ColibriTD Announces H-DES PDE Solver as a Step Toward Accessible Quantum Simulation in Engineering

Insider Brief:

• ColibriTD successfully executed its Hybrid Differential Equation Solver on IBM’s 156-qubit Heron R2 processor. The company describes this as the first real-hardware solution of a PDE using a variational quantum algorithm.

• H-DES addresses high-dimensional and nonlinear PDE challenges by encoding candidate solutions into parameterized quantum circuits and optimizing them classically, which may provide additional scalability beyond classical solvers.

• The solver converged on the inviscid Burgers’ equation using 50 qubits and 10,000 shots per iteration, demonstrating robustness on noisy quantum hardware without heavy reliance on error mitigation.

• ColibriTD plans to expand H-DES to more complex PDE types and integrate it into the QUICK platform, with the intention of making quantum-powered multiphysics simulation accessible to users of classical engineering software.

According to a news release from ColibriTD, the quantum software company has successfully executed its Hybrid Differential Equation Solver, H-DES, on IBM’s latest Heron-series quantum processor via IBM’s cloud-accessible quantum computing platform. The execution represents what the company calls the first real-hardware solution of a partial differential equation using a variational quantum algorithm.

Overcoming the Curse of Dimensionality in PDEs via Quantum Methods

Partial differential equations represent a wide array of physical models from fluid dynamics and combustion to weather systems and material stress simulations. Classical methods such as Finite Element Methods or Finite Volume Methods are widely used in industry, but they do face computational bottlenecks as problems grow in complexity, dimensionality, or nonlinearity.

In contrast, H-DES targets these challenges using quantum-enhanced methods. As detailed in the accompanying white paper, H-DES encodes candidate solutions in parameterized quantum circuits and uses a classical optimizer to minimize the residuals of the differential equations. This approach allows the system to treat PDE-solving as an optimization problem—an approach that is potentially advantageous for handling problems suffering from the curse of dimensionality, which limits classical solvers’ scalability in high-dimensional spaces.

Quantum Hardware Validation by Solving Burgers’ Equation with H-DES

The experiment was carried out on IBM’s 156-qubit Heron R2 device. ColibriTD used a hardware-efficient ansatz architecture involving native gates to reduce noise and execution time. The system was executed in session mode to allow for coherent classical-quantum iterations, using the CMA-ES optimizer, which is especially useful in noisy environments.

The specific test case was the inviscid Burgers’ equation, a fundamental nonlinear PDE used in fluid dynamics and wave propagation. Using 50 qubits and 10,000 shots per evaluation, H-DES successfully converged to a solution after 160 iterations with a final loss below 0.05. As noted in the white paper, “The results in this section constitute the first successful convergence of a VQA-based partial differential equation solver for the inviscid Burgers’ equation using 50 qubits on a NISQ 156-qubit ibm fez (Heron R2) quantum processor provided by IBM.”

Comparative Performance: Classical Solvers, Prior Quantum Attempts, and H-DES

According to the white paper, a selection of previous approaches to solving PDEs on quantum hardware have been limited in scope or effectiveness. For instance, a 2023 study found that the VQLS algorithm failed to converge even on the relatively simple 1D Poisson equation when executed on IBM hardware. Similarly, attempts by Song et al. to solve the incompressible Navier–Stokes equations failed to produce reliable results due to noise and resource limitations.

ColibriTD claims its method is differentiated not only by its robustness but also by its generality. As emphasized in the white paper, the solver does not rely on grid discretization or derivative approximations, which are standard in classical methods. Instead, it uses a spectral representation, decomposing solution functions into orthogonal polynomial bases, which allows accurate approximations with relatively shallow quantum circuits and limited qubit resources. This enables the reuse of optimized circuits across varying sample points, increasing flexibility and precision without added cost.

Still, classical methods remain more mature and practical for many PDE applications today. Established solvers can efficiently handle well-conditioned linear PDEs and many nonlinear systems on classical high-performance computing infrastructure. However, these methods often require intensive mesh refinement and can become computationally infeasible when tackling highly nonlinear, coupled, or high-dimensional PDEs.

The purpose of exploring quantum approaches, therefore, is not to replace classical solvers outright but to assess whether quantum hardware can provide scaling advantages as both hardware and algorithms mature. H-DES’s controlled growth in circuit depth and qubit usage means it may be a potential candidate for scaling to more demanding industrial use cases, including multi-physics simulations.

Looking Ahead: From Heron to Flamingo and Broader PDE Applications

According to the white paper, future plans include adapting H-DES to handle stochastic and integro-differential equations. The authors also note that expected improvements in quantum hardware, such as IBM’s upcoming Flamingo processor with more than 1000 qubits and improved error rates, could support more advanced versions of the algorithm and make broader use cases viable.

“Our latest findings using IBM’s Heron QPU mark a significant step towards harnessing the power of quantum computing for solving partial differential equations,” said Dr. Laurent Guiraud, Co-Founder and CEO of ColibriTD, in the company’s release. “This opens up exciting new avenues for research and development in fields such as fluid dynamics, materials science, and weather forecasting.”

Dr. Frédéric du Bois-Reymond, a partner at Earlybird-X, added: “We are super happy about the great work of the team at ColibriTD to enable the relevant use of quantum computing performance solving partial differential equations. This opens strong opportunities to enter big markets with a solid value proposition.”

Overall, ColibriTD’s QUICK platform is designed to lower the entry barrier for users accustomed to classical simulation software. By integrating H-DES into a user-friendly interface, the company intends to make quantum-powered simulation more accessible.

As more use cases are benchmarked and validated, the potential for quantum computing to augment or complement classical simulation workflows will become clearer. While not yet a replacement, ColibriTD’s demonstration is an example of how we might practically apply quantum technology toward applications in scientific computing.