We investigate pulse design problems arising in diverse applications in quantum science and technology. In modern approaches, pulse design is cast as an ensemble control problem involving the control of a continuum of nuclear spin systems, which, however, is typically challenging to solve. In this paper, we present a new pulse design paradigm by introducing moment representations of the spin ensemble system and transforming the ensemble control problem associated to pulse design to a moment control problem. We show that feasible and optimal pulses can be effectively designed using the moment system with performance guarantees across the entire ensemble. We also illustrate the versatility and robustness of our moment-based approach by designing uniform and selective pulses essential to enable prominent applications in magnetic resonance.
Portfolio optimization is one of the most studied optimization problems at the intersection of quantum computing and finance. In this work, we develop the first quantum formulation for a portfolio optimization problem with higherorder moments, skewness and kurtosis. Including higher-order moments leads to more detailed modeling of portfolio return distributions. Portfolio optimization with higher-order moments has been studied in classical portfolio optimization approaches but with limited exploration within quantum formulations. In the context of quantum optimization, higher-order moments generate higher-order terms in the cost Hamiltonian. Thus, instead of obtaining a quadratic unconstrained binary optimization problem, we obtain a higher-order unconstrained binary optimization (HUBO) problem, which has a natural formulation as a parametrized circuit. Additionally, we employ realistic integer variable encoding and a capital-based budget constraint. We consider the classical continuous variable solution with integer programming-based discretization to be the computationally efficient classical baseline for the problem. Our extensive experimental evaluation of
100portfolio optimization problems shows that the solutions to the HUBO formulation often correspond to better portfolio allocations than the classical baseline. This is a promising result for those who want to perform computationally challenging portfolio optimization on quantum hardware, as portfolio optimization with higher moments is classically complex. Moreover, the experimental evaluation studies QAOA's performance with higher-order terms in this practically relevant problem.