Optimizing Quantum Circuits for Arithmetic

TL;DR

This paper introduces optimized quantum circuits for evaluating common classical functions, facilitating better resource estimation and implementation of quantum algorithms involving oracles.

Contribution

It presents a quantum software stack for automatic generation of circuits for piecewise smooth functions, integrating classical HPC insights for optimization.

Findings

Enables detailed cost analysis of quantum algorithms

Provides resource estimates for function evaluation circuits

Supports identification of applications for future quantum devices

Abstract

Many quantum algorithms make use of oracles which evaluate classical functions on a superposition of inputs. In order to facilitate implementation, testing, and resource estimation of such algorithms, we present quantum circuits for evaluating functions that are often encountered in the quantum algorithm literature. This includes Gaussians, hyperbolic tangent, sine/cosine, inverse square root, arcsine, and exponentials. We use insights from classical high-performance computing in order to optimize our circuits and implement a quantum software stack module which allows to automatically generate circuits for evaluating piecewise smooth functions in the computational basis. Our circuits enable more detailed cost analyses of various quantum algorithms, allowing to identify concrete applications of future quantum computing devices. Furthermore, our resource estimates may guide future research aiming to reduce the costs or even the need for arithmetic in the computational basis altogether.