Quantum error correction
Error correction is the gate to usefulness: physical qubits are far too noisy, so many are combined into fewer, more reliable LOGICAL qubits. Exponential error suppression only kicks in BELOW a physical-error threshold (~1% for surface/qLDPC). 2024-26 crossed that line experimentally; the frontier is now overhead (qLDPC), leakage, universality (magic states / transversal gates), and real-time decoding.
Concepts
Threshold. The physical error rate below which adding qubits reduces logical error. ~1% for surface code and high-rate qLDPC (independent depolarizing noise).
Overhead. Physical qubits per logical qubit. Surface code ~121:1 at distance-11 (plus ancillae); qLDPC far lower; bosonic cat codes push to single digits for one error type.
Break-even. When a logical qubit outlives its best physical qubit - the minimum bar for QEC to help. Crossed by Google Willow (2.4x).
Magic states / universality. QEC alone protects only Clifford gates; magic-state cultivation or transversal non-Clifford gates are needed for a universal fault-tolerant computer.
Code families
| Code | Family | Threshold | Overhead | Status |
|---|---|---|---|---|
| Surface code | topological stabilizer | ~1% | high (~O(d^2) qubits/logical) | below-threshold demonstrated (Google Willow, 2024-25) |
| qLDPC (e.g. bivariate-bicycle, Vine) | quantum LDPC | ~1% | much lower than surface | IBM Kookaburra qLDPC memory targeted 2026; new planar-grid constructions (Vine, heavy-hex) 2026 |
| Cat / bosonic codes | bosonic | bit-flip -> ~0 via hardware; phase-flip via outer code | single digits per logical (one error type) | hardware-protected qubits (Alice & Bob, AWS) |
| Color / concatenated / newer nonstabilizer | various | varies | varies | research; some ultrahigh-threshold nonlinear codes proposed 2025-26 |
Milestones
| Date | Who | Claim | Source |
|---|---|---|---|
| 2024-12 | Below-threshold surface code on Willow (distance-7, Lambda=2.14, 2.4x break-even)fact | Nature 638:920 (2025); arXiv 2408.13687 | |
| 2025 | Harvard (Lukin) | Neutral-atom FT ingredients in one 448-atom processor (below-threshold + transversal + teleportation + reuse)demo | Lukin group 2025 |
| 2025 | IBM | All-microwave leakage suppression below threshold on distance-7 surface code (72x leakage reduction @40 cycles)fact | PRL 135:260601 (2025) |
| 2025 | superconducting groups | Magic-state cultivation on a superconducting processordemo | arXiv 2512.13908 |
| 2026-03 | Quantinuum + Microsoft | 12 logical qubits below physical error ratedemo | Microsoft/Quantinuum H2 |
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