Efficient realization of quantum primitives for Shor's algorithm using PennyLane library

TL;DR

This paper introduces a PennyLane-based software package that efficiently implements quantum gates and algorithms, including a native decomposition technique for trapped-ion quantum processors to optimize Shor's algorithm execution.

Contribution

The paper presents a novel decomposition method tailored for trapped-ion quantum computers and provides a comprehensive PennyLane package for implementing key quantum algorithms.

Findings

Decomposition coefficients for native gate implementation derived.

Efficient modular exponentiation and quantum Fourier transform templates provided.

Resource analysis for Shor's algorithm on trapped-ion hardware conducted.

Abstract

Efficient realization of quantum algorithms is among main challenges on the way towards practical quantum computing. Various libraries and frameworks for quantum software engineering have been developed. Here we present a software package containing implementations of various quantum gates and well-known quantum algorithms using PennyLane library. Additoinally, we used a simplified technique for decomposition of algorithms into a set of gates which are native for trapped-ion quantum processor and realized this technique using PennyLane library. The decomposition is used to analyze resources required for an execution of Shor's algorithm on the level of native operations of trapped-ion quantum computer. Our original contribution is the derivation of coefficients needed for implementation of the decomposition. Templates within the package include all required elements from the quantum part of Shor's algorithm, specifically, efficient modular exponentiation and quantum Fourier transform that can be realized for an arbitrary number of qubits specified by a user. All the qubit operations are decomposed into elementary gates realized in PennyLane library. Templates from the developed package can be used as qubit-operations when defining a QNode.