Quantum error mitigations for quantum approximate optimization algorithms on IBM quantum processors
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97 MATHEMATICS AND COMPUTING↗
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Algorithmic Optimizations for DPUs
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Karamati, Sara [External Affiliation]↗
Integration and Optimization of a Waste Heat Driven Organic Rankine Cycle for Power Generation in Wastewater Treatment Plants
The study focuses on achieving energy self-sufficiency in Wastewater Treatment Plants by proposing a comprehensive model for integrating, sizing, and optimizing an Organic Rankine Cycle system. The Organic Rankine Cycle system is designed to utilize waste heat from the gensets at As Samra Wastewater Treatment Plant in Jordan, where it will contribute to the overall electrical energy supply of the plant. Real data from As Samra Wastewater Treatment Plant is used to model and calculate the available waste heat using TRNSYS® software. The Organic Rankine Cycle model is then developed using ASPEN PLUS® software to explore the impact of operational parameters and determine their optimal values for maximizing the plant's energy profile. An economic analysis is conducted to assess the feasibility of the proposed model, considering system components, installation, operation, and maintenance costs. To optimize the Organic Rankine Cycle system, the study employs the Multi-Output Support Vector Regression technique to capture nonlinear relationships between independent variables (fluid type, turbine inlet pressure, turbine inlet temperature, turbine outlet pressure, and mass flow rate) and dependent variables (pump power input, waste heat input, and turbine specific work). The Osprey optimization algorithm is used to address the multi-objective optimization problem, with the proposed Pareto-based Osprey Optimization Algorithm and the Multi-Objective Particle Swarm Optimization technique being employed to evaluate critical performance and economic parameters such as system thermal efficiency, net power output, and the levelized cost of electricity. The results of the optimization strategies indicate that the M-SVR model's prediction accuracy is significantly improved after parameter optimization, with the model returning high R 2 and low Mean Square Error values of 0.991 and 0.00216, respectively. The Pareto-Based Osprey Optimization Algorithm optimizer identifies the best working fluid as Isobutane/Isopentane in a ratio of 66:34, with optimal turbine inlet pressure and temperature of 15 bars and 218 °C, respectively. In conclusion, the Organic Rankine Cycle model at these optimal conditions achieves a cycle efficiency of 19.93% and an Levelized Cost of Electricity value of 0.0353 USD/kWh.
32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
Riemannian Optimization Applied to AC Optimal Power Flow: Preprint
The nonlinear, nonconvex AC optimal power flow problem is of growing importance as the nature of the power grid evolves. This problem can be difficult to solve for interior point methods. However, the advent of optimization algorithms over smooth Riemannian manifolds presents an alternative approach. The nonlinear, nonconvex constraints in the AC power flow problem form an embedded submanifold of Euclidean space. In this paper, the authors explore the performance of Riemannian optimization algorithms for the ACOPF problem where the optimization is performed directly on the AC power flow manifold. They demonstrate that these are viable computational alternatives to interior point methods. This is done by using Julia and the packages PowerModels.jl and Manopt.jl.
manifold optimization↗
Two-Stage Estimation and Variance Modeling for Latency-Constrained Variational Quantum Algorithms
The quantum approximate optimization algorithm (QAOA) has enjoyed increasing attention in noisy, intermediate-scale quantum computing with its application to combinatorial optimization problems. QAOA has the potential to demonstrate a quantum advantage for NP-hard combinatorial optimization problems. As a hybrid quantum-classical algorithm, the classical component of QAOA resembles a simulation optimization problem in which the simulation outcomes are attainable only through a quantum computer. The simulation that derives from QAOA exhibits two unique features that can have a substantial impact on the optimization process: (i) the variance of the stochastic objective values typically decreases in proportion to the optimality gap, and (ii) querying samples from a quantum computer introduces an additional latency overhead. In this paper, we introduce a novel stochastic trust-region method derived from a derivative-free, adaptive sampling trust-region optimization method intended to efficiently solve the classical optimization problem in QAOA by explicitly taking into account the two mentioned characteristics. The key idea behind the proposed algorithm involves constructing two separate local models in each iteration: a model of the objective function and a model of the variance of the objective function. Exploiting the variance model allows us to restrict the number of communications with the quantum computer and also helps navigate the nonconvex objective landscapes typical in QAOA optimization problems. In conclusion, we numerically demonstrate the superiority of our proposed algorithm using the SimOpt library and Qiskit when we consider a metric of computational burden that explicitly accounts for communication costs.
