# Quantum control robust with respect to coupling with an external environment

Quantum control robust with respect to coupling with an external environment We study coherent quantum control strategy that is robust with respect to coupling with an external environment. We model this interaction by appending an additional subsystem to the initial system and we choose the strength of the coupling to be proportional to the magnitude of the control pulses. Therefore, to minimize the interaction, we impose $$L_1$$ L 1 norm restrictions on the control pulses. In order to efficiently solve this optimization problem, we employ the BFGS algorithm. We use three different functions as the derivative of the $$L1$$ L 1 norm of control pulses: the signum function, a fractional derivative $$\frac{\mathrm {d}^\alpha |x|}{\mathrm {d}x^\alpha }$$ d α | x | d x α , where $$0<\alpha <1$$ 0 < α < 1 , and the Fermi–Dirac distribution. We show that our method allows to efficiently obtain the control pulses which neglect the coupling with an external environment. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# Quantum control robust with respect to coupling with an external environment

, Volume 14 (2) – Nov 27, 2014
10 pages

/lp/springer_journal/quantum-control-robust-with-respect-to-coupling-with-an-external-aqEPZI5NUd
Publisher
Springer Journals
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-014-0879-7
Publisher site
See Article on Publisher Site

### Abstract

We study coherent quantum control strategy that is robust with respect to coupling with an external environment. We model this interaction by appending an additional subsystem to the initial system and we choose the strength of the coupling to be proportional to the magnitude of the control pulses. Therefore, to minimize the interaction, we impose $$L_1$$ L 1 norm restrictions on the control pulses. In order to efficiently solve this optimization problem, we employ the BFGS algorithm. We use three different functions as the derivative of the $$L1$$ L 1 norm of control pulses: the signum function, a fractional derivative $$\frac{\mathrm {d}^\alpha |x|}{\mathrm {d}x^\alpha }$$ d α | x | d x α , where $$0<\alpha <1$$ 0 < α < 1 , and the Fermi–Dirac distribution. We show that our method allows to efficiently obtain the control pulses which neglect the coupling with an external environment.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Nov 27, 2014

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