Quantum Algorithms and Circuits for Scientific Computing

TL;DR

This paper develops quantum algorithms for fundamental mathematical functions like square root and logarithm, ensuring accuracy, efficiency, and reversibility, with performance validated against classical numerical software.

Contribution

It introduces new quantum algorithms for key functions with proven error bounds and efficiency, advancing quantum scientific computing capabilities.

Findings

Quantum algorithms achieve comparable accuracy to classical methods.

Algorithms are efficient and scalable for large inputs.

Performance tests show promising results against classical software.

Abstract

Quantum algorithms for scientific computing require modules implementing fundamental functions, such as the square root, the logarithm, and others. We require algorithms that have a well-controlled numerical error, that are uniformly scalable and reversible (unitary), and that can be implemented efficiently. We present quantum algorithms and circuits for computing the square root, the natural logarithm, and arbitrary fractional powers. We provide performance guarantees in terms of their worst-case accuracy and cost. We further illustrate their performance by providing tests comparing them to the respective floating point implementations found in widely used numerical software.