20 November 2020
##
Quantum algorithm for solving nonlinear differential equations

Qu&Co in collaboration with our academic advisor Oleksandr Kyriienko at the University of Exeter has developed a proprietary quantum algorithm which promises a generic and efficient way to solve nonlinear differential equations. The algorithm is compatible with near-term quantum-processors, with promising extensions for fault-tolerant implementation. Using a quantum feature map encoding, we define functions as expectation values of parametrized quantum circuits. We use automatic differentiation to represent function derivatives in an analytical form as differentiable quantum circuits (DQCs), thus avoiding inaccurate finite difference procedures for calculating gradients. We describe a hybrid quantum-classical workflow where DQCs are trained to satisfy differential equations and specified boundary conditions. As a particular example setting, we show how this approach can implement a spectral method for solving differential equations in a high-dimensional feature space. From a technical perspective, we design a Chebyshev quantum feature map that offers a powerful basis set of fitting polynomials and possesses rich expressivity. We simulate the algorithm to solve an instance of Navier-Stokes equations, and compute density, temperature and velocity profiles for the fluid flow in a convergent-divergent nozzle.

Published in
Blog

Tagged under

- Unifying Quantum Error Mitigation 29 July 2021 in Blog
- Quantum Training of a Classical DNN 22 July 2021 in Blog
- Exploiting fermion number in factorized decompositions of the electronic structure Hamiltonian 17 July 2021 in Blog
- Quantum Evolution Kernel 09 July 2021 in Blog
- Efficient ML for quantum many-body problems 28 June 2021 in Blog
- Quantum computing 40 years later 21 June 2021 in Blog

Copyright © Qu & Co BV