Simulated coherent electron shuttling in silicon quantum dots

Abstract: Shuttling of single electrons in gate-defined silicon quantum dots is numerically simulated. A minimal gate geometry without explicit tunnel barrier gates is introduced, and used to define a chain of accumulation mode quantum dots, each controlled by a single gate voltage. One-dimensional potentials are derived from a three-dimensional electrostatic model, and used to construct an effective Hamiltonian for efficient simulation. Control pulse sequences are designed by maintaining a fixed adiabaticity, so that different shuttling conditions can be systematically compared. We first use these tools to optimize the device geometry for maximum transport velocity, considering only orbital states and neglecting valley and spin degrees of freedom. Taking realistic geometrical constraints into account, charge shuttling speeds up to $\sim$300 m/s preserve adiabaticity. Coherent spin transport is simulated by including spin-orbit and valley terms in an effective Hamiltonian, shuttling one member of a singlet pair and tracking the entanglement fidelity. With realistic device and material parameters, shuttle speeds in the range 10-100 m/s with high spin entanglement fidelities are obtained when the tunneling energy exceeds the Zeeman energy. High fidelity also requires the inter-dot valley phase difference to be below a threshold determined by the ratio of tunneling and Zeeman energies, so that spin-valley-orbit mixing is weak. In this regime, we find that the primary source of infidelity is a coherent spin rotation that is correctable, in principle. The results pertain to proposals for large-scale spin qubit processors in isotopically purified silicon that rely on coherent shuttling of spins to rapidly distribute quantum information between computational nodes.