Digital quantum simulation of Schr\"odinger dynamics using adaptive approximations of potential functions

TL;DR

This paper presents an efficient method for digital quantum simulation of Schrödinger dynamics, using adaptive approximations of potential functions to reduce gate counts while maintaining precision.

Contribution

It introduces adaptive grid techniques for approximating potential functions, improving efficiency in quantum simulations compared to uniform approaches.

Findings

Adaptive grids reduce gate count significantly.

Method applies to both physical and artificial potentials.

Potential for extension to higher-dimensional systems.

Abstract

Digital quantum simulation (DQS) of continuous-variable quantum systems in the position basis requires efficient implementation of diagonal unitaries approximating the time evolution operator generated by the potential energy function. In this work, we provide efficient implementations suitable for potential functions approximable by piecewise polynomials, with either uniform or adaptively chosen subdomains. For a fixed precision of approximation, we show how adaptive grids can significantly reduce the total gate count at the cost of introducing a small number of ancillary qubits. We demonstrate the circuit construction with both physically motivated and artificially designed potential functions, and discuss their generalizations to higher dimensions.