Quantum control

Quantum control aims to influence the temporal development of quantum systems with the help of external electromagnetic fields. The desired goal must be mathematically expressed as a real-valued functional of the outer fields. The precondition for a successful quantum control is the controllability of the quantum system. The optimization, i.e. H. The control functional can be minimized or maximized by generating matter wave interference, which is also referred to as coherent control , or by pulse sequences whose shape is e.g. B. can be derived with the help of the mathematical theory of the optimal control . These methods are receiving greater attention with the emergence of quantum technologies , for which the precise control of quantum dynamics with as few resources as possible is of central importance.

development

The control of quantum systems by a clever choice of external electromagnetic fields was first discussed independently in the 1980s in the research fields of chemical reaction dynamics (there under the name of coherent control ) and in nuclear magnetic resonance spectroscopy. Experimental applications were also initially carried out in these two areas. With the emergence of quantum information science , interest in the methods of quantum control has increased, initially in order to be able to perform arithmetic operations in a quantum computer as quickly and precisely as possible. In the meantime, however, concepts of quantum control can also be found in other areas of quantum information, e.g. B. in quantum sensors, application.

variants

Methods of quantum control can be differentiated according to various criteria:

• Use of quantum measurements or only purely classical information ( closed loop or open loop ),
• quantum mechanical or purely classical description of the external fields,
• Evaluation of only the control functional or also the gradient or higher derivatives ( Hessian matrix ) of the control functional.

Gradient-based methods

In gradient-based methods, the extreme condition, i.e. H. the disappearance of the control functional with variation of the external fields, implemented numerically through forward and backward propagation of the quantum system. The starting point for the backward propagation is the control objective. Popular examples of gradient-based methods are the method introduced by the Russian mathematician Krotow and named after him, as well as Gradient Ascent Pulse Engineering (GRAPE).

Gradient-free method

Gradient-free methods use methods of non-linear optimization to minimize or maximize the control goal. No backward propagation is necessary for this, but these methods generally converge more slowly than gradient-based methods, in particular with a large number of optimization parameters.

literature

• D'Alessandro, Domenico: Introduction to quantum control and dynamics . CRC press, 2007. ISBN 978-1-584-88884-0
• Moshe Shapiro and Paul Brumer : Quantum control of molecular processes . 2nd ed. Weinheim 2012. ISBN 978-3-527-40904-4

Web links

• World of physics: Quantum control - targeted control of quantum effects
• Python implementation of the Krotov method for quantum control

Individual evidence

1. ↑ ^{a b c} Glaser, SJ, et al. "Schrödinger's cat training: quantum optimal control". The European Journal of Physics D 69 (2015): 279. https://dx.doi.org/10.1140/epjd/e2015-60464-1
2. ^ DM Reich, M. Ndong, and Christiane P. Koch. "Monotonically convergent optimization in quantum control using Krotov's method." The Journal of Chemical Physics 136 (2012): 104103. https://dx.doi.org/10.1063/1.3691827
3. ↑ Khaneja, N., Reiss, T., Kehlet C., Schulte-Herbrüggen, T., Glaser, SJ "Optimal control of coupled spin dynamics: design of NMR pulse sequences by gradient ascent algorithms." Journal of Magnetic Resonance 172, no.2 (2005): 296-305. https://doi.org/10.1016/j.jmr.2004.11.004