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DOE OSTI2025

Simulations of Quantum Approximate Optimization Algorithm on HPC-QC Integrated Systems

The Quantum Approximate Optimization Algorithm (QAOA) has emerged as a promising tool for accelerating optimization processes in the Noisy Intermediate-Scale Quantum (NISQ) era. Compared to classical methods, QAOA efficiently solves optimization problems, often formulated as Quadratic Unconstrained Binary Optimization (QUBO) problems. Classical quantum simulators are crucial for evaluating quantum algorithms due to limited quantum resources. However, QAOA's performance can vary with different simulation methods. This study analyzes QAOA's performance using various quantum simulators (e.g., density _matrix, statevector, and matrix_product_state) and demonstrates the benefits of HPC-QC integrated systems in solving QUBO problems on an active learning workflow. By simulating QAOA on dense, large-matrix QUBO problems, we evaluate accuracy and problem-solving time. We also assess QAOA's performance on local computers and HPC-QC inte-grated systems, using Oak Ridge Leadership Computing Facility (OLCF)'s Frontier supercomputer with local Qiskit Aer and remote IBM Quantum simulators.

Kim, Seongmin [ORNL] (ORCID:0000000159063004)↗
DOE OSTI2025

Quantum Approximate Optimization Algorithm on Different Qubit Systems

Solving optimization problems is critical across many research domains, but the high dimensionality of parameter spaces often poses significant challenges. The Quantum Approximate Optimization Algorithm (QAOA) has emerged as a promising approach for accelerating optimization in the Noisy Intermediate-Scale Quantum (NISQ) era by leveraging both classical and quantum computational resources. However, its performance can vary depending on the underlying quantum hardware architecture. In this work, we evaluate the performance of QAOA on different quantum hardware platforms, specifically, superconducting transmon qubits and trapped-ion qubits, targetting real-world optimization problems formulated as fully connected Quadratic Unconstrained Binary Optimization (QUBO) instances. We evaluate both the solution quality and time-to-solution using dense QUBO matrices. Furthermore, we show that large-scale problems, such as a 100-bit QUBO instance, can be effectively tackled by integrating quantum computing with high-performance computing (HPC) resources. This study provides practical insights into the strengths and limitations of different qubit technologies and advances the application of quantum computing in solving real-world optimization problems.

Kim, Seongmin [ORNL] (ORCID:0000000159063004)↗
DOE OSTI2023

Comparative Study of Variations in Quantum Approximate Optimization Algorithms for the Traveling Salesman Problem

The traveling salesman problem (TSP) is one of the most often-used NP-hard problems in computer science to study the effectiveness of computing models and hardware platforms. In this regard, it is also heavily used as a vehicle to study the feasibility of the quantum computing paradigm for this class of problems. In this paper, we tackle the TSP using the quantum approximate optimization algorithm (QAOA) approach by formulating it as an optimization problem. By adopting an improved qubit encoding strategy and a layer-wise learning optimization protocol, we present numerical results obtained from the gate-based digital quantum simulator, specifically targeting TSP instances with 3, 4, and 5 cities. We focus on the evaluations of three distinctive QAOA mixer designs, considering their performances in terms of numerical accuracy and optimization cost. Notably, we find that a well-balanced QAOA mixer design exhibits more promising potential for gate-based simulators and realistic quantum devices in the long run, an observation further supported by our noise model simulations. Furthermore, we investigate the sensitivity of the simulations to the TSP graph. Overall, our simulation results show that the digital quantum simulation of problem-inspired ansatz is a successful candidate for finding optimal TSP solutions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Data-driven quantum approximate optimization algorithm for power systems

Abstract Quantum technology provides a ground-breaking methodology to tackle challenging computational issues in power systems. It is especially promising for Distributed Energy Resources (DERs) dominant systems that have been widely developed to promote energy sustainability. In those systems, knowing the maximum sections of power and data delivery is essential for monitoring, operation, and control. However, high computational effort is required. By leveraging quantum resources, Quantum Approximate Optimization Algorithm (QAOA) provides a means to search for these sections efficiently. However, QAOA performance relies heavily on critical parameters, especially for weighted graphs. Here we present a data-driven QAOA, which transfers quasi-optimal parameters between weighted graphs based on the normalized graph density. We verify the strategy with 39,774 expectation value calculations. Without parameter optimization, our data-driven QAOA is comparable with the Goemans-Williamson algorithm. This work advances QAOA and pilots its practical application to power systems in noisy intermediate-scale quantum devices.

