arXiv:2503.19109 · Case Studies in Thermal Engineering
Leveraging quantum computing for heat conduction analysis: A case study in thermal engineering
Pietro Asinari, Matteo Maria Piredda, Giulio Barletta, Paolo De Angelis, Nada M. Alghamdi, Giovanni Trezza, Marina Provenzano, Matteo Fasano, Eliodoro Chiavazzo
The rapid development of quantum computing is creating new opportunities in thermal sciences for the exploration and simulation of heat and mass transfer phenomena, turbulent flows, as well as plasma and multiphase flows in porous media. In particular, high-fidelity simulations of turbulent flows could benefit from quantum computing through the acceleration of linear algebra solvers. However, the practical performance of current quantum computers remains limited. Major challenges include noise and fault tolerance—or, at least, effective error mitigation—as well as the development of improved quantum and hybrid quantum–classical algorithms, the tuning of algorithms for specific problem classes, and the management of both cloud-based platforms and physical quantum hardware. This work presents a case study on heat conduction as a paradigmatic test case to promote the exploration of quantum computing for thermal science. Innovative algorithmic strategies are discussed, supported by numerical and experimental case studies, and the performance of real quantum hardware (IQM Lagrange at Torino) is compared with classical computational methods. In particular, preliminary investigations on this quantum hardware yielded a mean nodal outcome error of up to 14% for the problem under consideration. In the current Noisy Intermediate-Scale Quantum (NISQ) era, these numerical results obtained on real quantum hardware are preliminary but provide valuable insights for guiding further hardware development, an effort that also requires advanced metrology. The paper highlights opportunities, current challenges, and future directions, with a particular emphasis on engineering applications.
The rapid development of quantum computing is creating new opportunities in thermal sciences for the exploration and simulation of heat and mass transfer phenomena, turbulent flows, as well as plasma and multiphase flows in porous media. In particular, high-fidelity simulations of turbulent flows could benefit from quantum computing through the acceleration of linear algebra solvers. However, the practical performance of current quantum computers remains limited. Major challenges include noise and fault tolerance—or, at least, effective error mitigation—as well as the development of improved quantum and hybrid quantum–classical algorithms, the tuning of algorithms for specific problem classes, and the management of both cloud-based platforms and physical quantum hardware. This work presents a case study on heat conduction as a paradigmatic test case to promote the exploration of quantum computing for thermal science. Innovative algorithmic strategies are discussed, supported by numerical and experimental case studies, and the performance of real quantum hardware (IQM Lagrange at Torino) is compared with classical computational methods. In particular, preliminary investigations on this quantum hardware yielded a mean nodal outcome error of up to 14% for the problem under consideration. In the current Noisy Intermediate-Scale Quantum (NISQ) era, these numerical results obtained on real quantum hardware are preliminary but provide valuable insights for guiding further hardware development, an effort that also requires advanced metrology. The paper highlights opportunities, current challenges, and future directions, with a particular emphasis on engineering applications.
Quantum computing has emerged as a transformative paradigm, leveraging principles of quantum mechanics to tackle computationally intractable problems. This manuscript explores the potential of quantum computing for solving complex engineering problems—specifically optimization, simulation, and data analysis tasks—using technologies and methodologies available up to 2022. We examine both gate-based and quantum annealing approaches, outline experimental frameworks, and compare performance against classical counterparts. Results from simulated benchmark problems demonstrate promising speedups in select cases, though practical adoption is constrained by hardware limitations such as qubit coherence times and noise. The study concludes by highlighting avenues for integrating hybrid quantum-classical workflows in engineering, along with a discussion of current constraints and future directions. Over the past decade, research efforts have focused on understanding how quantum phenomena like superposition and entanglement can be harnessed to realize computational advantages for specific problem classes. In particular, combinatorial optimization problems—ubiquitous in engineering design and logistics—offer fertile ground for quantum algorithms such as the Quantum Approximate Optimization Algorithm (QAOA) and quantum annealing. Additionally, quantum simulation techniques, including the Variational Quantum Eigensolver (VQE), promise to accelerate the modeling of physical systems at the molecular and materials level, potentially informing the design of next-generation structural and functional materials. Beyond raw algorithmic performance, this paper carefully assesses the end‑to‑end workflow, accounting for overheads in problem encoding, error mitigation, and classical post‑processing. We also present a detailed analysis of resource utilization—quantified by qubit counts, circuit depths, and annealing schedules—highlighting trade‑offs between solution quality and execution time. Ultimately, our findings underscore that, while pure quantum speedups remain rare in 2022, hybrid approaches harnessing both quantum and classical resources can yield practical benefits for small‑to‑medium scale engineering tasks. This expanded evaluation provides a roadmap for researchers and practitioners interested in applying quantum computing to real‑world engineering challenges.
Computational Fluid Dynamics (CFD) plays a central role in mechanical system design by enabling the simulation of complex flow phenomena such as turbulence, phase transitions, and fluid–structure interactions. However, high-fidelity CFD simulations—particularly those involving turbulent and multiphase flows—are often limited by the computational cost of solving large-scale, nonlinear, and high-dimensional systems of equations. This study explores the potential of quantum-enhanced computational fluid dynamics, focusing on hybrid quantum–classical solvers as a next-generation approach to overcoming these limitations. By integrating quantum algorithms with classical numerical methods, hybrid frameworks aim to accelerate key CFD tasks such as linear system solving, optimization, and high-dimensional state exploration while preserving the stability and accuracy of established solvers. The paper examines how quantum principles such as superposition and entanglement can be leveraged to improve convergence rates and design-space exploration in turbulence modeling and multiphase flow simulations. Through a conceptual and methodological analysis, this work highlights the opportunities, current constraints, and future implications of quantum-enhanced CFD for mechanical system design, offering a forward-looking perspective on the convergence of quantum computing and fluid mechanics.
