Mitigating errors in logical qubits
arXiv:2405.03766 · doi:10.1038/s42005-024-01883-4
Abstract
Quantum error correcting codes protect quantum information, allowing for large quantum computations provided that physical error rates are sufficiently low. We combine post-selection with surface code error correction through the use of a parameterized family of exclusive decoders, which are able to abort on decoding instances that are deemed too difficult. We develop new numerical sampling methods to quantify logical failure rates with exclusive decoders as well as the trade-off in terms of the amount of post-selection required. For the most discriminating of exclusive decoders, we demonstrate a threshold of 50\% under depolarizing noise for the surface code (or for the fault-tolerant case with phenomenological measurement errors), and up to a quadratic improvement in logical failure rates below threshold. Furthermore, surprisingly, with a modest exclusion criterion, we identify a regime at low error rates where the exclusion rate decays with code distance, providing a pathway for scalable and time-efficient quantum computing with post-selection. We apply our exclusive decoder to the 15-to-1 magic state distillation protocol, and report a reduction in the number of physical qubits required, and a reduction in the total spacetime volume required, including accounting for repetitions required for post-selection. We also consider other applications, as an error mitigation technique, and in concatenated schemes. Our work highlights the importance of post-selection as a powerful tool in quantum error correction.
20 pages, 17 figures, comments welcome
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Cited by in corpus (7)
- Experimental Demonstration of Logical Magic State Distillation
- Leveraging Qubit Loss Detection in Fault Tolerant Quantum Algorithms
- Low-overhead magic state distillation with color codes
- Locality-aware Pauli-based computation for local magic state preparation
- Thresholds for post-selected quantum error correction from statistical mechanics
- Symmetric channel verification for purifying noisy quantum channels
- Decoder Dependence in Surface-Code Threshold Estimation under Digitized Hybrid Continuous-Variable and Discrete Noise