# A Silicon Surface Code Architecture Resilient Against Leakage Errors

## TL;DR

This paper introduces a silicon quantum dot surface code architecture that effectively mitigates leakage errors using mediator dots and charge reservoirs, enhancing fault tolerance for scalable quantum computing.

## Contribution

The authors propose a novel surface code architecture with multi-electron mediator dots and optimized stabilizer cycles to suppress leakage errors in silicon spin qubits.

## Key findings

- Charge leakage errors are reduced to levels comparable to depolarising noise.
- The architecture maintains high fidelity in the presence of leakage errors.
- Scalability is achieved through elongated mediator dots with integrated charge reservoirs.

## Abstract

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.