  Surface acoustic waves (SAWs) can create moving quantum dots in piezoelectric
materials. Here we show how electron-spin qubits located on dynamic quantum
dots can be entangled. Previous theoretical and numerical models of quantum-dot
entanglement generation have been insufficient to study quantum dynamics in
realistic experimental devices. We utilize state-of-the-art graphics processing
units to simulate the wave function dynamics of two electrons carried by a SAW
through a 2D semiconductor heterostructure. We build a methodology to implement
a power-of-SWAP gate via the Coulomb interaction. A benefit of the SAW
architecture is that it provides a coherent way of transporting the qubits
through an electrostatic potential. This architecture allows us to avoid
problems associated with fast control pulses and guarantees operation
consistency, providing an advantage over static qubits. For inter-dot barrier
heights where the double occupation energy is sufficiently greater than the
double-dot hopping energy, we find that parameters based on experiments in
GaAs/AlGaAs heterostructures can produce a high-fidelity root-of-SWAP
operation. Our results provide a methodology for a crucial component of
dynamic-qubit quantum computing.
