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Wavelength-Uniform Quantum Algorithms for Quantum Dynamics
Shi Jin, Chuwen Ma
One of the main challenges in quantum simulation is the prohibitive cost of computing its solutions in the semi-classical regime, in which the de Broglie wavelength is small compar…
Quantum simulation of the Liouville equation in classical mechanics with discontinuous potential via Schrödingerization
Shi Jin, Shuyi Zhang
We develop quantum simulation algorithms for the Liouville equation of classical mechanics with discontinuous potential. Such discontinuities represent potential barriers at which…
Analog photonic simulator for large-scale transport
Mengyu Zhao, Xuezhi Zhu, Nikita Guseynov +9
Transport equations describe how physical quantities -- such as mass, energy, momentum, concentration, probability, or fields -- are carried, propagated, or redistributed through s…
Hybrid quantum-classical algorithms for complex nonlinear partial differential equations with Ginzburg-Landau potential and vortex motion laws
Shi Jin, Nana Liu, Chuwen Ma
We propose quantum algorithms for complex-valued nonlinear partial differential equations in the strongly nonlinear regime, where the dynamics is governed by vortex cores, phase si…
Quantum algorithms for Young measures: applications to nonlinear partial differential equations
Shi Jin, Nana Liu, Maria Lukacova-Medvidova +1
Many nonlinear PDEs have singular or oscillatory solutions or may exhibit physical instabilities or uncertainties. This requires a suitable concept of physically relevant generaliz…
Quantum simulation of Liouville equation in geometrical optics with partial transmission and reflection via Schrödingerization
Shi Jin, Shuyi Zhang
This paper investigates quantum simulation algorithms for the Liouville equation in geometrical optics with partial transmission and reflection at sharp interfaces, based on the Sc…