Jing, Hang (ORCID:0000000256343489)↗
DOE OSTI2024

Low-depth Clifford circuits approximately solve MaxCut

We introduce a quantum-inspired approximation algorithm for MaxCut based on low-depth Clifford circuits. We start by showing that the solution unitaries found by the adaptive quantum approximation optimization algorithm (ADAPT-QAOA) for the MaxCut problem on weighted fully connected graphs are (almost) Clifford circuits. Motivated by this observation, we devise an approximation algorithm for MaxCut, ADAPT-Clifford, that searches through the Clifford manifold by combining a minimal set of generating elements of the Clifford group. Our algorithm finds an approximate solution of MaxCut on an N -vertex graph by building a depth O ( N ) Clifford circuit. The algorithm has runtime complexity O ( N 2 ) and O ( N 3 ) for sparse and dense graphs, respectively, and space complexity O ( N 2 ) , with improved solution quality achieved at the expense of more demanding runtimes. We implement ADAPT-Clifford and characterize its performance on graphs with positive and signed weights. The case of signed weights is illustrated with the paradigmatic Sherrington-Kirkpatrick model, for which our algorithm finds solutions with ground-state mean energy density corresponding to ∼ 94 % of the Parisi value in the thermodynamic limit. The case of positive weights is investigated by comparing the cut found by ADAPT-Clifford with the cut found with the Goemans-Williamson (GW) algorithm. For both sparse and dense instances we provide copious evidence that, up to hundreds of nodes, ADAPT-Clifford finds cuts of lower energy than GW. Published by the American Physical Society 2024

Muñoz-Arias, Manuel H. (ORCID:000000025711029X)↗
DOE OSTI2021

A MIMO AAA Agorithm for Frequency Dependent Line Modeling

Modeling of power distribution system components that are valid for a wide range of frequencies are crucial for highly accurate modeling of electromagnetic transient (EMT) events. This has recently become of interest due to the improvements needed for the resilient operation of distribution systems. Vector fitting (VF) is a very popular and commonly used algorithm for wide band representations of power system components in EMT simulations. In this research, we present a new multi-input rational approximation algorithm (MIAAA) and illustrate its advantages with respect to VF using examples of approximations of admittance matrices discussed in the literature. We show that MIAAA not only outperforms VF in terms of achieving better accuracy using lesser number of poles, but also has no numerical issues achieving convergence. In contrast to VF, MIAAA is not sensitive to the location of input sample points and it does not require good estimates for the location of the desired approximation poles. The novelty of this research work is the use of recent mathematical results to solve existing challenges in distribution system modeling and to develop rational approximations for power system models that intend to be optimal in terms of accuracy and performance.

AAA algorithm↗
DOE OSTI2025

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↗
DOE OSTI2023

Efficient generalized boundary detection

Fast, efficient, and robust compression-based methods for detecting boundaries in arbitrary datasets, including sequences (1D datasets), are desired. The methods, each employing three simple algorithms, approximate the information distance between two adjacent sliding windows within a dataset. One of the algorithms calculates an initial ordered list of subsequences; while a second algorithm updates the ordered list of subsequences by dropping a first entry and appending a last entry rather than calculating completely new ordered lists with each iteration. Large values in the distance metric are indicative of boundary locations. A smoothed z-score or a wavelet-based algorithm may then be used to locate peaks in the distance metric, thereby identifying boundary locations. An adaptive version of the method employs a collection of window sizes and corresponding weighting functions, making it more amenable to real datasets with unknown, complex, and changing structures.

