Shor's quantum algorithm using electrons in semiconductor nanostructures

TL;DR

This paper proposes and numerically investigates a quantum algorithm for factoring 15 using electrons in semiconductor nanostructures, demonstrating high fidelity and robustness in a solid-state quantum computing platform.

Contribution

It introduces a novel implementation of Shor's algorithm using electron transport in quantum wires with surface acoustic waves, showing promising simulation results.

Findings

High estimated fidelity of the quantum algorithm

Robustness against small destabilizing effects

Efficient implementation in semiconductor nanostructures

Abstract

Shor's factoring algorithm illustrates the potential power of quantum computation. Here we present and numerically investigate a proposal for a compiled version of such an algorithm based on a quantum-wire network exploiting the potentialities of fully coherent electron transport assisted by the surface acoustic waves. Specifically, a non standard approach is used to implement, in a simple form, the quantum circuits of the modular exponentiation execution for the simplest instance of the Shor's algorithm, that is the factorization of $N$=15. The numerical procedure is based on a time-dependent solution of the multi-particle Schr\"odinger equation. The near-ideal algorithm performance and the large estimated fidelity indicate the efficiency of the protocol implemented, which also results to be almost unsensitive to small destabilizing effects during quantum computation.