The Experts below are selected from a list of 324 Experts worldwide ranked by ideXlab platform
Boris F Samsonov - One of the best experts on this subject based on the ideXlab platform.
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naimark dilated pt symmetric Brachistochrone
Physical Review Letters, 2008Co-Authors: Uwe Gunther, Boris F SamsonovAbstract:The quantum mechanical Brachistochrone system with a PT-symmetric Hamiltonian is Naimark-dilated and reinterpreted as a subsystem of a Hermitian system in a higher-dimensional Hilbert space. This opens a way to a direct experimental implementation of the recently hypothesized PT-symmetric ultrafast Brachistochrone regime of Bender et al. [Phys. Rev. Lett. 98, 040403 (2007)] in an entangled two-spin system.
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pt symmetric Brachistochrone problem lorentz boosts and nonunitary operator equivalence classes
Physical Review A, 2008Co-Authors: Uwe Gunther, Boris F SamsonovAbstract:The $\mathcal{P}\mathcal{T}$-symmetric (PTS) quantum Brachistochrone problem is re-analyzed as a quantum system consisting of a non-Hermitian PTS component and a purely Hermitian component simultaneously. Interpreting this specific setup as a subsystem of a larger Hermitian system, we find nonunitary operator equivalence classes (conjugacy classes) as natural ingredients which contain at least one Dirac-Hermitian representative. With the help of a geometric analysis the compatibility of the vanishing passage time solution of a PTS Brachistochrone with the Anandan-Aharonov lower bound for passage times of Hermitian Brachistochrones is demonstrated.
Uwe Gunther - One of the best experts on this subject based on the ideXlab platform.
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naimark dilated pt symmetric Brachistochrone
Physical Review Letters, 2008Co-Authors: Uwe Gunther, Boris F SamsonovAbstract:The quantum mechanical Brachistochrone system with a PT-symmetric Hamiltonian is Naimark-dilated and reinterpreted as a subsystem of a Hermitian system in a higher-dimensional Hilbert space. This opens a way to a direct experimental implementation of the recently hypothesized PT-symmetric ultrafast Brachistochrone regime of Bender et al. [Phys. Rev. Lett. 98, 040403 (2007)] in an entangled two-spin system.
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pt symmetric Brachistochrone problem lorentz boosts and nonunitary operator equivalence classes
Physical Review A, 2008Co-Authors: Uwe Gunther, Boris F SamsonovAbstract:The $\mathcal{P}\mathcal{T}$-symmetric (PTS) quantum Brachistochrone problem is re-analyzed as a quantum system consisting of a non-Hermitian PTS component and a purely Hermitian component simultaneously. Interpreting this specific setup as a subsystem of a larger Hermitian system, we find nonunitary operator equivalence classes (conjugacy classes) as natural ingredients which contain at least one Dirac-Hermitian representative. With the help of a geometric analysis the compatibility of the vanishing passage time solution of a PTS Brachistochrone with the Anandan-Aharonov lower bound for passage times of Hermitian Brachistochrones is demonstrated.
Xiaoting Wang - One of the best experts on this subject based on the ideXlab platform.
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time optimal quantum control via differential geometry
Proceedings of SPIE, 2017Co-Authors: Xiaoting Wang, Michele Allegra, Kurt Jacobs, Seth Lloyd, Cosmo Lupo, Masoud MohseniAbstract:Compared with many other methods which only give time sub-optimal designs, the quantum Brachistochrone equation has a great potential to provide accurate time-optimal protocols for essentially any quantum control problem. So far it has been of limited use, however, due to the inadequacy of conventional numerical methods to solve it. Here, using differential geometry, we reformulate the quantum Brachistochrone curves as geodesics on the unitary group. This identification allows us to design a numerical method that can efficiently solve the Brachistochrone problem by first solving a family of geodesic equations.
