Proposal for Quantum Error Correction Scheme for Biased Errors Using Sparsely Connected Quasi-One-Dimensional Qubit Array

In recent years, semiconductor qubits have gained attention as a promising platform for quantum computing. While these qubits offer advantages such as the ability to operate at high temperatures and semiconductor integration technology, they also present challenges, including the qubits arrangement and highly biased noise. The experimentally realized arrangement of semiconductor qubits is mainly one-dimensional, and hence the realization of a sparsely connected quasi-one-dimensional qubit array is experimentally feasible. In this study, we propose a quantum error correction scheme for such a qubit arrangement, utilizing the concatenated code of the repetition code and the rotated surface code, where strongly biased errors are harnessed by exploiting the one-dimensional structure using the repetition code. Numerical calculations demonstrate that this approach significantly extends the lifetime of the logical qubit compared to the approach simply using the surface code on the same lattice. These findings make an important contribution to the realization of fault-tolerant quantum computation in semiconductor quantum computer.