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Related Experiment Video

Updated: Apr 8, 2026

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

Hamiltonian simulation for nonlinear partial differential equation by Schrödingerization.

Shoya Sasaki¹, Katsuhiro Endo², Mayu Muramatsu³

¹Department of Science for Open and Environmental Systems, Keio University, 3-14-1 Hiyoshi, Yokohama, Kanagawa, 223-8522, Japan.

Scientific Reports

|April 6, 2026

Summary

This summary is machine-generated.

We introduce Carleman linearization + Schrödingerization (CLS), a new quantum computing method for simulating nonlinear partial differential equations (PDEs). This approach enables efficient Hamiltonian simulations for complex nonlinear systems.

Keywords:

Carleman linearization Hamiltonian simulation Partial differential equations Quantum computing Schrödingerization Warped phase transformation

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Area of Science:

Quantum Computing
Computational Physics
Applied Mathematics

Background:

Hamiltonian simulation offers potential for efficient classical system equation solving.
Existing methods are often limited to linear equations, restricting applications.
Research on Hamiltonian simulation for nonlinear governing equations is limited.

Purpose of the Study:

To propose a novel Hamiltonian simulation method for nonlinear partial differential equations (PDEs).
To extend the applicability of quantum computing to a broader range of complex physical systems.

Main Methods:

Introduced Carleman linearization + Schrödingerization (CLS) method.
Applied Carleman linearization (CL) to convert nonlinear PDEs into linear differential equations.
Utilized warped phase transformation (WPT) to map linearized equations to the Schrödinger equation.

Main Results:

Demonstrated the successful application of CLS to nonlinear PDEs.
Showcased Hamiltonian simulation applicability to nonlinear systems via a nonlinear reaction-diffusion equation example.
Validated the transformation of original nonlinear equations into solvable Schrödinger equations.

Conclusions:

The CLS method effectively enables Hamiltonian simulations for nonlinear PDEs.
This research expands the scope of quantum computational advantage to nonlinear systems.
Efficient analysis of nonlinear phenomena is achievable through quantum simulation techniques.