Modelling is the process of representing a model (e.g., physical, mathematical, or logical representation of a system, entity, phenomenon, or process) which includes its construction and working. This model is similar to a real system, which helps the analyst predict the effect of changes to the system. Simulation of a system is the operation of a model in terms of time or space, which helps analyze the performance of an existing or a proposed system. Modeling and simulation (M&S) is the use of models as a basis for simulations to develop data utilized for managerial or technical decision making.

In a broad sense, multiphysics refers to simulations that involve multiple physical models or multiple simultaneous physical phenomena. Multiphysics is defined as the coupled processes or systems involving more than one simultaneously occurring physical field and the studies of and knowledge about these processes and systems. As an interdisciplinary study area, multiphysics spans over many science and engineering disciplines. Multiphysics is a practice built on mathematics, physics, application, and numerical analysis. The mathematics involved usually contains partial differential equations and tensor analysis.

In fact, we live in a multiphysics world. Natural and artificial systems are running with various types of physical phenomena at different spatial and temporal scales: from atoms to galaxies and from pico-seconds to centuries. A few representative examples in fundamental and applied sciences are loads and deformations on solids, complex flows, fluid-structure interactions, plasma and chemical processes, thermo-mechanical and electromagnetic systems.

The physics refers to common types of physical processes, e.g., heat transfer (thermo-), pore water movement (hydro-), concentration field (concentro or diffuso/convecto/advecto), stress and strain (mechano-), dynamics (dyno-), chemical reactions (chemo- or chemico-), electrostatics (electro-), neutronics (neutro-), and magnetostatics (magneto-).

The implementation of multiphysics usually follows the following procedure: identifying a multiphysical process/system, developing a mathematical description of this process/system, discretizing this mathematical model into an algebraic system, solving this algebraic equation system, and postprocessing the data.

Coupling individual simulations may introduce limitations on stability, accuracy, or robustness that are more severe than the limitations imposed by the individual components. Furthermore, the data motion and data structure conversions required to iterate between independent simulations for each component may be more costly in latency and electrical power than those of the individually tuned components. Thus, “one plus one” may cost significantly more than “two” and may be less amenable to scalable execution than expected.

Conventional computer technology stores information as 0s and 1s, but a quantum computer uses qubits, which can be a 1 or a 0 or both at the same time. This enables quantum computers to consider and manipulate all combinations of bits simultaneously, making quantum computation powerful – and extremely fast.

### Multiphysics Simulations using Quantum Computing

Quantum computing as an area has undergone rapid development both in hardware and software over the last decade. Used in appropriate ways, quantum mechanics can provide powerful resources for solving certain classes of problems, achieving cost scalings with the size of the problem that are not achievable with existing “classical” computers. This is known as “quantum speedup.” Amongst the oldest and best known examples of quantum algorithms are Shor’s algorithm for factorization of integers and Grover’s algorithm for unstructured search problems. The gain in efficiency of the scaling of these algorithms can either be exponential (i.e., a problem where the solution time on a classical computer scales exponentially in the size of the problem N can have a solution time that scales polynomially for the same size on a quantum computer); or polynomial (i.e., the problem scales polynomially with N on a classical computer and with a smaller power of N on a quantum computer). In either case, for the solution of large-scale problems for which quantum algorithms have been developed, quantum computers represent a potentially transformative new paradigm in computing.

Within the last few years, much progress has been made in experimental realizations of quantum computing hardware. Several architectures have been proposed based on a variety of physical hardware. On a small scale, quantum information has been stored and manipulated in a range of2 devices, including superconducting quantum bits, trapped atomic ions, neutral atoms, silicon quantum electronics, electron spins, nuclear spins in the liquid or solid-state, and photons.

Some of these devices already make it possible to study problems from quantum physics at a scale that would be intractable to classical high-performance computing. The challenge is now to adapt the control over these devices and improve certification techniques in order to tailor them for the solution of problems that are of interest beyond basic science in physics.