Ting, Christina↗
DOE OSTI2022

Scalable and Memory-Efficient Algorithms for Controlling Networked Epidemic Processes Using Multiplicative Weights Update Method

We study the problem of designing scalable algorithms to find effective intervention strategies for controlling stochastic epidemic processes on networks. This is a common problem arising in agent based models for epidemic spread. Previous approaches to this problem focus on either heuristics with no guarantees or approximation algorithms that scale only to networks corresponding to county-sized populations, typically, with less than a million nodes. In particular, the mathematical-programming based approaches need to solve the Linear Program (LP) relaxation of the problem using an LP solver, which restricts the scalability of this approach. In this work, we overcome this restriction by designing an algorithm that adapts the multiplicative weights update (MWU) framework, along with the sample average approximation (SAA) technique, to approximately solve the linear program (LP) relaxation for the problem. To scale this approach further, we provide a memory-efficient algorithm that enables scaling to large networks, corresponding to country-size populations, with over 300 million nodes and 30 billion edges. Furthermore, we show that this approach provides near-optimal solutions to the LP in practice.

Sambaturu, Prathyush↗
DOE OSTI2023

HBMax: Optimizing Memory Efficiency for Parallel Influence Maximization on Multicore Architectures

The goal of influence maximization is to select k most-influential vertices or seeds in a network, where influence is defined by a given diffusion process. The problem has a number of important applications such as viral marketing, information spread, and epidemic control. Although computing optimal seed set is NP-Hard, due to the submodular nature of the problem efficient approximation algorithms exist. However, even state-of-the-art parallel implementations are limited by a sampling step that incurs large memory footprints. This in turn limits the problem size reach and approximation quality. In this work, we study the memory footprint of the sampling process collecting reverse reachability information in the IMM algorithm over large real-world social networks. We present an adaptive and memory-efficient optimization approach for a state-of-the-art multi-threaded parallel influence maximization algorithm. Our approach,HuffMax, uses a portion of the reverse reachable (RR) sets collected by the algorithm to learn the characteristics of the graph. Then, it compresses the intermediate reverse reachability information with Huffman coding, and queries directly on the compressed data to preserve the memory savings obtained through compression. We also propose an efficient sampling strategy based on the distribution of RR sets, which can further reduce the computation time for typical social networks with long-tail distributions. Considering a NUMA architecture, we scale up our solution on 128-core CPUs and reduce the memory footprint by up to 45.7% with negligible time overhead (or even faster) and without perceivable loss of accuracy.

Chen, Xinyu↗
DOE OSTI2024

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↗
DOE OSTI2024

Fully quantum algorithm for mesoscale fluid simulations with application to partial differential equations

Fluid flow simulations marshal our most powerful computational resources. In many cases, even this is not enough. Quantum computers provide an opportunity to speed up traditional algorithms for flow simulations. We show that lattice-based mesoscale numerical methods can be executed as efficient quantum algorithms due to their statistical features. This approach revises a quantum algorithm for lattice gas automata to reduce classical computations and state preparation at every time step. For this, the algorithm approximates the qubit relative phases and subtracts them at the end of each time step. Phases are evaluated using the iterative phase estimation algorithm and subtracted using single-qubit rotation phase gates. Further, this method optimizes the quantum resource required and makes it more appropriate for near-term quantum hardware. We also demonstrate how the checkerboard deficiency that the D1Q2 scheme presents can be resolved using the D1Q3 scheme. The algorithm is validated by simulating two canonical partial differential equations: the diffusion and Burgers' equations on different quantum simulators. We find good agreement between quantum simulations and classical solutions for the presented algorithm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Graph decomposition techniques for solving combinatorial optimization problems with variational quantum algorithms

