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DOE OSTI2025

A time-parallel multiple-shooting method for large-scale quantum optimal control

Quantum optimal control plays a crucial role in quantum computing by providing the interface between compiler and hardware. Solving the optimal control problem is particularly challenging for multi-qubit gates, due to the exponential growth in computational complexity with the system's dimensionality and the deterioration of optimization convergence. To ameliorate the computational complexity of time-integration, this paper introduces a multiple-shooting approach in which the time domain is divided into multiple windows and the intermediate states at window boundaries are treated as additional optimization variables. Further, this enables parallel computation of state evolution across time-windows, significantly accelerating objective function and gradient evaluations. Since the initial state matrix in each window is only guaranteed to be unitary upon convergence of the optimization algorithm, the conventional gate trace infidelity is replaced by a generalized infidelity that is convex for non-unitary state matrices. Continuity of the state across window boundaries is enforced by equality constraints. A quadratic penalty optimization method is used to solve the constrained optimal control problem, and an efficient adjoint technique is employed to calculate the gradients in each iteration. We demonstrate the effectiveness of the proposed method through numerical experiments on quantum Fourier transform gates in systems with 2, 3, and 4 qubits, noting a speedup of 80x for evaluating the gradient in the 4-qubit case, highlighting the method's potential for optimizing control pulses in multi-qubit quantum systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

A new method to compute periodic orbits in general symplectic maps

The search of high-order periodic orbits has been typically restricted to problems with symmetries that help to reduce the dimension of the search space. Well-known examples include reversible maps with symmetry lines. The present work proposes a new method to compute high-order periodic orbits in twist maps without the use of symmetries. The method is a combination of the parameterization method in Fourier space and a Newton–Gauss multiple shooting scheme. The parameterization method has been successfully used in the past to compute quasi-periodic invariant circles. However, this is the first time that this method is used in the context of periodic orbits. Numerical examples are presented showing the accuracy and efficiency of the proposed method. Furthermore, the method is also applied to verify the renormalization prediction of the residues’ convergence at criticality (extensively studied in reversible maps) in the relatively unexplored case of maps without symmetries.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2022

A modified model parametrization algorithm for solving a special type of heat and mass transfer systems

A new method for solving nonlinear heat and mass transfer design tasks was considered. Systems using the Number of Transfer Units (NTU) method are a special type of mathematical model of heat and mass exchangers. It was observed, that the NTU models in a form of differential-algebraic equations (DAEs) cannot be directly solved with higher values of NTU. The requirements for consistent initial conditions, as well as numerical limitations of DAEs solvers, result, that the solution to the considered design problems that cannot be obtained by a classical direct shooting procedure. To overcome the presented difficulties, the αDAE model optimization algorithm was adjusted for solving NTU-based models. The new approach consists of 3 main steps: 1) task discretization by a multiple-shooting approach, 2) design an appropriate function $f_{NTU}$(α) to effectively influence the variability of the state variables described by dynamical relations, 3) the iterative numerical optimization algorithm for the new parametrized system. Moreover, computations can be performed by a chosen numerical optimization approach, which can be communicated with an available outer procedure for solving differential-algebraic equations. The presented algorithm was implemented and applied to solve the design task with the NTU model of a counter-flow exchanger. Here, the new approach was used to modify the system dynamics to influence the difficulty of the considered problem. Finally, the presented method enabled failure-free numerical computations for the higher values of the NTU parameter.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Improved node culture methods for rapid vegetative propagation of switchgrass (Panicum virgatum L.)

Abstract Background Switchgrass ( Panicum virgatum L.) is an important bioenergy and forage crop. The outcrossing nature of switchgrass makes it infeasible to maintain a genotype through sexual propagation. Current asexual propagation protocols in switchgrass have various limitations. An easy and highly-efficient vegetative propagation method is needed to propagate large natural collections of switchgrass genotypes for genome-wide association studies (GWAS). Results Micropropagation by node culture was found to be a rapid method for vegetative propagation of switchgrass. Bacterial and fungal contamination during node culture is a major cause for cultural failure. Adding the biocide, Plant Preservative Mixture (PPM, 0.2%), and the fungicide, Benomyl (5 mg/l), in the incubation solution after surface sterilization and in the culture medium significantly decreased bacterial and fungal contamination. In addition, “shoot trimming” before subculture had a positive effect on shoot multiplication for most genotypes tested. Using the optimized node culture procedure, we successfully propagated 330 genotypes from a switchgrass GWAS panel in three separate experiments. Large variations in shoot induction efficiency and shoot growth were observed among genotypes. Separately, we developed an in planta node culture method by stimulating the growth of aerial axillary buds into shoots directly on the parent plants, through which rooted plants can be generated within 6 weeks. By circumventing the tissue culture step and avoiding application of exterior hormones, the in planta node culture method is labor- and cost-efficient, easy to master, and has a high success rate. Plants generated by the in planta node culture method are similar to seedlings and can be used directly for various experiments. Conclusions In this study, we optimized a switchgrass node culture protocol by minimizing bacterial and fungal contamination and increasing shoot multiplication. With this improved protocol, we successfully propagated three quarters of the genotypes in a diverse switchgrass GWAS panel. Furthermore, we established a novel and high-throughput in planta node culture method. Together, these methods provide better options for researchers to accelerate vegetative propagation of switchgrass.

