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ColibriTD

The IBM Qiskit Functions Catalogue now offers QUICK-PDE, a quantum-classical hybrid partial differential equation (PDE) solution developed by ColibriTD. QUICK-PDE, which is based on the company’s H-DES (Hybrid Differential Equation Solver) method, allows researchers and developers to use IBM’s utility-scale quantum systems through cloud access to solve domain-specific multiphysics PDEs.

QUICK-PDE

ColibriTD, a business that specializes in quantum-powered multiphysics simulation, created the multiphysics solver QUICK-PDE. It can be found in the IBM Qiskit Functions Catalogue as an application function. The QUICK (Quantum Innovative Computing Kit) platform from ColibriTD includes QUICK-PDE.

By using IBM’s quantum computers via the cloud, the function enables researchers, developers, and simulation engineers to solve multiphysics partial differential equations (PDEs). It offers a simplified, developer-friendly interface for partial differential equation solutions unique to a certain domain.

How it works

• The patented H-DES (Quantum-Classical Hybrid Differential Equation Solver) algorithm developed by ColibriTD serves as the foundation for QUICK-PDE.
• The approach encodes trial answers as linear combinations of orthogonal functions, usually Chebyshev polynomials, in order to solve differential equations. In particular, the function is encoded using $2^n$ Chebyshev polynomials, where $n$ is the number of qubits.
• The angles of a Variable Quantum Circuit (VQC) parametrise these orthogonal functions.
• The function is encoded in a state created by the ansatz and evaluated by observables whose combinations enable the function to be assessed at any point in time.
• The differential equations are encoded using a loss function. Until a good outcome is obtained, the trial solutions are progressively brought closer to the real solutions by adjusting the VQC’s angles in a hybrid loop.
• Various optimisers can be used by the solution. By utilising a global optimiser like “CMAES” (from the cma Python library) initially, and then a fine-tuned optimiser (like those from Scipy, such “SLSQP” for the Material Deformation scenario), you can, for example, chain together optimisers to follow a gradient.
• Noise reduction strategies are incorporated into the algorithm. Using the noise learner approach, it may perform noise mitigation within the CMA optimisation process by stacking identical circuits and evaluating identical observables on various qubits within a bigger circuit, hence lowering the number of shots required.
• Each variable’s function can be encoded using a different amount of qubits. Although the function may select optimal default values, users have the option to modify these. Likewise, it is possible to modify the depth of the ansatz per function.
• Another variable that can be adjusted is the quantity of shots required to complete each circuit. The shots parameter is given as a list, whose length corresponds to the number of optimisers utilised, because there are several optimisation processes involved. Both the Material Deformation and Computational Fluid Dynamics use cases come with default shot values.
• Users have the option to select “RANDOM” or “PHYSICALLY_INFORMED” as their initialization approach for the VQC angles. Although “PHYSICALLY_INFORMED” is the default and frequently works, it might not be appropriate in every situation; in these situations, “RANDOM” can be used.

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Multiphysics Capabilities and Use Cases:

The purpose of QUICK-PDE is to resolve challenging multiphysics issues. Currently, two main use cases are supported:

Computational Fluid Dynamics (CFD)

• Issues include the inviscid Burgers’ equation, a basic CFD model. This equation mimics non-viscous fluid flow and shockwave propagation, which is important for automotive and aerospace applications.
• The Navier-Stokes equations for fluid motion have an inviscid Burgers’ equation when viscosity is null ($\nu = 0$). $\frac{\partial u}{\partial t} + u\frac{\partial u}{\partial x} = 0$1117, where $u(x,t)$ is the fluid speed field.
• The current implementation only accepts linear functions as initial conditions for this use case: where $a$ and $b$ are random constants, and $u(t=0, x) = ax + b$. To observe how these constants affect the solution, users can change them.
• The CFD differential equation arguments are on a fixed grid: space ($x$) between 0 and 0.95 with a step size of 0.2375, and time ($t$) between 0 and 0.95 with 30 sample points.
  The use of QUICK-PDE to investigate the dynamics of innovative reactive fluids for heat transfer in small modular reactors is one example given.

Material Deformation (MD)

• The second is Material Deformation (MD), which is concerned with mechanical deformation in 1D under a hypoelastic regime, like in a tensile test. This is essential for manufacturing and materials research since it simulates how materials react to stress.
• A bar that is dragged at one end and fixed at the other is described in the problem. A system of two equations comprising a strain function ($\sigma$) and a stress function ($u$) characterises it.
• In this use instance, the work required to stretch the bar is represented by a boundary condition associated with surface stress ($t$).
• MD differential equation arguments are on a fixed grid, which is space ($x$) between 0 and 1 with a 0.04 step size.

The H-DES algorithm will be incorporated into QUICK-PDE in future iterations to expand its functionality to higher-dimensional issues and other physics fields, such as electromagnetic simulations and heat transfer.

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Usability and Accessibility:

• Users of the IBM Quantum Premium Plan, Dedicated Service, or Flex Plan can access QUICK-PDE.
• Access to the function must be requested by users.
• The complexity of the quantum workflow is abstracted away by application functions such as QUICK-PDE. They make it simpler to incorporate quantum methods into current processes without having to create a whole quantum pipeline from scratch by taking classical inputs (such as physical parameters) and returning domain-familiar classical outputs.
• This makes it possible for researchers with domain expertise, data scientists, and corporate developers to investigate issues that are difficult for traditional solutions or call for high-performance computing (HPC) resources.
• Several execution modes, such as “job,” “session,” and “batch,” are supported by the function. “job” is the default mode.
• A dictionary containing the input parameters is provided. Use_case (“CFD” or “MD”) and physical_parameters unique to the selected use case (e.g., a, b for CFD; t, K, n, b, epsilon_0, sigma_0 for MD) are important parameters. Users can modify nb_qubits, depth, optimiser, shots, optimizer_options, initialisation, backend_name, and mode using the optional arguments.
• A dictionary with the sample points for every variable and the function(s)’s computed values at these points is the function’s output. The CFD scenario, for instance, gives function values for u(t,x) and samples for t and x. Samples for x and function values for u(x) and sigma(x) are provided in the MD case. The output array’s structure corresponds to the sample points in the variables’ alphabetic order.
• For examples such as the Inviscid Burgers’ equation and Hypoelastic 1D tensile test, benchmarks are available that display statistics such as the number of qubits utilised, initialisation approach, error obtained ($\approx 10^{-2}$), total duration, and runtime usage.
• There is a tutorial that walks through the process of modelling a flowing non-viscous fluid with QUICK-PDE, including setting up beginning conditions, modifying the parameters of the quantum hardware, executing the function, and applying the outcomes. The documentation includes examples for both MD and CFD use cases.

In conclusion, QUICK-PDE provides a useful foundation for investigating hybrid quantum-classical algorithms for resolving intricate multiphysics issues, which may improve modelling precision and cut down on simulation time in comparison to traditional approaches. It is seen as an important illustration of quantum value in scientific computing and a step towards opening doors that were previously thought to be unattainable with traditional instruments.