Derivative-free Optimization↗
Quantum approximate multi-objective optimization
The goal of multi-objective optimization is to understand optimal trade-offs between competing objective functions by finding the Pareto front, that is, the set of all Pareto-optimal solutions, where no objective can be improved without degrading another one. Multi-objective optimization can be challenging classically, even if the corresponding single-objective optimization problems are efficiently solvable. Thus, multi-objective optimization represents a compelling problem class to analyze with quantum computers. Here we use a low-depth quantum approximate optimization algorithm to approximate the optimal Pareto front of certain multi-objective weighted maximum-cut problems. We demonstrate its performance on an IBM Quantum computer, as well as with matrix product state numerical simulation, and show its potential to outperform classical approaches.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Randomized Adiabatic Quantum Linear Solver Algorithm with Optimal Complexity Scaling and Detailed Running Costs
Solving linear systems of equations is a fundamental problem with a wide variety of applications across many fields of science, and there is increasing effort to develop quantum linear solver algorithms. Subaşı et al. [Phys. Rev. Lett. 122, 060504 (2019)] proposed a randomized algorithm inspired by adiabatic quantum computing, based on a sequence of random Hamiltonian simulation steps, with suboptimal scaling in the condition number 𝜅 of the linear system and the target error 𝜖. Here we go beyond these results in several ways. Firstly, using filtering [Lin and Tong, Quantum 4, 361 (2020)] and Poissonization techniques [Cunningham and Roland, ArXiv:2406.03972 (2024)], the algorithm complexity is improved to the optimal scaling 𝑂(𝜅log (1/𝜖))—an exponential improvement in 𝜖, and a shaving of a log 𝜅 scaling factor in 𝜅. Secondly, the algorithm is further modified to achieve constant factor improvements, which are vital as we progress towards hardware implementations on fault-tolerant devices. We introduce a cheaper randomized walk operator method replacing Hamiltonian simulation—which also removes the need for potentially challenging classical precomputations; randomized routines are sampled over optimized random variables; circuit constructions are improved. We obtain a closed formula rigorously upper bounding the expected number of times one needs to apply a block-encoding of the linear system matrix to output a quantum state encoding the solution to the linear system. The upper bound is 837𝜅 at 𝜖 = 10 −10 for Hermitian matrices.
97 MATHEMATICS AND COMPUTING↗
Optimizing and Exploring Untapped Micro-Hydro Hybrid Systems: a Multi-Objective Approach for Crystal Lake as a Large-Scale Energy Storage Solution
Increasing electricity demand and concerns about climate change and fossil fuel consumption have highlighted the importance of renewable energy resources and storage systems. This paper proposes a method for exploring untapped pumped hydro storage potentials to accommodate intermittent renewable energy generation profiles. Hourly measured data from 2022 in Benzie County, Michigan, United States, were gathered for system sizing and a thorough, realistic analysis. By employing the multi-objective grey wolf optimization algorithm, we formulated optimal sizing and energy-management strategies for three different scenarios. Unlike similar studies, the 3rd with triple objective functions (OFs) scenario aims to maximize both reliability and ecological OFs while minimizing the cost OF. It has shown promising results with multiple solutions, considering economic, environmental, and reliability factors. A case study conducted in Crystal Lake, Michigan, revealed that although Crystal Lake would function only as a micro-hydro power facility, it is a promising and huge storage unit with a substantial storage capacity of around 14.9734GWh. The system investigated is significant in the USA due to its rapid deployment capabilities, minimal construction requirements, and ease of integration with the distribution grid. The fuzzy logic method was employed to identify the best non-dominant solution among the other solutions. Furthermore, these outcomes include a notably low levelized cost of energy at 0.046147$/kWh, a robust index of reliability of 99.705%, and a significant reduction in CO₂ emissions amounting to 7.9142×10 3 tons/year, when considering the triple OFs. The paper’s methodology provides valuable insights for regions aiming to utilize renewable energy from untapped storage sources.