There is growing evidence that QIS in general, and QC in particular, is approaching an inflection point with significant opportunities and challenges for various scientific and engineering fields. In the fields of aeroscience and engineering, there are important implications for various national missions and responsibilities, including mission planning, autonomy, air space management, and material esign, as well as advancing current high-performance computing (HPC) applications such as computational materials research, computational fluid dynamics (CFD), combustion, aerothermodynamics, and multidisciplinary design and optimization (MDAO).

The CFD Vision 2030 report commissioned by NASA advocates the need for continuous advances in HPC in the context of CFD and design optimization, notes the revolutionary impact that advances in quantum computing may have in these areas, and emphasizes the need to carefully monitor advances in this field as they develop.

Solving classical multidimensional nonlinear partial differential equations, typical of those in CFD or other applications, on a digital universal quantum computer would generally require a fault-tolerant quantum computer and could require millions of gates and qubits. Again, typical estimates imply that it could be at least a decade, and most likely more before we have universal quantum computers at this scale.

However, quantum gates do not necessarily need to reach the fault-tolerant threshold for us to conduct quantum computations. As an example, on NISQ hardware, variational quantum algorithms belonging to the family of HQCC might be useful for solving differential

equations. Moreover, analog machines and quantum annealers have been effective for implementing quantum dynamics, which themselves are described by classes of differential equations. These machines are expected to be developed earlier than their digital quantum counterparts. If so, they could be useful for simulating some specific aspects of aeroscience and engineering if the differential equations of interest can be mapped into the form of the equations describing quantum dynamics. We can also combine such NISQ computational capabilities with existing classical computer to produce a hybrid approach to computing that could have substantial advantages.

### D-Wave Systems Uses ANSYS Engineering Simulation To Help Design Next Generation Of World’s Most Advanced Quantum Computers, reported in 2015

D-Wave Systems is designing and building the world’s most advanced quantum computers with help from engineering simulation solutions from ANSYS (NASDAQ: ANSS). This next generation of supercomputers uses quantum mechanics to massively accelerate computation and has the potential to solve some of the most complex computing problems facing organizations today.

Quantum computing places extreme demands on the operating environment. The system must be isolated from external electromagnetic fields and the temperature must be maintained near absolute zero. Multiphysics simulation is a powerful tool to accurately predict the kinds of environments that can be engineered in the real world. D-Wave is using ANSYS® multiphysics solutions ranging from electromagnetic solutions for simulating how integrated circuits function and interact at extremely low temperatures, to structural and computational fluid dynamics to simulate the systems used to cool the quantum processor.

“ANSYS offers a broad product portfolio with consistently high performance across all of its multiphysics products,” said Jeremy Hilton, D-Wave’s vice president of processor development. “If we weren’t using ANSYS, we’d be forced to use disparate tools that don’t communicate with each other. These solutions are helping D-Wave optimize today’s quantum computers, while giving us valuable insight as we begin planning for the next generation.”

“D-Wave is breaking new ground every day – creating computers that are the stuff of science fiction,” said Larry Williams, director of product management, ANSYS. “It has never been tried before, but by using the power of ANSYS engineering simulation, this global leader is turning a vision into reality.”

### LG Electronics to develop quantum computing tech with Dutch firm, reported in April 2021

LG Electronics Inc. said in April 2021 that it has formed ties with Dutch quantum algorithm developer Qu & Co to conduct joint research on quantum computing technology in a move to boost competitiveness in future technologies. Under the research agreement, the two companies will develop quantum computing technology for multiphysic simulations over the next three years. Multiphysics refer to systems that involve simultaneously occurring multiple physical phenomena. Multiphysics simulations are used to analyze and verify such systems.

LG said current computers are limited in analyzing complex systems, and expects the substantially faster quantum computing technology to process them and help resolve industrial problems that account for multiple physical phenomena. LG said it expects quantum computing technology to be implemented in promising fields, including big data, connected vehicles and robotics, and to improve its competitiveness in future tech businesses.

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