Develops a quantum algorithm for linear matrix differential equations with query complexity O~(ν L t / ε) that is nearly optimal and yields polynomial to exponential speedups for open quantum system simulation.
Improved Quantum Algorithms for Linear and Nonlinear Differential Equations
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Quantum algorithms achieve polylog(N) complexity for high-dimensional linear SDEs by amplitude-encoding the solution and noise via Dyson series or Euler-Maruyama approximations plus quantum linear systems solvers.
The reduced basis algorithm exactly reproduces the nonlinear dynamics of polynomial ODEs and PDEs over m timesteps using a linear quantum operator on a reduced monomial basis, with qubit scaling logarithmic in grid size for PDEs.
A hybrid quantum-classical variational method using polynomial approximations to the energy functional enables finite element analysis of a 1D Neo-Hookean hyperelastic model on near-term quantum hardware.
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Reduced basis algorithm for solving nonlinear differential equations on quantum computers
The reduced basis algorithm exactly reproduces the nonlinear dynamics of polynomial ODEs and PDEs over m timesteps using a linear quantum operator on a reduced monomial basis, with qubit scaling logarithmic in grid size for PDEs.