Solving large-scale sparse linear systems is a challenging computational task due to the introduction of non-zero elements, or "fill-in." The Graph Partitioning Problem (GPP) arises naturally when minimizing fill-in and accelerating solvers. In this paper, we measure the end-to-end performance of a hybrid quantum-classical framework designed to accelerate Finite Element Analysis (FEA) by integrating a quantum solver for GPP into Synopsys/Ansys' LS-DYNA multiphysics simulation software. The quantum solver we use is based on Iterative-QAOA, a scalable, non-variational quantum approach for optimization. We focus on two specific classes of FEA problems, namely vibrational (eigenmode) analysis and transient simulation. We report numerical simulations on up to 150 qubits done on NVIDIA's CUDA-Q/cuTensorNet and implementation on IonQ's Forte quantum hardware. The potential impact on LS-DYNA workflows is quantified by measuring the wall-clock time-to-solution for complex problem instances, including vibrational analysis of large finite element models of a sedan car and a Rolls-Royce jet engine, as well as transient simulations of a drill and an impeller. We performed end-to-end performance measurements on meshes comprising up to 35 million elements. Measurements were conducted using LS-DYNA in distributed-memory mode via Message Passing Interface (MPI) on AWS and Synopsys compute clusters. Our findings indicate that with a quantum computer in the loop, amortized LS-DYNA wall-clock time can be improved by up to 14.6% for specific cases and by at least 5.9% for all models considered. These results highlight the significant potential of quantum computing to reduce time-to-solution for large-scale FEA simulations within the Noisy Intermediate-Scale Quantum (NISQ) era, offering an approach that is scalable and extendable into the fault-tolerant quantum computing regime.
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Solving large-scale sparse linear systems is a challenging computational task due to the introduction of non-zero elements, or "fill-in." The Graph Partitioning Problem (GPP) arises naturally when minimizing fill-in and accelerating solvers. In this paper, we measure the end-to-end performance of a hybrid quantum-classical framework designed to accelerate Finite Element Analysis (FEA) by integrating a quantum solver for GPP into Synopsys/Ansys' LS-DYNA multiphysics simulation software. The quantum solver we use is based on Iterative-QAOA, a scalable, non-variational quantum approach for optimization. We focus on two specific classes of FEA problems, namely vibrational (eigenmode) analysis and transient simulation. We report numerical simulations on up to 150 qubits done on NVIDIA's CUDA-Q/cuTensorNet and implementation on IonQ's Forte quantum hardware. The potential impact on LS-DYNA workflows is quantified by measuring the wall-clock time-to-solution for complex problem instances, including vibrational analysis of large finite element models of a sedan car and a Rolls-Royce jet engine, as well as transient simulations of a drill and an impeller. We performed end-to-end performance measurements on meshes comprising up to 35 million elements. Measurements were conducted using LS-DYNA in distributed-memory mode via Message Passing Interface (MPI) on AWS and Synopsys compute clusters. Our findings indicate that with a quantum computer in the loop, amortized LS-DYNA wall-clock time can be improved by up to 14.6% for specific cases and by at least 5.9% for all models considered. These results highlight the significant potential of quantum computing to reduce time-to-solution for large-scale FEA simulations within the Noisy Intermediate-Scale Quantum (NISQ) era, offering an approach that is scalable and extendable into the fault-tolerant quantum computing regime.
The solution of large sparse linear systems via factorization methods such as LU or Cholesky decomposition, can be computationally expensive due to the introduction of non-zero elements, or “fill-in.” Graph partitioning can be used to reduce the “fill-in,” thereby speeding up the solution of the linear system. We introduce a quantum approach to the graph partitioning problem based on variational quantum imaginary time evolution (VarQITE). We develop a hybrid quantum/classical method to accelerate Finite Element Analysis (FEA) by using VarQITE in Ansys's LS-DYNA multiphysics simulation software. This allows us to study different types of FEA problems, from mechanical engineering to computational fluid dynamics in simulations and on quantum hardware (IonQ Aria and IonQ Forte). We demonstrate that VarQITE has the potential to impact LSDYNA workflows by measuring the wall-clock time to solution of FEA problems. We report performance results for our hybrid quantum/classical workflow on selected FEA problem instances, including simulation of blood pumps, automotive roof crush, and vibration analysis of car bodies on meshes of up to six million elements. We find that the LS-DYNA wall clock time can be improved by up to 12% for some problems. Finally, we introduce a classical heuristic inspired by Fiduccia-Mattheyses to improve the quality of VarQITE solutions obtained from hardware runs. Our results highlight the potential impact of quantum computing on large-scale FEA problems in the NISQ era.
Hybrid quantum-high performance computing (Q-HPC) workflows are emerging as a key strategy for running quantum applications at scale in current noisy intermediate-scale quantum (NISQ) devices. These workflows must operate seamlessly across diverse simulators and hardware backends since no single simulator offers the best performance for every circuit type. Simulation efficiency depends strongly on circuit structure, entanglement, and depth, making a flexible and backend-agnostic execution model essential for fair benchmarking, informed platform selection, and ultimately the identification of quantum advantage opportunities. In this work, we extend the Quantum Framework (QFw), a modular and HPC-aware orchestration layer, to integrate multiple local backends (Qiskit Aer, NWQ-Sim, QTensor, and TN-QVM) and a cloud-based quantum backend (IonQ) under a unified interface. Using this integration, we execute a number of non-variational as well as variational workloads. The results highlight workload-specific backend advantages: while Qiskit Aer’s matrix product state excels for large Ising models, NWQ-Sim not only leads on large-scale entanglement and Hamiltonian but also shows the benefits of concurrent subproblem execution in a distributed manner for optimization problems. These findings demonstrate that simulator-agnostic, HPC-aware orchestration is a practical path toward scalable, reproducible, and portable Q-HPC ecosystems, thereby accelerating progress toward demonstrating quantum advantage.