The prosperous development of both hardware and algorithms for quantum computing (QC) potentially prompts a paradigm shift in scientific computing in various fields. As an increasingly active topic in QC, the variational quantum algorithm leads a promising tool for solving partial differential equations on noisy intermediate scale quantum devices. Although a clear perspective on the advantages of QC over classical computing techniques for specific mathematical and physical problems exists, applications of QC in computational fluid dynamics to solve practical flow problems, though promising, are still at the early stage of development. To explore QC in practical simulation of flow problems, this work applies a variational hybrid quantum-classical algorithm, namely the variational quantum linear solver (VQLS), to resolve the heat conduction equation through finite difference discretization of the Laplacian operator. Details of the VQLS implementation are discussed by various test instances of linear systems. The effect of the number of shots on the accuracy is studied, which reveals a logarithmic relationship. Furthermore, the heuristic scaling of the VQLS with the precision ε, the number of qubits n and the condition number k validates its time complexity reported in the literature. In addition, the successful state vector simulations of the heat conduction equation in one and two dimensions demonstrate the validity of the present VQLS-based algorithm by proof-of-concept results. Finally, the heuristic scaling for the heat conduction problem indicates that the time complexity of the present approach is logarithmically dependent on the precision ε and linearly dependent on the number of qubits n.
This report provides a comprehensive analysis of hybrid quantum-classical computing's role in addressing complex physical problems. It delineates the foundational principles of both classical and quantum paradigms, explores advanced architectural models and integration strategies, and details the application of cutting-edge quantum algorithms—including Variational Quantum Eigensolver (VQE), Quantum Phase Estimation (QPE), and Quantum Approximate Optimization Algorithm (QAOA)—alongside classical numerical methods such as Finite Element Method (FEM) and Finite Difference Method (FDM). Through a review of real-world case studies in materials science, chemistry, fluid dynamics, and high-energy physics, the report illustrates the transformative potential of this synergistic approach. Furthermore, it critically examines the prevailing challenges, encompassing hardware limitations, quantum error correction, software-hardware co-design, scalability, and data handling complexities, while forecasting the convergence with exascale computing. The aim is to elucidate the current state and future trajectory of hybrid quantum-classical computing as a pivotal tool for scientific discovery and engineering innovation in the networked era.
Quantum computing has the potential to revolutionize computational problem-solving by leveraging the quantum mechanical phenomena such as superposition and entanglement, enabling fundamentally different computational strategies compared to classical computing. Classical methods for solving complex and high dimensional partial differential equations (PDEs), crucial for modeling diverse physical phenomena, suffer from an exponential growth in computational complexity known as the curse of dimensionality. This can limit their effectiveness for certain high-resolution simulations and real-time computational applications. In contrast, quantum computing inherently exploits superposition and entanglement to efficiently represent and simultaneously manipulate large-scale discretized PDEs, using exponentially fewer resources compared to classical systems. There are currently many quantum techniques available for solving partial differential equations (PDEs), which are mainly based on variational quantum circuits. However, the existing quantum PDE solvers, particularly those based on variational quantum eigensolver (VQE) techniques, suffer from several limitations. These include low accuracy, high execution times, and low scalability on quantum simulators as well as on noisy intermediate-scale quantum (NISQ) devices, especially for multidimensional PDEs. In this work, we propose an efficient and scalable algorithm for solving multidimensional PDEs. We present two variants of our algorithm: the first leverages finite-difference method (FDM), classical-to-quantum (C2Q) encoding, and numerical instantiation, while the second employs FDM, C2Q, and column-by-column decomposition (CCD). Both variants are designed to enhance accuracy and scalability while reducing execution times. We have validated and evaluated our proposed concepts using a number of case studies including multidimensional Poisson equation, multidimensional heat equation, Black Scholes equation for financial option pricing, and Navier-Stokes equation for computational fluid dynamics (CFD), achieving promising results. Our results demonstrate higher accuracy, higher scalability, and faster execution times compared to VQE-based solvers on noise-free and noisy quantum simulators from IBM. Additionally, we validated our approach on hardware emulators and actual quantum hardware, employing noise mitigation techniques. This work establishes a practical and effective approach for solving PDEs using quantum computing for engineering and scientific applications.
Quantum computing has transitioned from a theoretical curiosity to an emerging technological paradigm with demonstrable computational advantages in specific problem domains. This paper presents a comprehensive review of current advances in quantum computing hardware, software, and near-term applications within the Noisy Intermediate-Scale Quantum (NISQ) era. We examine the architectural evolution of leading quantum platforms, including superconducting, trapped-ion, and photonic systems, analyzing their qubit counts, gate fidelities, and coherence times. The paper evaluates key quantum algorithms Shor's factoring algorithm [1], Grover's search algorithm [2], the Variational Quantum Eigensolver (VQE) [3], and the Quantum Approximate Optimization Algorithm (QAOA) [4] in the context of their practical applicability to real-world problems. We further discuss the milestone of quantum computational advantage demonstrated by Google's Sycamore processor [5] and IBM's ambitious hardware roadmap toward fault-tolerant quantum computing [6]. Our analysis reveals that while universal fault-tolerant quantum computing remains a long-term objective, NISQ-era devices are already yielding valuable results in quantum chemistry simulation, combinatorial optimization, and quantum machine learning. We conclude by identifying the critical challenges—error correction, scalability, and algorithm design that must be addressed to realize the full potential of quantum computing.