Quantum simulation of a noisy classical nonlinear dynamics

          @misc{ scivideos_PIRSA:25100059,
            doi = {10.48660/25100059},
            url = {https://pirsa.org/25100059},
            author = {Bravyi, Sergey},
            keywords = {Quantum Information},
            language = {en},
            title = {Quantum simulation of a noisy classical nonlinear dynamics},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2025},
            month = {oct},
            note = {PIRSA:25100059 see, \url{https://scivideos.org/index.php/pirsa/25100059}}
          }
          

Abstract

We consider the problem of simulating dynamics of classical nonlinear dissipative systems with N>>1 degrees of freedom. To make the problem tractable for quantum computers, we add a weak Gaussian noise to the equation of motion and the initial state. Our main result is an end-to-end quantum algorithm for simulating the noisy dynamics of nonlinear systems satisfying certain sparsity and divergence-free conditions. For any constant nonzero noise rate, the quantum runtime scales polynomially with log(N), evolution time, inverse error tolerance, and the relative strength of nonlinearity and dissipation.