Performance Evaluation of Three Kinds of Quantum Optimization

Euimin Lee, Shiho Kim

Théo Lisart-Liebermann, Arcesio Castañeda Medina

The optimization of parametric quantum circuits is technically hindered by three major obstacles: the non-convex nature of the objective function, noisy gradient evaluations, and the presence of barren plateaus. As a result, the selection of classical optimizer becomes a critical factor in assessing and exploiting quantum-classical applications. One promising approach to tackle these challenges involves incorporating curvature information into the parameter update. The most prominent methods in this field are quasi-Newton and quantum natural gradient methods, which can facilitate faster convergence compared to first-order approaches. Second order methods however exhibit a significant trade-off between computational cost and accuracy, as well as heightened sensitivity to noise. This study evaluates the performance of three families of optimizers on synthetically generated MaxCut problems on a shallow QAOA algorithm. To address noise sensitivity and iteration cost, we demonstrate that incorporating secant-penalization in the BFGS update rule (SP-BFGS) yields improved outcomes for QAOA optimization problems, introducing a novel approach to stabilizing BFGS updates against gradient noise.

Jiahua Wei, Weiwei Zhou, Hong‐Yi Dai +2 more

In this paper, we explicitly explore how to manipulate single qubits by one-rotation controls under various manipulation conditions. It is revealed that one can construct control Hamiltonian and adjust the control to manipulate quantum states. Furthermore, we comprehensively discuss how to optimize control magnitude in terms of a new kind of weighted time-energy performance. A comparison has been made among the optimal performances under different manipulation conditions. Three concrete examples indicate the feasibility and efficiency of this approach on optimal control of two-level quantum systems.

András Czégel

He Jianhao Li Lüzhou

Shunyan Wang, You Wang, Juhong Han +8 more

In the recent years, alkali vapor lasers have become the most promising candidates for realization of a light source with both good beam quality and high output power because of their excellent performances. A rubidium laser is a typical kind of alkali vapor lasers. In this study, we developed a theoretical mode to evaluate the population densities of three levels as well as mode-matching efficiency of a rubidium laser pumped by a narrow-linewidth Ti:Sapphire laser under two different focal conditions. In the evaluation, at least two values of the output power of a rubidium laser must be known, which are usually obtained from the experiment. We performed a series of experiments by using two pump lenses with two focal lengths of 150 and 200 mm, and acquired two corresponding values of the laser output power. Then, we applied the experimental results in the theoretical calculation and then obtained the population densities of three levels and mode-matching efficiency of the rubidium laser. The study demonstrates that the outputted pump power can be used for evaluation of the population densities of three levels and mode-matching efficiency of an alkali laser under the different experimental conditions. The study might be valuable to better understand the physical features of an alkali vapor laser and to optimize the configuration of a high-powered alkali laser in the future.