Wang, Yongqin↗

DOE OSTI2023

Probing reaction channels via reinforcement learning

Abstract Chemical reactions are dynamical processes involving the correlated reorganization of atomic configurations, driving the conversion of an initial reactant into a result product. By virtue of the metastability of both the reactants and products, chemical reactions are rare events, proceeding fleetingly. Reaction pathways can be modelled probabilistically by using the notion of reactive density in the phase space of the molecular system. Such density is related to a function known as the committor function, which describes the likelihood of a configuration evolving to one of the nearby metastable regions. In theory, the committor function can be obtained by solving the backward Kolmogorov equation (BKE), which is a partial differential equation (PDE) defined in the full dimensional phase space. However, using traditional methods to solve this problem is not practical for high dimensional systems. In this work, we propose a reinforcement learning based method to identify important configurations that connect reactant and product states along chemical reaction paths. By shooting multiple trajectories from these configurations, we can generate an ensemble of states that concentrate on the transition path ensemble. This configuration ensemble can be effectively employed in a neural network-based PDE solver to obtain an approximation solution of a restricted BKE, even when the dimension of the problem is very high. The resulting solution provides an approximation for the committor function that encodes mechanistic information for the reaction, paving a new way for understanding of complex chemical reactions and evaluation of reaction rates.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

A direct transcription-based multiple shooting formulation for dynamic optimization

The growing need for fast and efficient solution techniques for solving dynamic optimization problems is driven by a broad spectrum of applications in scheduling and control. We suggest a novel framework for dynamic optimization that utilizes a multiple shooting “backbone” with discrete rather than continuous subproblems, thereby eliminating need for repeated time-integration. A Lagrangian relaxation (LR)-based decomposition scheme is proposed, which dualizes the state continuity requirements between subproblems and enables parallel solution of the problem. We demonstrate the applicability of our method on two case studies: the Van der Pol oscillator and a batch reactor.

42 ENGINEERING↗

DOE OSTI2025

Effects of Subhalos on Interpreting Highly Magnified Sources Near Lensing Caustics

Large magnification factors near gravitational lensing caustics of galaxy-cluster lenses allow the study of individual stars or compact stellar associations at cosmological distances. We study how the presence of sub-galactic subhalos, an inevitable consequence of cold dark matter, can alter the property of caustics and hence change the interpretation of highly magnified sources that lie atop them. First, we consider a galaxy-cluster halo populated with subhalos sampled from a realistic subhalo mass function calibrated to N-body simulations. Then, we compare a semianalytical approximation and an adaptive ray-shooting method that we employ to quantify the property of the caustics. As a case study, we investigate Earendel, a z = 6.2 candidate of magnified single- or multiple-star system with a lone lensed image atop the critical curve in the Sunrise Arc. We find that the source size constraint (≲0.3 pc) previously derived from macrolens models should be relaxed by a factor of a few to 10 when subhalos are accounted for, therefore allowing the possibility of a compact star cluster. The subhalos could introduce an astrometric perturbation that is ≲0$^{"}_{.}$5, which does not contradict observation. These conclusions are largely robust to changes in the subhalo population. Subhalos therefore should be seriously accounted for when interpreting the astrophysical nature of similar highly magnified sources uncovered in recent high-z observations.

Caustic curve↗

DOE OSTI2022

Protoplast-Based Transient Expression and Gene Editing in Shrub Willow ( Salix purpurea L .)

Shrub willows (Salix section Vetrix) are grown as a bioenergy crop in multiple countries and as ornamentals across the northern hemisphere. To facilitate the breeding and genetic advancement of shrub willow, there is a strong interest in the characterization and functional validation of genes involved in plant growth and biomass production. While protocols for shoot regeneration in tissue culture and production of stably transformed lines have greatly advanced this research in the closely related genus Populus, a lack of efficient methods for regeneration and transformation has stymied similar advancements in willow functional genomics. Moreover, transient expression assays in willow have been limited to callus tissue and hairy root systems. Here we report an efficient method for protoplast isolation from S. purpurea leaf tissue, along with transient overexpression and CRISPR-Cas9 mediated mutations. This is the first such report of transient gene expression in Salix protoplasts as well as the first application of CRISPR technology in this genus. These new capabilities pave the way for future functional genomics studies in this important bioenergy and ornamental crop.

59 BASIC BIOLOGICAL SCIENCES↗