Distance-four quantum codes with combined postselection and error correction
arXiv:2112.03785 · doi:10.1103/PhysRevA.110.012419
Abstract
When storing encoded qubits, if single faults can be corrected and double faults postselected against, logical errors only occur due to at least three faults. At current noise rates, having to restart when two errors are detected prevents very long-term storage, but this should not be an issue for low-depth computations. We consider distance-four, efficient encodings of multiple qubits into a modified planar patch of the -qubit surface code. We simulate postselected error correction for up to rounds of parallel stabilizer measurements, and subsequently estimate the cumulative probability of logical error for up to twelve encoded qubits. Our results demonstrate a combination of low logical error rate and low physical overhead. For example, the distance-four surface code, using postselection, accumulates times less error than its distance-five counterpart. For encoded qubits, a distance-four code using qubits protects as well as the distance-five surface code using qubits. Hence distance-four codes, using postselection and in a planar geometry, are qubit-efficient candidates for fault-tolerant, moderate-depth computations.
12 pages, 13 figures
References in corpus (11)
- Supplementary information for "Quantum supremacy using a programmable superconducting processor"
- Variational Quantum Algorithms
- Surface codes: Towards practical large-scale quantum computation
- Noisy intermediate-scale quantum (NISQ) algorithms
- Experimental Quantum Computations on a Topologically Encoded Qubit
- A compact ion-trap quantum computing demonstrator
- Low-distance Surface Codes under Realistic Quantum Noise
- Experimental demonstration of fault-tolerant state preparation with superconducting qubits
- Optimal Resources for Topological 2D Stabilizer Codes: Comparative Study
- A Fault-Tolerant Honeycomb Memory
- Whole-device entanglement in a 65-qubit superconducting quantum computer