAL FORMULAS APPENDIX F: PROOF OF THEOREM 6.2.1 REFERENCES INDEX Notes and Exercises appear at the end of every chapter.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

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Citations in the corpus

Challenges and opportunities in quantum machine learning (2022, background): “Here, the states contain information obtained from some physical process such as quantum sensing [15], quantum metrology [16], quantum networks [17], quantum control [18], or even quantum analog-digital transduction [19].”
Quantum control of molecular rotation (2018, background): “Controllability of quantum dynamics is of fundamental as well as practical importance since it determines the extent to which a quantum system can be manipulated and brought to a desired target state (D’Alessandro, 2008).”
Training Schrödinger’s cat: quantum optimal control (2015, background): “Eventually, a new research domain, mathematical quantum control theory [14–23] has emerged (see also [11,24], Sect.”
Quantum-enhanced measurements without entanglement (2017, background): “This is a whole field by itself (see e.g. (D’Alessandro, 2007; Serafini, 2012; Wiseman and Milburn, 2009) for reviews).”
Diagnosing Barren Plateaus with Tools from Quantum Optimal Control (2021, background): “, see [63] for an introduction to quantum control theory).”
Quantum control theory and applications: A survey (2009, neutral): “This subsection will introduce four types of models used in quantum control: bilinear models (BLM), Markovian master equations (MME), stochastic master equation models (SME) and linear quantum stochastic diﬀerential equations (LQSDE).”
Supervised learning with quantum-enhanced feature spaces (2018, background): “It is known that this set of drift steps together with all single control pulses are universal, so we have that any state can be prepared this way with suﬃcient circuit depth [35].”
Introduction to the Pontryagin Maximum Principle for Quantum Optimal Control (2020, background): “Quantum control encompasses a set of techniques to find the time evolution of control parameters which perform specific tasks in quantum physics [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19].”
Controllability of the discrete-spectrum Schrödinger equation driven by an external field (2008, neutral): “Ces méthodes permettent en plus d’obtenir des résultats de contrôlabilité des matrices de densité.”
Fast universal control of an oscillator with weak dispersive coupling to a qubit (2021, positive): “By repeated application of the identities above, we can generate evolution which is any superposition of nested commutators of the original set of generators [62].”