Southwest Quantum Information and Technology

Bounding the costs of quantum simulation of many-body physics in real space

Presenting Author: Ian Kivlichan, Harvard
Contributing Author(s): Nathan Wiebe, Ryan Babbush and Alán Aspuru-Guzik

Simulating many-particle dynamics, such as first-quantized quantum chemistry, with logarithmic dependence on the accuracy has proven to be a challenge. This is because the traditional approach, based on the quantum Fourier transform, introduces Hamiltonians with large max-norms. We solve this problem by using a new approach based on high-order finite difference formulae. This change makes the approach practical, and we further demonstrate that it can simulate n interacting particles using Õ(n^4) calculations of the pairwise interactions for a fixed spatial grid spacing, versus the Õ(n^5) time required by previous methods, assuming the number of particles is proportional to the number of orbitals. We also show that previous work has overlooked the fact that discretization errors can remove these exponential speedups, and address this by providing bounds on the discretization error and sufficient conditions to guarantee efficiency.

Read this article online: https://arxiv.org/abs/1608.05696

(Session 4 : Thursday from 4:00pm - 4:30pm)