Exploiting landscape geometry to enhance quantum optimal control

Abstract

The successful application of Quantum Optimal Control (QOC) over the past decades unlocked the possibility of directing the dynamics of quantum systems. Nevertheless, solutions obtained from QOC algorithms are usually highly irregular, making them unsuitable for direct experimental implementation. In this paper, we propose a method to reshape those unattractive optimal controls. The approach is based on the fact that solutions to QOC problems are not isolated policies but constitute multidimensional submanifolds of control space. This was originally shown for finitedimensional systems. Here, we analytically prove that this property is still valid in a continuous variable system. The degenerate subspace can be effectively traversed by moving in the null subspace of the hessian of the cost function, allowing for the pursuit of secondary objectives. To demonstrate the usefulness of this procedure, we apply the method to smooth and compress optimal protocols in order to meet laboratory demands.

Nonadiabatic Energy Fluctuations of Scale-Invariant Quantum Systems in a Time-Dependent Trap

“…The exact results for the nonadiabatic energy fluctuations we have provided are expected to have widespread applications in both theoretical and experimental studies of these systems. For example, they can be used to characterize far-from-equilibrium dynamics in ultracold gases, quantify the cost of quantum control such as the use of optimal protocols [ 68 , 76 , 77 , 78 ] and shortcuts to adiabaticity [ 41 , 42 ], characterize the performance of devices and processes in quantum thermodynamics [ 30 ], and study the ultimate speed limits [ 37 , 38 ], quantum decay [ 35 ] and orthogonality catastrophe [ 79 ] under scale-invariant quantum dynamics.…”

Fourier compression: A customization method for quantum control protocols

“…Global optima constitute continuous submanifolds, level sets of control space [19,20]. Although general results for infinite-dimensional systems are still missing, in a recent publication [21], a frequency-driven quantum harmonic oscillator (QHO) was studied and it was proven that, when targeting frictionless evolution, solutions form level sets with at most two directions of decreasing fidelity. The existence of continuous manifolds of solutions has very interesting practical consequences.…”

“…The existence of continuous manifolds of solutions has very interesting practical consequences. For example, it allows for the achievement of secondary features in the control protocols [21]. The idea is the following.…”

“…Originally, the navigations were used to either smooth PWC protocols (penalizing the difference between successive pulses) or compress them into few-pulse solutions [21]. Here, we extend the compression idea to arbitrary bases (we exemplify with a Fourier basis, but using other bases is straightforward).…”

Connection between Inverse Engineering and Optimal Control in Shortcuts to Adiabaticity

“…Interestingly, shortcut protocols can be readily engineered to accommodate for various physical constraints [ 39 ] or to mitigate an environmental noise. In this respect, the combination of inverse engineering (IE) method and optimal control theory (OCT) has been particularly fruitful [ 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 ].…”