Alternatives to a nonhomogeneous partial differential equation quantum algorithm

TL;DR

This paper proposes modifications to a quantum algorithm for solving nonhomogeneous linear PDEs, reducing preparation costs and improving precision, thus making it more feasible with current technology.

Contribution

It introduces structural modifications to the existing quantum PDE solver to lower resource requirements and enhance accuracy for specific inputs.

Findings

Reduced ancillary state preparation costs

Improved algorithmic precision for certain inputs

Enhanced feasibility for experimental implementation

Abstract

Recently J. M. Arrazola et al. [Phys. Rev. A 100, 032306 (2019)] proposed a quantum algorithm for solving nonhomogeneous linear partial differential equations of the form $A\psi(\textbf{r})=f(\textbf{r})$. Its nonhomogeneous solution is obtained by inverting the operator $A$ along with the preparation and measurement of special ancillary modes. In this work we suggest modifications in its structure to reduce the costs of preparing the initial ancillary states and improve the precision of the algorithm for a specific set of inputs. These achievements enable easier experimental implementation of the quantum algorithm based on nowadays technology.