13 HYDRO ENERGY↗
591 MHz Single-Cell Cavity Optimization Using Evolutionary Algorithms
Reports on the use of evolutionary optimization algorithms to refine the geometry of a 591 MHz single-cell superconducting RF cavity, aiming to improve RF performance parameters such as peak surface fields and shunt impedance.
43 PARTICLE ACCELERATORS↗
Uncertainty propagation and sensitivity analysis for constrained optimization of nuclear waste vitrification
Abstract The vitrification of high‐level waste (HLW) by heating a mixture of glass‐forming chemicals (GFCs) with the waste can be improved using a constrained optimization problem. This study explores how different uncertainty propagation (UP) methods implemented with the optimization process can affect the glass formulation of nuclear waste glasses. UP is the effort of propagating uncertain inputs through a system to understand and quantify output distributions. Uncertainty intervals are crafted from output distributions to inform the optimization algorithm. UP is often implemented with Monte Carlo (MC) sampling for large nonlinear systems, which can be difficult to implement within a constrained optimization algorithm that requires derivative information. Other UP methods often used for optimization under uncertainty (OUU) can be designed to work within an established constrained optimization framework. Methods of UP are evaluated in this study including iterative sampling approaches, first‐order approximations, and surrogate modeling with machine learning (ML). A method of dimensional reduction based on global sensitivity analysis is introduced to support the UP methods for the large dimensionality of the problem. Analytical UP methods able to achieve similar optimums 10 times faster than the baseline MC approach, and produce 93.9% similar output distributions are reported.
12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
Algorithm-guided experimentation for autonomous AI systems in self-driving laboratories
This presentation summarizes our work in the PrOMMiS project on benchmarking of data-driven optimization algorithms and their applications in self-driving laboratories. This work supports the broader project goal of accelerating the identification of promising separation methods and operating conditions for critical minerals separation processes. We present a systematic benchmarking study of 42 data-driven optimization algorithms on a broad collection of 502 test problems. The results identify BAM, GLCCLUSTER, and MULTIMIN as the most effective optimization solvers, with BAM showing the highest overall performance and solving more than 80% of the benchmark problems. The study also shows that no single solver consistently outperforms the others across all problem types, indicating that our future laboratory applications may benefit from using a small set of strong solvers rather than relying on a single method. The presentation also illustrates an in-silico chemical reactor case study showing that data-driven optimization methods can guide autonomous experimentation in a self-driving laboratory and identify optimal operating conditions within a small number of experiments. Overall, the results provide a basis for selecting efficient optimization methods and demonstrate the practical use of data-driven optimization in self-driving laboratory workflows.
36 MATERIALS SCIENCE↗
Riemannian Optimization Applied to AC Optimal Power Flow
The nonlinear, nonconvex AC optimal power flow problem is of growing importance as the nature of the power grid evolves. This problem can be difficult to solve for interior point methods. However, the advent of optimization algorithms over smooth Riemannian manifolds presents an alternative approach. The nonlinear, nonconvex constraints in the AC power flow problem form an embedded submanifold of Euclidean space. In this paper, the authors explore the performance of Riemannian optimization algorithms for the ACOPF problem where the optimization is performed directly on the AC power flow manifold. This is done by using the Julia programming language and the Julia packages PowerModels.jl and Manopt.jl.