The quantum approximate optimization algorithm (QAOA) has the potential to approximately solve complex combinatorial optimization problems in polynomial time. However, current noisy quantum devices cannot solve large problems due to hardware constraints. In this work, we develop an algorithm that decomposes the QAOA input problem graph into a smaller problem and solves MaxCut using QAOA on the reduced graph. The algorithm requires a subroutine that can be classical or quantum—in this work, we implement the algorithm twice on each graph. One implementation uses the classical solver Gurobi in the subroutine and the other uses QAOA. We solve these reduced problems with QAOA. On average, the reduced problems require only approximately 1/10 of the number of vertices than the original MaxCut instances. Furthermore, the average approximation ratio of the original MaxCut problems is 0.75, while the approximation ratios of the decomposed graphs are on average of 0.96 for both Gurobi and QAOA. With this decomposition, we are able to measure optimal solutions for ten 100-vertex graphs by running single-layer QAOA circuits on the Quantinuum trapped-ion quantum computer H1-1, sampling each circuit only 500 times. This approach is best suited for sparse, particularly k-regular graphs, as k-regular graphs on n vertices can be decomposed into a graph with at most $\frac{nk}{k+1}$ vertices in polynomial time. Further reductions can be obtained with a potential trade-off in computational time. In conclusion, while this paper applies the decomposition method to the MaxCut problem, it can be applied to more general classes of combinatorial optimization problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

DONKEY: A Flexible and Accurate Algorithm for Clustering

We propose an accurate clustering algorithm suitable for the varied and multidimensional data sets that correspond to temporal snapshots from on-the-fly nonadiabatic trajectory-based simulations of photoexcited dynamics. The algorithm approximates the underlying probability density function using variable kernel density estimation, with local maxima corresponding to cluster centers. Each data point is then assigned to one of the maxima by employing a maximization procedure. Finally, clusters artificially separated by minor fluctuations in the probability density are merged. The algorithm does not require parameter tuning, which ensures flexibility and reduces the risk of bias. It is tested on several synthetic data sets, where it consistently outperforms conventional clustering algorithms. As a final example, the algorithm is applied to the excited dynamics of the norbornadiene ⇌ quadricyclane (C 7 H 8 ) molecular photoswitch, demonstrating how distinct reaction pathways can be identified.

algorithms↗
DOE OSTI2021

Scaling Out a Combinatorial Algorithm for Discovering Carcinogenic Gene Combinations to Thousands of GPUs

Cancer is a leading cause of death in the US, second only to heart disease. It is primarily a result of a combination of an estimated two-nine genetic mutations (multi-hit combinations). Although a body of research has identified hundreds of cancer-causing genetic mutations, we don’t know the specific combination of mutations responsible for specific instances of cancer for most cancer types. An approximate algorithm for solving the weighted set cover problem was previously adapted to identify combinations of genes with mutations that may be responsible for individual instances of cancer. However, the algorithm’s computational requirement scales exponentially with the number of genes, making it impractical for identifying more than three-hit combinations, even after the algorithm was parallelized and scaled up to a V100 GPU. Since most cancers have been estimated to require more than three hits, we scaled out the algorithm to identify combinations of four or more hits using 1000 nodes (6000 V100 GPUs with ≈48×106 processing cores) on the Summit supercomputer at Oak Ridge National Laboratory. Efficiently scaling out the algorithm required a series of algorithmic innovations and optimizations for balancing an exponentially divergent workload across processors and for minimizing memory latency and inter-node communication. We achieved an average strong scaling efficiency of 90.14% (80.96%–97.96% for 200 to 1000 nodes), compared to a 100 node run, with 84.18% scaling efficiency for 1000 nodes. With experimental validation, the multi-hit combinations identified here could provide further insight into the etiology of different cancer subtypes and provide a rational basis for targeted combination therapy.

Dash, Sajal↗
DOE OSTI2026

A Structure-Preserving Decorated Particle Method for the Vlasov-Poisson System

We revisit the Scovel-Weinstein framework (Scovel & Weinstein, CPAM 1994) for reducing the Vlasov-Poisson system while preserving its Hamiltonian structure. Standard particle-in-cell (PIC) algorithms approximate the distribution function by macro-particles with position and velocity. In contrast, Scovel-Weinstein decorated particles involve additional shape degrees of freedom, while maintaining a finite-dimensional reduction with Hamiltonian structure inherited from the continuum model. Although the original work established this structure three decades ago, its computational potential has remained largely unexplored. We present a practical implementation of the Scovel-Weinstein model and compare it with a standard PIC algorithm. Numerical experiments demonstrate that macro-particles in standard PIC can be replaced by far fewer decorated particles while retaining comparable accuracy. This decorated particle approach offers a new structure-preserving paradigm for kinetic plasma simulation.

65M75, 70H05, 70G65↗