Dephasing and error dynamics affecting a singlet-triplet qubit during coherent spin shuttling

Abstract: Quantum information transport over micron to millimeter scale distances is critical for the operation of practical quantum processors based on spin qubits. One method of achieving a long-range interaction is by coherent electron spin shuttling through an array of silicon quantum dots. In order to execute many shuttling operations with high fidelity, it is essential to understand the dynamics of qubit dephasing and relaxation during the shuttling process in order to mitigate them. However, errors arising after many repeated shuttles are not yet well documented. Here, we probe decay dynamics contributing to dephasing and relaxation of a singlet-triplet qubit during coherent spin shuttling over many $N$ repeated shuttle operations. We find that losses are dominated by magnetic dephasing for small $N<10^3$ and by incoherent shuttle errors for large $N>10^3$. Additionally, we estimate shuttle error rates below $1\times10^{-4}$ out to at least $N=10^3$, representing an encouraging figure for future implementations of spin shuttling to entangle distant qubits.