Simulating Dual Rail Erasure Errors on Quantum Error Correcting Codes

Quantum computers exploit the properties of matter at small scales to solve problems that classical computers cannot easily solve. However, the advantages of quantum states dissolve when subjected to excessive noise. Quantum error correcting codes (QECCs) redundantly store the information of physical qubits so that errors can be checked and corrected without interfering with quantum states. Erasure errors occur when the qubit is removed from the computational subspace spanned by |0〉 and |1〉. Since they are easier to detect, by converting other errors to erasures, we can improve the fidelity of QECCs. Dual rail qubits are well-suited for detecting erasure errors because they are two transmons coupled such that only one can be in the physical excited state at a time. The Quantum Nanoelectronics Laboratory of UC Berkeley’s dual rail transmons have a worst case physical error rate of 1.00 × 10−2. At this physical error rate, we characterize Λ, the decrease in logical error rate per cycle due to increasing distance of a code. Additionally, we place erasure error detectors in varying locations in a round of error correction to find the best scheme for reducing errors in dual rail qubits. We find that one to two detectors per round results in better thresholds and Λs. Erasure errors increase the repetition code threshold from 2.7 × 10^−2 to 8.30 × 10^−2 and increase the surface code threshold from 1.6 × 10−2 to 3.9 × 10−2 for an erasure error fraction of 0.70. Erasure checks

also improve Λ from 2.91 to 13.89 for the repetition code and 1.64 to 27.52 for the surface code.