AC optimal power flow↗
A modular GUI-based program for genetic algorithm-based feedback-assisted wavefront shaping
Abstract We have developed a modular graphical user interface (GUI)-based program for use in genetic algorithm-based feedback-assisted wavefront shaping. The program uses a class-based structure to separate out the universal modules (e.g. GUI, multithreading, optimization algorithms) and hardware-specific modules (e.g. code for different SLMs and cameras). This modular design makes the program easily adaptable to a wide range of lab equipment, while providing easy access to a GUI, multithreading, and three optimization algorithms (phase-stepping, simple genetic, and microgenetic).
97 MATHEMATICS AND COMPUTING↗
Extreme Longitudinal Compression of Optimized Beams for MEV Ultrafast Electron Diffraction (Final Technical Report)
We worked out the design of a high repetition rate MeV energy ultrafast electron diffraction instrument based on the existing Cornell photoinjector, which can readily be applied to the presented findings. This example is a blueprint of other similarly arranged UED setups. Using particle tracking simulations in conjunction with multiobjective genetic algorithm optimization, we explored the smallest bunch lengths, emittance, and probe spot sizes achievable. As two limits, we defined stroboscopic conditions (with single electrons per pulse) and operation with 10 5 electrons per bunch which may be suitable for single-shot diffraction images. In the stroboscopic case, the flexibility provided by the many cavity bunching and acceleration allows for longitudinal phase space linearization without a higher harmonic field, providing sub-fs bunch lengths at the sample. Given low emittance photoemission conditions, these small bunch lengths can be maintained with probe transverse sizes at the single micron (1 μm) scale and below. In the case of 10 5 electrons per pulse, we simulated state-of-the-art 5D brightness conditions: rms bunch lengths of 10 fs with 3-nm normalized emittances, while permitting repetition rates as high as 1.3 GHz. We showed that in conjunction with collimating apertures, a novel focusing scheme achieves very high-quality emittance compensation for the central core of the beam composing 40% of particles, for a resulting beam size of 5 μm (rms). Finally, to aid in the design of new SRF-based ultrafast electron diffraction machines, we simulated the trade-off between the number of cavities used and achievable bunch length and emittance. In the longitudinal dimension, we made use of the fact that MeV UED requires much lower energy than the 15-MeV maxi mum energy of Cornell’s CBETA injector, and we may therefore use several of the SRF cavities for bunch length compression. In practice, we used a genetic optimization algorithm to choose the phases and amplitudes of the cavities appropriately for optimal bunching. In the zero space charge case, we found that bunching and acceleration are distributed across the six cavities in a way that produces a linearizing effect. And we showed that the ultimate bunch length can be limited by time-of-flight differences arising from transverse size and transverse momentum spread. The space charge code developed and used for this development is now permanent part of the Bmad accelerator simulation code and has already contributed to other developments, e.g., for the EIC electron cooler design.
43 PARTICLE ACCELERATORS↗
Leveraging prior mean models for faster Bayesian optimization of particle accelerators
Tuning particle accelerators is a challenging and time-consuming task that can be automated and carried out efficiently using suitable optimization algorithms, such as model-based Bayesian optimization techniques. One of the major advantages of Bayesian algorithms is the ability to incorporate prior information about beam physics and historical behavior into the model used to make control decisions. In this work, we examine incorporating prior accelerator physics information into Bayesian optimization algorithms by utilizing fast executing, neural network models trained on simulated or historical datasets as prior mean functions in Gaussian process models. We show that in ideal cases, this technique substantially increases convergence speed to optimal solutions in high-dimensional tuning parameter spaces. Additionally, we demonstrate that even in non-ideal cases, where prior models of beam dynamics do not exactly match experimental conditions, the use of this technique can still enhance convergence speed. Finally, we demonstrate how these methods can be used to improve optimization in practical applications, such as transferring information gained from beam dynamics simulations to online control of the LCLS injector, and transferring knowledge gained from experimental measurements across different operating modes, such as accelerating different ion species at the ATLAS heavy ion accelerator.
