Time-optimal Control of Spin Systems

By J. Swoboda. 2006

301 citations recorded by the source corpus.

The paper discusses various aspects of time-optimal control of quantum spin systems, modelled as right-invariant systems on a compact Lie group G. The main results are the reduction of such a system to an equivalent system on a homogeneous space G/H, and the explicit determination of optimal trajectories on G/H in the case where G/H is a Riemannian symmetric space. These results are mainly obtained by using methods from Lie theory and geometric control.

Subfields: Algebra and Number Theory, Spectroscopy, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/0610beae43ad5a33dc92b1cd4af8810d29004a8d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Center for Bits
2. Isaac L. Chuang Kavli Institute of NanoScience
3. A. O. Physics
4. Thomas Schulte-Herbrüggen
5. Lieven M. K. Vandersypen
6. Ingemar Bengtsson
7. Ronnie Kosloff
8. Karol Zyczkowski

In Spectroscopy

1. Ugo V. Boscain
2. Frank K. Wilhelm
3. Steffen J. Glaser
4. Thomas Schulte-Herbrüggen
5. Tommaso Calarco
6. Center for Bits
7. Isaac L. Chuang Kavli Institute of NanoScience
8. A. O. Physics

In Statistical and Nonlinear Physics

1. Dominique Sugny
2. Christiane P. Koch
3. Center for Bits
4. Isaac L. Chuang Kavli Institute of NanoScience
5. A. O. Physics
6. Thomas Schulte-Herbrüggen
7. Lieven M. K. Vandersypen
8. Ingemar Bengtsson

Citations in the corpus

• NMR techniques for quantum control and computation (2004, methodology): “Such optimization problems have been extensively studied in mathematics s Brockett, 1981 d and have been solved explicitly for elementary quantum gates on two coupled spins s Khaneja et al. , 2001 d and a three-spin chain with nearest-neighbor couplings s Khaneja et al. , 2002 d .”
• Training Schrödinger’s cat: quantum optimal control (2015, methodology): “Also, the Cartan decomposition method turned out to be an efficient tool for the control of spin systems [201, 208].”
• Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe (2022, background): “As a result, arbitrarily strong fields are not sufficient to speed up the system dynamics, and it is impossible to prepare a desired state or carry out a desired quantum gate in arbitrarily short time [326, 327].”
• Optimal control of coupled spin dynamics: design of NMR pulse sequences by gradient ascent algorithms. (2005, background): “The figure shows that up to this relative phase shift of the S pulse, the sequences are almost identical, as expected in order to create the required effective Hamiltonian [24].”
• Geometry of Quantum States: Index (2007, background): “A canonical form of a two-qubit gate is known [522, 558, 640], and various measures of entangling power of U have been proposed [995, 993, 210].”