Quantum optimal control theory and dynamic coupling in the spin-boson model

Abstract

A Markovian master equation describing the evolution of open quantum systems in the presence of a time-dependent external field is derived within the Bloch-Redfield formalism. It leads to a system-bath interaction which depends on the control field. Optimal control theory is used to select control fields which allow accelerated or decelerated system relaxation, or suppression of relaxation (dissipation) altogether, depending on the dynamics we impose on the quantum system. The control-dissipation correlation and the non-perturbative treatment of the control field are essential for reaching this goal. The optimal control problem is formulated within Pontryagin's minimum principle and the resulting optimal differential system is solved numerically. As an application, we study the dynamics of a spin-boson model in the strong coupling regime under the influence of an external control field. We show how trapping the system in unstable quantum states and transfer of population can be achieved by optimized control of the dissipative quantum system. We also used optimal control theory to find the driving field that generates the quantum Z-gate. In several cases studied, we find that the selected optimal field which reduces the purity loss significatively is a multi-component low-frequency field including higher harmonics, all of which lie below the phonon cutoff frequency. Finally, in the undriven case we present an analytic result for the Lamb shift at zero temperature.

Comparing, optimizing, and benchmarking quantum-control algorithms in a unifying programming framework

“…In many problems (3,5,6,8,9,11,12,14,18,19,21, and 22), we observe a crossing point in time course of the fidelity of the two algorithms. The sequential-update algorithm is overtaken by the concurrent-update scheme between a quality of 0.9 and 0.99 (see, e.g., Problem 21 in Fig.…”

“…In order to tackle these challenging quantum engineering tasks, optimal control algorithms are establishing themselves as indispensable tools. They have matured from principles [3] and early implementations [4][5][6] via spectroscopic applications [7][8][9] to advanced numerical algorithms [10,11] for state-to-state transfer and quantumgate synthesis [12] alike.…”

Fidelity of optimally controlled quantum gates with randomly coupled multiparticle environments

“…One of the most difficult problems of QC is that unavoidable coupling of the quantum information processor (QIP) to the environment results in a loss of coherence. In recent years, significant attention was devoted to various methods of dynamic suppression of environmentally-induced decoherence in open quantum systems, including applications of pre-designed external fields [4,5,6,7,8] and optimal control techniques [9,10,11,12,13,14,15]. In a separate line of research, several works [16,17,18,19,20,21] considered the generation of optimally controlled unitary quantum gates in ideal situations where coupling to the environment can be neglected during the gate operation.…”

A smoothing monotonic convergent optimal control algorithm for nuclear magnetic resonance pulse sequence design

“…[1,2] During the past decade or so, optimal-control-based methods have been increasingly used for a development of new experiments within optical spectroscopy, [3][4][5][6][7][8] quantum information processing, [9][10][11][12][13][14] liquid-and solid-state nuclear magnetic resonance (NMR) spectroscopy, [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29] magnetic resonance imaging (MRI), [30][31][32][33][34][35][36] and dynamic nuclear polarization (DNP) hybrids between electron and nuclear magnetic resonance. [37][38][39][40] Such applications have not only been useful for the specific disciplines taking advantage of new efficient design procedures and improved experimental methods, but it has also stimulated mathematical investigations in quantum optimal control theory.…”