A quantum dot implementation of the quantum NAND algorithm

TL;DR

This paper presents a physical implementation of the quantum NAND algorithm using quantum dots and continuous time quantum walks, demonstrating robustness against disorder and potential for analyzing complex quantum systems.

Contribution

It introduces a novel quantum dot-based platform for executing the quantum NAND algorithm with resilience to environmental disturbances.

Findings

Query complexity remains stable despite disorder and dephasing.

Implementation is feasible in 2D structures without temperature or dimensionality constraints.

Potential application in evaluating high-order correlation functions.

Abstract

We propose a physical implementation of the quantum NAND tree evaluation algorithm. Our approach, based on continuous time quantum walks, uses the wave interference of a single electron in a heirarchical set of tunnel coupled quantum dots. We find that the query complexity of the NAND tree evaluation does not suffer strongly from disorder and dephasing, nor is it directly limited by temperature or restricted dimensionality for 2-d structures. Finally, we suggest a potential application of this algorithm to the efficient determination of high-order correlation functions of complex quantum systems.