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Analog quantum simulation of parabolic partial differential equations using Jaynes-Cummings-like models
Shi Jin, Nana Liu
We present a simplified analog quantum simulation protocol for preparing quantum states that embed solutions of parabolic partial differential equations, including the heat, Black-…
Dilation theorem via Schrödingerisation, with applications to the quantum simulation of differential equations
Junpeng Hu, Shi Jin, Nana Liu +1
Nagy's unitary dilation theorem in operator theory asserts the possibility of dilating a contraction into a unitary operator. When used in quantum computing, its practical implemen…
Quantum Simulation for Partial Differential Equations with Physical Boundary or Interface Conditions
Shi Jin, Xiantao Li, Nana Liu +1
This paper explores the feasibility of quantum simulation for partial differential equations (PDEs) with physical boundary or interface conditions. Semi-discretisation of such prob…
Quantum Simulation for Quantum Dynamics with Artificial Boundary Conditions
Shi Jin, Nana Liu, Xiantao Li +1
Quantum dynamics, typically expressed in the form of a time-dependent Schrödinger equation with a Hermitian Hamiltonian, is a natural application for quantum computing. However, wh…