The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Harry Dym - One of the best experts on this subject based on the ideXlab platform.
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functional models for entire symmetric operators in rigged de branges Pontryagin spaces
Journal of Functional Analysis, 2021Co-Authors: Volodymyr Derkach, Harry DymAbstract:Abstract The theory of operator extensions in rigged Pontryagin spaces is used to develop two functional models for closed symmetric entire operators S with finite deficiency indices ( p , p ) acting in a separable Pontryagin space K . In the first functional model it is shown that every such operator S is unitarily equivalent to the multiplication operator in a de Branges-Pontryagin space B ( E ) of p × 1 vector valued entire functions. The second functional model is used to parametrize a class of compressed resolvents of extensions S ˜ of S in terms of the range of a linear fractional transformation that is associated with the model. This approach is independent of the methods used by Krein and Langer to parameterize a related class of extensions.
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rigged de branges Pontryagin spaces and their application to extensions and embedding
Journal of Functional Analysis, 2019Co-Authors: Vladimir Derkach, Harry DymAbstract:Abstract De Branges–Pontryagin spaces B ( E ) with negative index κ of entire p × 1 vector valued functions based on an entire p × 2 p entire matrix valued function E ( λ ) (called the de Branges matrix) are studied. An explicit description of these spaces and an explicit formula for the indefinite inner product are presented. A characterization of those spaces B ( E ) that are invariant under the generalized backward shift operator that extends known results when κ = 0 is given. The theory of rigged de Branges–Pontryagin spaces is developed and then applied to obtain an embedding of de Branges matrices with negative squares in generalized J-inner matrices and selfadjoint extensions of the multiplication operator in B ( E ) . A formula for factoring an arbitrary generalized J-inner matrix valued function into the product of a singular factor and a perfect factor is found analogous to the known factorization formulas for J-inner matrix valued functions.
Armin Rahmani - One of the best experts on this subject based on the ideXlab platform.
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Optimal control of superconducting gmon qubits using Pontryagin's minimum principle: Preparing a maximally entangled state with singular bang-bang protocols
Physical Review A, 2018Co-Authors: S. Bao, Silken Kleer, Ruoyu Wang, Armin RahmaniAbstract:We apply the theory of optimal control to the dynamics of two ``gmon'' qubits, with the goal of preparing a desired entangled ground state from an initial unentangled one. Given an initial state, a target state, and a Hamiltonian with a set of permissible controls, can we reach the target state with coherent quantum evolution, and, in that case, what is the minimum time required? The adiabatic theorem provides a far from optimal solution in the presence of a spectral gap. Optimal control yields the fastest possible way of reaching the target state and helps identify unreachable states. In the context of a simple quantum system, we provide examples of both reachable and unreachable target ground states, and show that the unreachability is due to a symmetry. We find the optimal protocol in the reachable case using three different approaches: (i) a brute-force numerical minimization, (ii) an efficient numerical minimization using the bang-bang ansatz expected from the Pontryagin minimum principle, and (iii) direct solution of the Pontryagin boundary value problem, which yields an analytical understanding of the numerically obtained optimal protocols. Interestingly, our system provides an example of singular control, where the Pontryagin theorem does not guarantee bang-bang protocols. Nevertheless, all three approaches give the same bang-bang protocol.
Volodymyr Derkach - One of the best experts on this subject based on the ideXlab platform.
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functional models for entire symmetric operators in rigged de branges Pontryagin spaces
Journal of Functional Analysis, 2021Co-Authors: Volodymyr Derkach, Harry DymAbstract:Abstract The theory of operator extensions in rigged Pontryagin spaces is used to develop two functional models for closed symmetric entire operators S with finite deficiency indices ( p , p ) acting in a separable Pontryagin space K . In the first functional model it is shown that every such operator S is unitarily equivalent to the multiplication operator in a de Branges-Pontryagin space B ( E ) of p × 1 vector valued entire functions. The second functional model is used to parametrize a class of compressed resolvents of extensions S ˜ of S in terms of the range of a linear fractional transformation that is associated with the model. This approach is independent of the methods used by Krein and Langer to parameterize a related class of extensions.
S. Bao - One of the best experts on this subject based on the ideXlab platform.
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Optimal control of superconducting gmon qubits using Pontryagin's minimum principle: Preparing a maximally entangled state with singular bang-bang protocols
Physical Review A, 2018Co-Authors: S. Bao, Silken Kleer, Ruoyu Wang, Armin RahmaniAbstract:We apply the theory of optimal control to the dynamics of two ``gmon'' qubits, with the goal of preparing a desired entangled ground state from an initial unentangled one. Given an initial state, a target state, and a Hamiltonian with a set of permissible controls, can we reach the target state with coherent quantum evolution, and, in that case, what is the minimum time required? The adiabatic theorem provides a far from optimal solution in the presence of a spectral gap. Optimal control yields the fastest possible way of reaching the target state and helps identify unreachable states. In the context of a simple quantum system, we provide examples of both reachable and unreachable target ground states, and show that the unreachability is due to a symmetry. We find the optimal protocol in the reachable case using three different approaches: (i) a brute-force numerical minimization, (ii) an efficient numerical minimization using the bang-bang ansatz expected from the Pontryagin minimum principle, and (iii) direct solution of the Pontryagin boundary value problem, which yields an analytical understanding of the numerically obtained optimal protocols. Interestingly, our system provides an example of singular control, where the Pontryagin theorem does not guarantee bang-bang protocols. Nevertheless, all three approaches give the same bang-bang protocol.
Ruoyu Wang - One of the best experts on this subject based on the ideXlab platform.
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Optimal control of superconducting gmon qubits using Pontryagin's minimum principle: Preparing a maximally entangled state with singular bang-bang protocols
Physical Review A, 2018Co-Authors: S. Bao, Silken Kleer, Ruoyu Wang, Armin RahmaniAbstract:We apply the theory of optimal control to the dynamics of two ``gmon'' qubits, with the goal of preparing a desired entangled ground state from an initial unentangled one. Given an initial state, a target state, and a Hamiltonian with a set of permissible controls, can we reach the target state with coherent quantum evolution, and, in that case, what is the minimum time required? The adiabatic theorem provides a far from optimal solution in the presence of a spectral gap. Optimal control yields the fastest possible way of reaching the target state and helps identify unreachable states. In the context of a simple quantum system, we provide examples of both reachable and unreachable target ground states, and show that the unreachability is due to a symmetry. We find the optimal protocol in the reachable case using three different approaches: (i) a brute-force numerical minimization, (ii) an efficient numerical minimization using the bang-bang ansatz expected from the Pontryagin minimum principle, and (iii) direct solution of the Pontryagin boundary value problem, which yields an analytical understanding of the numerically obtained optimal protocols. Interestingly, our system provides an example of singular control, where the Pontryagin theorem does not guarantee bang-bang protocols. Nevertheless, all three approaches give the same bang-bang protocol.