The solution for non-linear, complex partial differential Equations (PDEs) is achieved through numerical approximations, which yield a linear system of equations. This approach is prevalent in Computational Fluid Dynamics (CFD), but it restricts the mesh size since the solution of the linear system becomes computationally intractable when the mesh resolution increases. The reliance on the ability of High-Performance Computers (HPC) to scale up and meet these requirements is myopic; such very high-fidelity simulations require a paradigm shift in computing. This paper presents an exploration of quantum methodologies aimed at achieving high accuracy in solving such a large system of equations. Leveraging recent works in Quantum Linear Solver Algorithms (QLSA) and variational algorithms suitable for Quantum Simulation in HPC, we aspire to push the boundaries of CFD-relevant problems that can be solved on hybrid quantum-classical framework. To this end, we consider the 2D, transient, incompressible, viscous, non-linear coupled Burgers equation as a test problem and investigate the accuracy of our approach by comparing results with a classical linear system of equation solvers, such as the Generalized Minimal RESidual method (GMRES). Through rigorous testing, our findings demonstrate that our quantum methods yield results comparable in accuracy to traditional approaches. Additionally, we demonstrate the accuracy, scalability, and consistency of our quantum method. Lastly, we present an insightful estimation of the resources our quantum algorithm needs to solve systems with nearly 2 billion mesh points.
Electromagnetic analysis based on the finite element method is widely used in antenna design. At higher frequencies, however, the required mesh refinement makes solving large sparse linear systems the main contributor to computational cost. Quantum linear system solvers offer a potential means of accelerating this step, but their output is a superposition state: reconstructing all components of the classical solution vector would forfeit the quantum speedup. Prior studies have proposed methods for obtaining physical quantities such as scattering cross sections and scattering parameters from the solution state. To support antenna design using fault-tolerant quantum computers, we formulate the total radiated power, the radiated power within a prescribed solid angle, and the dielectric and conductive losses as observables for efficient evaluation from a quantum solution state. These observables avoid the measurement cost of reconstructing all components of the output quantum state. We develop an end-to-end hybrid quantum--classical workflow that combines finite-element electromagnetic analysis, matrix preconditioning, a quantum linear system solver, and the evaluation of antenna design metrics. To validate the workflow, we performed numerical experiments evaluating these observables for an axisymmetric coaxially fed monopole antenna. Under idealized conditions, the relative errors in the total radiated power and the dissipated power with respect to the classical finite-element solution were on the order of 10−3, confirming the consistency of the workflow. The proposed method is expected to provide a basis for using quantum linear system solvers to evaluate antenna performance and, in the future, to design high-frequency wireless devices.
Finite-element methods are industry standards for finding numerical solutions to partial differential equations. However, the application scale remains pivotal to the practical use of these methods, even for modern-day supercomputers. Large, multi-scale applications, for example, can be limited by their requirement of prohibitively large linear system solutions. It is therefore worthwhile to investigate whether near-term quantum algorithms have the potential for offering any kind of advantage over classical linear solvers. In this study, we investigate the recently proposed variational quantum linear solver (VQLS) for discrete solutions to partial differential equations. This method was found to scale polylogarithmically with the linear system size, and the method can be implemented using shallow quantum circuits on noisy intermediate-scale quantum (NISQ) computers. Herein, we utilize the hybrid VQLS to solve both the steady Poisson equation and the time-dependent heat and wave equations.
The Noisy Intermediate-Scale Quantum (NISQ) era, defined by qubit counts in the hundreds and gate error rates that preclude long coherence times, imposes severe constraints on purely quantum computation. The central problem is that achieving practical quantum advantage for real-world tasks must overcome these hardware limitations, yet fault-tolerant quantum computers with full error correction remain years away. To address this, we present a systematic survey of hybrid classical-quantum computing models, in which classical high-performance resources orchestrate the workflow, perform iterative optimization, and apply error mitigation to noisy quantum processing units. Our review encompasses variational quantum algorithms, such as the variational quantum eigensolver and quantum approximate optimization algorithm; classical optimizers tailored for noisy quantum landscapes; error mitigation techniques including zero-noise extrapolation and probabilistic error cancellation; and circuit knitting that partitions large circuits across small QPUs. We find that these hybrid architectures have already demonstrated domain-specific utility in quantum chemistry for molecular ground-state estimation, in logistics and finance for combinatorial optimization, and in machine learning for generative and recommendation models. Notably, they often surpass purely classical or purely quantum approaches on carefully chosen benchmarks. The evidence indicates that hybrid classical-quantum systems are not a temporary stopgap but a durable paradigm. Their role will persist into the early fault-tolerant era, where small, logical qubits will similarly require classical coordination. Consequently, the field urgently demands the establishment of standardized hybrid performance benchmarks, the maturation of robust quantum-classical middleware capable of efficient transpiration and execution management, and holistic co-design frameworks that seamlessly integrate hardware constraints, software stack layers, and application-specific requirements from the outset.