# Carleman linearization approach for chemical kinetics integration toward quantum computation

@article{Akiba2022CarlemanLA, title={Carleman linearization approach for chemical kinetics integration toward quantum computation}, author={Takaki Akiba and Youhi Morii and Kaoru Maruta}, journal={ArXiv}, year={2022}, volume={abs/2207.01818} }

The Harrow, Hassidim, Lloyd (HHL) algorithm is a quantum algorithm expected to accelerate solving large-scale linear ordinary differential equations (ODEs). To apply the HHL to non-linear problems such as chemical reactions, the system must be linearized. In this study, Carleman linearization was utilized to transform nonlinear first-order ODEs of chemical reactions into linear ODEs. Although this linearization theoretically requires the generation of an infinite matrix, the original nonlinear…

## References

SHOWING 1-10 OF 11 REFERENCES

### Efficient quantum algorithm for dissipative nonlinear differential equations

- Mathematics, Computer ScienceProceedings of the National Academy of Sciences
- 2021

A lower bound on the worst-case complexity of quantum algorithms for general quadratic differential equations is provided, showing that the problem is intractable for $R \ge \sqrt{2}$.

### Quantum algorithm for linear systems of equations.

- Computer Science, MathematicsPhysical review letters
- 2009

This work exhibits a quantum algorithm for estimating x(-->)(dagger) Mx(-->) whose runtime is a polynomial of log(N) and kappa, and proves that any classical algorithm for this problem generically requires exponentially more time than this quantum algorithm.

### Solving Burgers' equation with quantum computing

- PhysicsQuantum Inf. Process.
- 2022

A recently introduced quantum algorithm for partial differential equations to Burgers’ equation is adapted and developed to develop a quantum CFD solver that determines its solutions and verified the quantum Burgers' equation algorithm to find the flow solution when a shockwave is and is not present.

### Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control

- MathematicsPloS one
- 2016

This work presents a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space and demonstrates the usefulness of nonlinear observable subspaces in the design of Koop man operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.

### Sufficient conditions for stabilization of sampled-data nonlinear systems via discrete-time approximations

- Mathematics
- 1999

### IBM’s roadmap for scaling quantum technology

- https://research.ibm.com/blog/ibm-quantumroadmap
- 2020

### Application de la théorie des équations intégrales linéaires aux systèmes d'équations différentielles non linéaires

- Mathematics
- 1932

### Computational Fluid Dynamics Handbook

- (Maruzen,
- 2003