Coupling of topologically protected singlet-triplet qubits in synthetic spin-one chains realized in an InAsP quantum dot nanowires

Using atomistic theory and exact diagonalization tools we describe a chain of InAsP quantum dots in an InP nanowire with four electrons each. Two electrons in each dot occupy two p-shell orbitals forming a triplet state so that each dot simulates a spin-one object in the low-energy limit and a single chain simulates a synthetic spin-one chain. From atomistic interacting Hamiltonian we derive a Hubbard-Kanamori Hamiltonian. Using exact diagonalization and MPS tools we show that in a range of parameters the system has a low-energy spectrum similar to that of an anti-ferromagnetic spin-one chain, with the low-energy spectrum consisting of a singlet and a triplet (ST) separated by a topological gap from the rest of the spectrum, making the chain a candidate for realizing a robust macroscopic singlet-triplet (ST) qubit. Here we describe different possible couplings of two chains at their ends for realizing two-qubit gates. Previous proposals required tunable ST gap. The ST gap here depends on the chain length and is difficult to dynamically control. We show that this limitation may be overcome using different background magnetic fields for the two chains, avoiding the leakage out of computational basis, and implementing two-qubit gates with high accuracy.