43 PARTICLE ACCELERATORS↗
Xopt and Badger: a machine learning ecosystem for real-time accelerator control and optimization
Machine learning (ML)-based black-box optimization algorithms have demonstrated significant improvements in accelerator optimization speed, often by orders of magnitude. However, deploying these algorithms in real-time facility control remains challenging due to the specialized expertise and infrastructure required. To bridge this gap, we introduce the Xopt ecosystem, a versatile suite of tools designed to make advanced ML-based optimization accessible to the broader accelerator community. This ecosystem includes Xopt, a modular Python framework that facilitates the integration of ML-based optimization algorithms with arbitrary control problems, and Badger, a graphical user interface built on top of Xopt, which enables seamless deployment of ML algorithms in real-time control systems. The Xopt ecosystem has been successfully applied towards solving challenging real-time control problems at leading international accelerator facilities, including SLAC, LBNL, Argonne, Fermilab, BNL, DESY, and ESRF, demonstrating its effectiveness in real-world optimization tasks. In this presentation, we provide an overview of Xopt’s capabilities and illustrate its impact through case studies from SLAC accelerator facilities including LCLS, LCLS-II, and FACET-II.
Roussel, Ryan [SLAC]↗
Efficient First-Order Algorithms for Large-Scale, Non-Smooth Maximum Entropy Models with Application to Wildfire Science
Maximum entropy (MaxEnt) models are a class of statistical models that use the maximum entropy principle to estimate probability distributions from data. Due to the size of modern data sets, MaxEnt models need efficient optimization algorithms to scale well for big data applications. State-of-the-art algorithms for MaxEnt models, however, were not originally designed to handle big data sets; these algorithms either rely on technical devices that may yield unreliable numerical results, scale poorly, or require smoothness assumptions that many practical MaxEnt models lack. In this paper, we present novel optimization algorithms that overcome the shortcomings of state-of-the-art algorithms for training large-scale, non-smooth MaxEnt models. Our proposed first-order algorithms leverage the Kullback–Leibler divergence to train large-scale and non-smooth MaxEnt models efficiently. For MaxEnt models with discrete probability distribution of n elements built from samples, each containing m features, the stepsize parameter estimation and iterations in our algorithms scale on the order of O(mn) operations and can be trivially parallelized. Moreover, the strong ℓ1 convexity of the Kullback–Leibler divergence allows for larger stepsize parameters, thereby speeding up the convergence rate of our algorithms. To illustrate the efficiency of our novel algorithms, we consider the problem of estimating probabilities of fire occurrences as a function of ecological features in the Western US MTBS-Interagency wildfire data set. Our numerical results show that our algorithms outperform the state of the art by one order of magnitude and yield results that agree with physical models of wildfire occurrence and previous statistical analyses of wildfire drivers.
Physics↗
Bayesian Optimization for Reactor Design Optimization
This study present a test case in which the Bayesian Optimization method is applied to a simulation-based reactor core design optimization problem. The test case aims to showcase the potential of an automated design optimization algorithm for reactor designs by streamlining the reactor core design workflow, given the high computational cost of simulations. The contributions of this work are threefold. First, the existing HTGR model is converted into a simulation-based design optimization test case by developing a pipeline that enables modification of key design parameters and evaluates design performance based on simulation outputs. Second, Bayesian Optimization is implemented and adapted to demonstrate the feasibility of automatic design optimization for nuclear reactor core. Proposed approach leverages Gaussian Process models to characterize the relationship between design variables and performance metrics, while incorporating novel acquisition functions that balance exploration of the design space with exploitation of promising configurations. This implementation lays the foundation for the future developments of reactor design optimization algorithms.
22 - GENERAL STUDIES OF NUCLEAR REACTORS↗