Effective Hamiltonian for two interacting double-dot exchange-only qubits and their controlled-NOT operations

TL;DR

This paper develops an effective Hamiltonian model for two interacting double-dot exchange-only qubits, enabling the design of CNOT operations considering realistic constraints and geometries, with performance evaluations based on simulations.

Contribution

It introduces a simplified exchange interaction-based Hamiltonian for coupled qubits and analyzes CNOT sequences under realistic conditions using numerical algorithms.

Findings

CNOT sequences are identified for different geometries.

Gate performance depends on nanowire and gate sizes.

Realistic intra-dot interactions are incorporated into the model.

Abstract

Double-dot exchange-only qubit represents a promising compromise between high speed and simple fabrication in solid-state implementations. A couple of interacting double-dot exchange-only qubits, each composed by three electrons distributed in a double quantum dot, is exploited to realize controlled-NOT (CNOT) operations. The effective Hamiltonian model of the composite system is expressed by only exchange interactions between pairs of spins. Consequently, the evolution operator has a simple form and represents the starting point for the research of sequences of operations that realize CNOT gates. Two different geometrical configurations of the pair are considered, and a numerical mixed simplex and genetic algorithm is used. We compare the nonphysical case in which all the interactions are controllable from the external and the realistic condition in which intra-dot interactions are fixed by the geometry of the system. In the latter case, we find the CNOT sequences for both the geometrical configurations and we considered a qubit system where electrons are electrostatically confined in two quantum dots in a silicon nanowire. The effects of the geometrical sizes of the nanowire and of the gates on the fundamental parameters controlling the qubit are studied by exploiting a spin-density-functional theory-based simulator. Consequently, CNOT gate performances are evaluated.