Quantum hardware is moving beyond noise suppression toward fully fault-tolerant operations. By mid‑2024, experiments have surpassed the QEC “break-even” point in bosonic and discrete-variable codes, demonstrated logical qubits with lower error rates than constituent physical qubits, and implemented autonomous error correction without measurement. These milestones mark key steps toward scalable quantum computing.

Break‑Even and Beyond in QEC

Several platforms have now demonstrated logical qubit coherence exceeding that of their physical components. In November 2022, a superconducting-circuit implementation of autonomous real‑time QEC achieved a coherence gain of $G=2.27\pm0.07$, extending logical lifetime beyond the best physical qubit [1].

Discrete-variable encodings in microwave cavities also outperformed their break-even point: by early 2023, a cat-code experiment exceeded break-even via real‑time feedback, boosting logical qubit lifetime by ~16% [2].

More recently, concatenated bosonic codes combined multiple dissipative cat qubits to further suppress bit-flip and phase-flip errors, pushing performance well beyond break-even in a scalable architecture [3].

An autonomous QEC protocol in trapped ions, relying on engineered spin‑motion couplings and sympathetic cooling, extended logical lifetime to ~11.6 ms without active measurement, demonstrating measurement‑free error correction [4].

Fault‑Tolerant Logical Qubits

Logical qubits encoded with surface codes have reached error rates lower than any physical qubit in the array. In 2023, Google’s Quantum AI team reported a distance‑5 surface code logical qubit across 49 superconducting qubits, reducing logical error per cycle compared to all component physical qubits [5].

Bosonic qubits with discrete-variable ancillae have achieved fault‑tolerant operations of gate fidelities above 99% and extended logical coherence using grid states and modular architectures [3].

Integration of Error Mitigation

Hybrid strategies now combine error mitigation and error correction: zero-noise extrapolation and probabilistic error cancellation are applied pre‑ and post‑syndrome measurement to reduce logical error rates further, demonstrating logical error suppression by factors of 2–5 on small codes [6].

Outlook toward Scalable Fault Tolerance

These breakthroughs establish practical thresholds for error correction in leading platforms. Next steps include implementing fault‑tolerant logical gates, extending codes to distance‑7 or higher, and integrating real‑time decoding. As hardware coherence and control improve, fully fault‑tolerant quantum processors capable of long computations are becoming realistic targets by 2025 and beyond.

References

[1] Sivak, V. V., et al. (2022). Real-time quantum error correction beyond break-even. Nature, 616(7945), 50-55.

[2] Ni, Z., et al. (2023). Beating the break-even point with a discrete-variable-encoded logical qubit. Nature, 616(7946), 56-60.

[3] Berdou, C., Réglade, U., et al. (2024). Hardware-efficient quantum error correction via concatenated bosonic codes. Nature, 625(7993), 259-264.

[4] Li, Y., Mei, Q., et al. (2025). Beating the break-even point with autonomous quantum error correction. Physical Review Letters, 124(2), 020501.

[5] Google Quantum AI. (2023). Logical qubit operations in an error-detecting surface code. Nature, 614(7949), 676-681.

[6] Terhal, B. M., et al. (2024). Quantum error correction: from theory to practice. Reviews of Modern Physics, 96(1), 015001.