Molecular Realization of a Quantum NAND Tree

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.

arXiv comment17 pages, 6 figures, 1 table

References in corpus (9)

• Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
• Quantum Computation and Decision Trees
• Universal computation by quantum walk
• Observation of Quantum Interference in Molecular Charge Transport
• Universal computation by multi-particle quantum walk
• Quantum stochastic walks: A generalization of classical random walks and quantum walks
• IETS and quantum interference: propensity rules in the presence of an interference feature
• Levinson's theorem for graphs II
• Levinson's theorem for graphs

Cited by in corpus (4)

• Engineering topological states and quantum-inspired information processing using classical circuits
• Towards Quantum Computing with Molecular Electronics
• Quantum Slide and NAND Tree on a Photonic Chip
• Many-Body Effects in a Molecular Quantum NAND Tree