Quantum Hamiltonian Computing protocols for molecular electronics Boolean logic gates

Abstract

Quantum Hamiltonian Computing is a recent approach that uses quantum systems, in particular a single molecule, to perform computational tasks. Within this approach, we present explicit methods to construct logic gates using two different designs, where the logical outputs are encoded either at fixed energy and spatial positioning of the quantum states, or at different energies. We use these results to construct quantum Boolean adders involving a minimal number of quantum states with the two designs. We also establish a matrix algebra giving an analogy between classical Boolean logic gates and quantum ones, and assess the possibilities of both designs for more complex gates.

A tetrabenzophenazine low voltage single molecule XOR quantum Hamiltonian logic gate

“…The reading of the logical output status of our gate is obtained by positioning the STM tip apex exactly at one nitrogen location on the H-molecule and by selecting the measuring bias voltage. In QHC, different Boolean truth table can be found for different output reading energies [7]. As presented in Figure 3c, the + 1.1 V resonance is existing when only one Al is interacting with the central pyrazine corresponding to the (0,1) and (1,0) logical inputs.…”

“…However this architecture has its drawbacks due the exponential decay of the current intensity along the molecular circuit, such decay increases with the length of the molecular components hence constraining the implementation of a molecular network circuit [5]. A quantum molecule logic gate can be designed with or (more recently) without qubits [6,7]. Nevertheless using qubits in a molecule [3] also limits the complexity of the Boolean functions to be performed since the intramolecular qubits must be located far away from each other along the molecular structure to limit inter qubits through bond electron transfer processes.…”

“…The quantum Hamiltonian computing (QHC) approach was proposed as an alternative to surmount this problem [6,8]. QHC is a qubit free quantum computing approach where the Boolean logic functioning is ensured by the quantum level repulsion effects [7]. Classical logical inputs are here performed by directly perturbing the molecular electronic structure for example by bringing single metallic atoms in interaction with the calculating molecular board [9,10] or by switching chemical groups directly bonded to this board [11].…”

“…The universal quantum graph of the basic but fundamental "2 inputs -1 output" QHC logic gate is now known together with more complex QHC graphs like the one for the 2 digits Boolean ½ adder [7,11,12]. A molecule from the starphene series has been shown to be able to perform a QHC NOR logical operation [9].…”

Preparation of Tetrabenzo[4.4.2]undecastarphene by On‐Surface Synthesis

“…It has in particular been shown that [2,2,2]-heptastarphene could be implemented as a NOR logic gate [2] whereas the asymmetric [3,3,2]-nonastarphene was a NAND gate. [3] To go beyond and be able testing more powerful logic gates such as a half-adder, [4][5][6][7] it is necessary to increase the complexity and the asymmetry of these conjugated three branches molecules. However, the synthesis of large unsubstituted starphenes in solution is a difficult task due to their insolubility, and the largest starphene to-date, the [3,3,3]-decastarphene, [8,9] has been reported by Clar and Müllen more than fifty years ago.…”