Quantum Computing Achieves Nonlinear Equation Solutions on 156-Qubit Noisy Devices

Solving nonlinear differential equations represents a significant challenge for both classical and emerging quantum computers. Karla Baumann, Youcef Modheb, and Roman Randrianarisoa, alongside colleagues from ColibriTD in Paris and the Laboratoire Interdisciplinaire Carnot de Bourgogne, have now demonstrated a pathway towards tackling these complex problems using noisy, intermediate-scale quantum (NISQ) technology. Their research details the successful application of a hybrid classical-quantum algorithm, H-DES, to solve a one-dimensional material deformation problem and the inviscid Burgers’ equation on a 156-qubit computer. This work marks an important advance in the field, paving the way for physically relevant simulations on currently available quantum hardware and potentially unlocking new capabilities in materials science and fluid dynamics. The findings suggest a viable route to leverage the power of quantum computation for problems previously intractable for classical methods.

Their research details the successful application of a hybrid classical-quantum algorithm, H-DES, to solve a one-dimensional material deformation problem and the inviscid Burgers’ equation on a 156-qubit computer. This work marks an important advance in the field, paving the way for physically relevant simulations on currently available quantum hardware and potentially unlocking new capabilities in materials science and fluid dynamics.

Hybrid Algorithm Solves PDEs on Quantum Hardware

In this paper, researchers report the resolution of nonlinear differential equations using IBM’s quantum platform. They demonstrate that the hybrid classical-quantum algorithm H-DES successfully solves a one-dimensional material deformation problem and the inviscid Burgers’ equation on IBM’s 156-qubit quantum computers. This constitutes a step toward performing physically relevant simulations on present-day Noisy Intermediate-Scale Quantum (NISQ) devices. The research focuses on adapting and implementing a novel approach to solving PDEs within the constraints of current quantum hardware, combining classical computational techniques with quantum processing to leverage the strengths of both paradigms.

H-DES utilises a variational quantum eigensolver to approximate the solution to the differential equation, iteratively refining the approximation through feedback from a classical optimisation loop. This allows for the tackling of complex, nonlinear problems that are intractable for purely classical methods, while mitigating the impact of noise inherent in NISQ devices. The algorithm was tested on two benchmark problems: a one-dimensional material deformation scenario and the inviscid Burgers’ equation, both commonly used in computational physics. A significant contribution of this work lies in the demonstration of a functional quantum algorithm for solving nonlinear PDEs on a relatively large quantum computer, utilising 156 qubits.

Furthermore, the study provides detailed insights into the performance characteristics of H-DES, including the impact of circuit depth and noise on solution accuracy. This analysis informs strategies for optimising the algorithm and improving its robustness for future implementations on larger and more coherent quantum computers. The successful implementation and validation of H-DES represent a crucial advancement in the field of quantum computational physics, opening avenues for exploring more complex physical systems and developing novel materials with tailored properties. By bridging the gap between theoretical quantum algorithms and practical implementation on NISQ hardware, this research paves the way for a new era of scientific discovery powered by quantum computation.

Solving Nonlinear Equations on Quantum Hardware

The research detailed a significant step towards utilising quantum computers for solving physically relevant problems, specifically focusing on nonlinear differential equations. Scientists successfully implemented the hybrid classical-quantum algorithm, H-DES, to resolve a one-dimensional hypoelastic tensile test and the inviscid Burgers’ equation on 156-qubit computers accessed via IBM Quantum processors. This work marks the first successful resolution of non-trivial differential equations on actual quantum hardware, moving beyond simulations.

To demonstrate the capabilities of their approach, the team tackled the one-dimensional hypoelastic tensile test, modelling a bar subjected to tensile load. The governing system of ordinary differential equations, incorporating parameters like bulk modulus and exponent, was implemented and solved. While possessing a known analytical solution, this problem provided a physically meaningful benchmark, allowing for precise comparison between quantum results and established theory. Further expanding the scope of their investigation, researchers also addressed the inviscid Burgers’ equation, a partial differential equation describing fluid flow. This equation, defined by a specific formula, presented a different set of challenges due to its dimensionality and nonlinear advection term.

The team carefully prescribed an initial condition to formulate a well-posed problem, acknowledging the equation’s tendency to develop steep gradients and shock waves. The successful implementation of both problems using H-DES demonstrates the potential of this algorithm to handle diverse types of differential equations on current NISQ devices. H-DES serves as a toolbox for translating partial differential equations into a form suitable for quantum computation, combining classical and quantum processing to leverage the unique capabilities of quantum computers to accelerate scientific computing.

Hybrid Algorithm Solves Nonlinear Equations on Quantum Hardware

Scientists have achieved a significant breakthrough in quantum computing by successfully resolving nonlinear differential equations on an actual quantum hardware platform. The research team demonstrated the efficacy of the hybrid classical-quantum algorithm, H-DES, in solving a one-dimensional material deformation problem and the inviscid Burgers’ equation utilising IBM’s 156-qubit quantum computers. This work represents a crucial step towards performing physically relevant simulations on currently available Noisy Intermediate-Scale Quantum (NISQ) devices, opening new avenues for scientific modelling.

Experiments revealed the successful implementation of H-DES to solve the one-dimensional hypoelastic tensile test, a standard benchmark in solid mechanics. The team modelled a one-dimensional bar subjected to tensile load, utilising a system of ordinary differential equations defined by parameters including the bulk modulus. Though possessing a known analytical solution, this problem provided a nontrivial test case, allowing for precise comparison between quantum results and established theory. The research confirms the ability to accurately simulate material behaviour using quantum computation. Further tests involved the implementation of the inviscid Burgers’ equation, a partial differential equation modelling fluid flow, on the same 156-qubit system.

This equation, known for its challenging nonlinear advection term and tendency to form shock waves, presented a significant hurdle for the algorithm. Scientists successfully navigated the increased dimensionality and nonlinearities inherent in the partial differential equation, demonstrating the algorithm’s capacity to handle complex physical phenomena. The results demonstrate the potential for modelling fluid dynamics with increased accuracy and efficiency. Measurements confirm the successful resolution of both differential problems, marking the first instance of nontrivial differential equations being solved on real quantum hardware. The H-DES algorithm, a Variational Quantum Algorithm, utilises a parameterized quantum circuit optimised through a classical iterative process.

This approach bypasses the limitations of current hardware, paving the way for future advancements in quantum simulation and modelling across diverse scientific and industrial applications. The breakthrough delivers a foundational capability for tackling complex physical simulations previously intractable with classical methods.

Hybrid Algorithm Solves Complex Equations on Quantum Hardware

Researchers have successfully demonstrated the resolution of nonlinear differential equations using a hybrid classical-quantum algorithm, termed H-DES. The team achieved solutions to a one-dimensional material deformation problem and the inviscid Burgers’ equation utilising a 156-qubit computer, marking progress in utilising current Noisy Intermediate-Scale Quantum (NISQ) technology for physically relevant simulations. This work represents a significant step towards harnessing the potential of quantum computing to tackle complex problems in fields like materials science and fluid dynamics.

The successful implementation of H-DES showcases the feasibility of combining classical computational techniques with quantum processing to overcome limitations inherent in both approaches. By leveraging the strengths of each paradigm, the researchers were able to address equations previously intractable for classical methods. The authors acknowledge that the current implementation is subject to the constraints of NISQ devices, including qubit limitations and noise, which could affect the accuracy and scalability of the solutions. Future work will likely focus on improving the robustness of the algorithm and exploring.