  Spin qubits in silicon quantum dots are one of the most promising building
blocks for large scale quantum computers thanks to their high qubit density and
compatibility with the existing semiconductor technologies. High fidelity
single-qubit gates exceeding the threshold of error correction codes like the
surface code have been demonstrated, while two-qubit gates have reached 98\%
fidelity and are improving rapidly. However, there are other types of error ---
such as charge leakage and propagation --- that may occur in quantum dot arrays
and which cannot be corrected by quantum error correction codes, making them
potentially damaging even when their probability is small. We propose a surface
code architecture for silicon quantum dot spin qubits that is robust against
leakage errors by incorporating multi-electron mediator dots. Charge leakage in
the qubit dots is transferred to the mediator dots via charge relaxation
processes and then removed using charge reservoirs attached to the mediators. A
stabiliser-check cycle, optimised for our hardware, then removes the
correlations between the residual physical errors. Through simulations we
obtain the surface code threshold for the charge leakage errors and show that
in our architecture the damage due to charge leakage errors is reduced to a
similar level to that of the usual depolarising gate noise. Spin leakage errors
in our architecture are constrained to only ancilla qubits and can be removed
during quantum error correction via reinitialisations of ancillae, which ensure
the robustness of our architecture against spin leakage as well. Our use of an
elongated mediator dots creates spaces throughout the quantum dot array for
charge reservoirs, measuring devices and control gates, providing the
scalability in the design.

Quantum Physics