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quantum Brachistochrone curves as geodesics obtaining accurate minimum time protocols for the control of quantum systems
Physical Review Letters, 2015Co-Authors: Xiaoting Wang, Michele Allegra, Kurt Jacobs, Seth Lloyd, Cosmo Lupo, Masoud MohseniAbstract:: Most methods of optimal control cannot obtain accurate time-optimal protocols. The quantum Brachistochrone equation is an exception, and has the potential to provide accurate time-optimal protocols for a wide range of quantum control problems. So far, this potential has not been realized, however, due to the inadequacy of conventional numerical methods to solve it. Here we show that the quantum Brachistochrone problem can be recast as that of finding geodesic paths in the space of unitary operators. We expect this Brachistochrone-geodesic connection to have broad applications, as it opens up minimal-time control to the tools of geometry. As one such application, we use it to obtain a fast numerical method to solve the Brachistochrone problem, and apply this method to two examples demonstrating its power.
Masoud Mohseni - One of the best experts on this subject based on the ideXlab platform.
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time optimal quantum control via differential geometry
Proceedings of SPIE, 2017Co-Authors: Xiaoting Wang, Michele Allegra, Kurt Jacobs, Seth Lloyd, Cosmo Lupo, Masoud MohseniAbstract:Compared with many other methods which only give time sub-optimal designs, the quantum Brachistochrone equation has a great potential to provide accurate time-optimal protocols for essentially any quantum control problem. So far it has been of limited use, however, due to the inadequacy of conventional numerical methods to solve it. Here, using differential geometry, we reformulate the quantum Brachistochrone curves as geodesics on the unitary group. This identification allows us to design a numerical method that can efficiently solve the Brachistochrone problem by first solving a family of geodesic equations.
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quantum Brachistochrone curves as geodesics obtaining accurate minimum time protocols for the control of quantum systems
Physical Review Letters, 2015Co-Authors: Xiaoting Wang, Michele Allegra, Kurt Jacobs, Seth Lloyd, Cosmo Lupo, Masoud MohseniAbstract:: Most methods of optimal control cannot obtain accurate time-optimal protocols. The quantum Brachistochrone equation is an exception, and has the potential to provide accurate time-optimal protocols for a wide range of quantum control problems. So far, this potential has not been realized, however, due to the inadequacy of conventional numerical methods to solve it. Here we show that the quantum Brachistochrone problem can be recast as that of finding geodesic paths in the space of unitary operators. We expect this Brachistochrone-geodesic connection to have broad applications, as it opens up minimal-time control to the tools of geometry. As one such application, we use it to obtain a fast numerical method to solve the Brachistochrone problem, and apply this method to two examples demonstrating its power.
Kurt Jacobs - One of the best experts on this subject based on the ideXlab platform.
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time optimal quantum control via differential geometry
Proceedings of SPIE, 2017Co-Authors: Xiaoting Wang, Michele Allegra, Kurt Jacobs, Seth Lloyd, Cosmo Lupo, Masoud MohseniAbstract:Compared with many other methods which only give time sub-optimal designs, the quantum Brachistochrone equation has a great potential to provide accurate time-optimal protocols for essentially any quantum control problem. So far it has been of limited use, however, due to the inadequacy of conventional numerical methods to solve it. Here, using differential geometry, we reformulate the quantum Brachistochrone curves as geodesics on the unitary group. This identification allows us to design a numerical method that can efficiently solve the Brachistochrone problem by first solving a family of geodesic equations.
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quantum Brachistochrone curves as geodesics obtaining accurate minimum time protocols for the control of quantum systems
Physical Review Letters, 2015Co-Authors: Xiaoting Wang, Michele Allegra, Kurt Jacobs, Seth Lloyd, Cosmo Lupo, Masoud MohseniAbstract:: Most methods of optimal control cannot obtain accurate time-optimal protocols. The quantum Brachistochrone equation is an exception, and has the potential to provide accurate time-optimal protocols for a wide range of quantum control problems. So far, this potential has not been realized, however, due to the inadequacy of conventional numerical methods to solve it. Here we show that the quantum Brachistochrone problem can be recast as that of finding geodesic paths in the space of unitary operators. We expect this Brachistochrone-geodesic connection to have broad applications, as it opens up minimal-time control to the tools of geometry. As one such application, we use it to obtain a fast numerical method to solve the Brachistochrone problem, and apply this method to two examples demonstrating its power.