Microscopic design of a topologically protected singlet-triplet qubit in an InAsP quantum dot array

TL;DR

This paper details the microscopic design of a topologically protected singlet-triplet qubit in an InAsP quantum dot array, demonstrating a robust, gapped spin chain with edge quasiparticles suitable for quantum computing.

Contribution

It introduces a detailed microscopic model and analysis for a topologically protected qubit in quantum dot arrays, utilizing advanced computational methods to identify optimal parameters.

Findings

Identification of a four-fold quasidegenerate ground state with a finite energy gap.

Observation of spin-1/2 quasiparticles at the edges of the chain.

Mapping of parameter regions where the system exhibits a Haldane phase.

Abstract

We present here the steps enabling the microscopic design of a topologically protected singlet-triplet qubit in an InAsP quantum dot array embedded in an InP nanowire. The qubit is constructed with two Haldane spin-$\frac{1}{2}$ quasiparticles in a synthetic spin one chain. The qubit is described by a two-leg multi-orbital Hubbard Kanamori (HK) model with parameters obtained from the microscopic calculations of up to eight electrons in a single and double quantum dot. In this HK model describing long arrays of quantum dots, using both exact diagonalization and matrix product state (MPS) tools, we demonstrate a four-fold quasidegenerate ground state separated from excited states by a finite energy gap similar to a Heisenberg spin-1 chain in the Haldane phase. We demonstrate the existence of spin-$\frac{1}{2}$ quasiparticles at the edges of the chain by observing the magnetic field dependence of the low energy spectrum as a function of applied magnetic field. The applied magnetic field also isolates the singlet and $S^z=0$ triplet states from the other triplet components allowing these states to serve as a qubit basis. Most importantly, the regions in parameter space where the low energy spectrum of the multi-orbital Hubbard chain yields a Heisenberg spin-1 chain spectrum are mapped out. Due to the finite energy gap, this qubit has the potential to be protected against perturbations.