Lecture notes that organize quantum PDE algorithms around block encodings of finite-difference and finite-element operators, tracking discretization, preparation, normalization, postselection, and measurement costs.
Quantum Algorithm for Simulating the Wave Equation
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abstract
We present a quantum algorithm for simulating the wave equation under Dirichlet and Neumann boundary conditions. The algorithm uses Hamiltonian simulation and quantum linear system algorithms as subroutines. It relies on factorizations of discretized Laplacian operators to allow for improved scaling in truncation errors and improved scaling for state preparation relative to general purpose linear differential equation algorithms. We also consider using Hamiltonian simulation for Klein-Gordon equations and Maxwell's equations.
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A Quantum Path to Partial Differential Equations
Lecture notes that organize quantum PDE algorithms around block encodings of finite-difference and finite-element operators, tracking discretization, preparation, normalization, postselection, and measurement costs.