Molecular Realization of a Quantum NAND Tree

TL;DR

This paper demonstrates how a molecular system can realize a quantum NAND gate by mapping quantum scattering processes onto a tight-binding model and validating results with DFT and NEGF calculations, advancing molecular quantum computing.

Contribution

It analytically derives quantum NAND gate operation from scattering theory and maps it onto a molecular system, extending to other classical gates for quantum computing.

Findings

Analytical derivation of NAND outputs from scattering theory.

Mapping of quantum NAND onto molecular systems validated by DFT and NEGF.

Extension of molecular platform to realize other classical gates.

Abstract

The negative-AND (NAND) gate is universal for classical computation making it an important target for development. A seminal quantum computing algorithm by Farhi, Goldstone and Gutmann has demonstrated its realization by means of quantum scattering yielding a quantum algorithm that evaluates the output faster than any classical algorithm. Here, we derive the NAND outputs analytically from scattering theory using a tight-binding (TB) model and show the restrictions on the TB parameters in order to still maintain the NAND gate function. We map the quantum NAND tree onto a conjugated molecular system, and compare the NAND output with non-equilibrium Green's function (NEGF) transport calculations using density functional theory (DFT) and TB Hamiltonians for the electronic structure. Further, we extend our molecular platform to show other classical gates that can be realized for quantum computing by scattering on graphs.