We investigate the performance of two quantum error-correcting codes-the surface code and the Bacon-Shor code-for implementation with spin qubits in silicon.In each case, we construct a logical qubit using a planar array of quantum dots, exploring two encoding schemes: one based solely on single-electron Zeeman qubits (Loss-DiVincenzo qubits), and a hybrid approach combining Zeeman and singlet-triplet qubits.For both codes, we evaluate key performance metrics, including logical state preparation fidelity and cycle-level error correction performance, using state-of-theart experimental parameters.Our results show that the hybrid encoding consistently outperforms the pure Zeeman-qubit implementation.By identifying the dominant error mechanisms that limit quantum error correction performance, our study highlights concrete targets for improving spin qubit hardware and provides a path toward scalable fault-tolerant architectures.In particular, we find that the logical error rate is not limited by memory errors, but rather by gate errors, especially 1-and 2-qubit gate errors.
This paper investigates the implementation and performance of two quantum error-correcting codes—the surface code and the Bacon-Shor code—with spin qubits in silicon. It compares two qubit encoding schemes: one using solely single-electron Zeeman qubits (Loss-DiVincenzo qubits) and a hybrid scheme using both Zeeman and singlet-triplet qubits. The study evaluates performance metrics such as logical state preparation fidelity and cycle-level error correction performance using state-of-the-art experimental parameters. Results indicate that the hybrid approach consistently outperforms the pure Zeeman-qubit implementation. The study identifies dominant error mechanisms that limit performance, finding that logical error rates are mainly affected by gate errors instead of memory errors, highlighting areas for improving quantum qubit hardware and advancement toward scalable fault-tolerant architectures.
This paper employs the following methods:
- Simulation
- Error Correction
The following datasets were used in this research:
- Logical state preparation fidelity
- Cycle-level error correction performance
- Hybrid encoding outperforms all-LD scheme
- Logical error rate dominated by gate errors
- Surface code slightly better than BS code in QEC step, BS code better in logical state preparation
The authors identified the following limitations:
- Debates on the effect of noise correlations
- Focus on low-distance codes only, which may not represent higher-distance codes' performances
- Number of GPUs: None specified
- GPU Type: None specified
- Compute Requirements: None specified