  A design for a large-scale surface code quantum processor based on a
node/network approach is introduced for semiconductor quantum dot spin qubits.
The minimal node contains only 7 quantum dots, and nodes are separated on the
micron scale, creating useful space for wiring interconnects and integration of
conventional transistor circuits. Entanglement is distributed between
neighbouring nodes by loading spin singlets locally and then shuttling one
member of the pair through a linear array of empty dots. Each node contains one
data qubit, two ancilla qubits, and additional dots to facilitate electron
shuttling and measurement of the ancillas. A four-node GHZ state is realized by
sharing three internode singlets followed by local gate operations and ancilla
measurements. Further local operations and measurements produce an X or Z
stabilizer on four data qubits, which is the fundamental operation of the
surface code. Electron shuttling is simulated using a simplified gate electrode
geometry without explicit barrier gates, and demonstrates that adiabatic
transport is possible on timescales that do not present a speed bottleneck to
the processor. An important shuttling error in a clean system is uncontrolled
phase rotation due to the modulation of the electronic g-factor during
transport, owing to the Stark effect. This error can be reduced by appropriate
electrostatic tuning of the stationary electron's g-factor. Using reasonable
noise models, we estimate error thresholds with respect to single and two-qubit
gate fidelities as well as singlet dephasing errors during shuttling. A
twirling protocol transforms the non-Pauli noise associated with exchange gate
operations into Pauli noise, making it possible to use the Gottesman-Knill
theorem to efficiently simulate large codes.
