frontiers / frontier
The frontier at a glance, assembled from accepted state: what the frontier holds, the strongest findings with their evidence, and the open and contested edges. Copy it straight into a grant, paper, or lab-meeting doc.
Brief export contract
A brief is a portable package over frontier state. It helps humans write, but the frontier remains the inspectable record.
accepted slice
Significance should come from accepted findings first, with fallback labels when no formal acceptance exists yet.
inspect findings →
evidence table
Finding text, confidence, source citation, caveats, and contested edges should remain close to the exported finding.
find evidence →
open work
Open questions, contested findings, gaps, and missing sources stay in the packet instead of being smoothed away.
open workbench →
release return
A grant, paper, or lab note should be able to return to the frontier hash, source package, event log, and proof packet.
check trust →
strongest findings (none formally accepted yet)
bibliography · 16 sources
export · markdown
# Quantum error-correction thresholds This frontier holds 16 findings (0 accepted) over 16 sources. ## Significance - Threshold theorem (Aharonov-Ben-Or, Kitaev) predicts fault tolerance is possible iff physical error rate < threshold; below-threshold demonstrations now confirm this 30-year-old prediction. (reviewer:will-blair 2024) - Google's Willow chip demonstrated below-threshold surface code error correction, with a logical error rate of 0.143% per cycle for a distance-7 code and exponential suppression factor of 2.14 when distance increases by 2. (reviewer:will-blair 2024) - Harvard's neutral-atom processor encoded 48 logical qubits using LDPC codes on 280 physical qubits (distance-7), executing hundreds of logical gate operations with experimentally demonstrated distance-dependent error suppression. (reviewer:will-blair 2024) - Surface code threshold for depolarizing noise ranges from 0.57% to 1.40% per gate, with consensus around 1% optimal threshold depending on decoding algorithm and syndrome extraction model. (reviewer:will-blair 2024) - Biased-noise surface codes (XZZX variant) achieve thresholds of 28.2% for Z-biased noise ratio 10:1, and 43.7% for pure dephasing, demonstrating hardware-tailored thresholds exceed depolarizing assumptions. (reviewer:will-blair 2019) - LDPC codes (including bivariate bicycle codes) reduce overhead to ~4x fewer physical qubits per logical qubit vs. surface codes, enabling 50+ logical qubits on current hardware scales. (reviewer:will-blair 2024) - IBM's 288-qubit biplanar chip with 144 qubits per layer encodes 12 logical qubits using distance-12 LDPC codes, achieving 10x overhead improvement over prior surface-code designs. (reviewer:will-blair 2024) - Quantinuum achieved exponential error suppression with concatenated codes, demonstrating a logical qubit where inner-code protection is augmented by outer-code error suppression. (reviewer:will-blair 2025) - Syndrome extraction errors (measurement errors) reduce effective threshold by ~2-10x vs. ideal syndrome measurements; realistic thresholds drop to 0.1-0.5% when syndrome noise is included. (reviewer:will-blair 2024) - Current superconducting qubit fidelities (two-qubit gates 99.5-99.9%) require code distances 15-30 to reach below-threshold, but neutral atoms and trapped ions approach lower overhead at distance 7-10. (reviewer:will-blair 2024) - Practical fault tolerance requires 1,000-10,000 logical qubits for useful algorithm classes; current hardware (48-50 logical qubits) is early-stage proof-of-concept with 50-100 gate operations before coherence loss. (reviewer:will-blair 2025) - Concatenated code protocols now achieve 2.5% thresholds (vs. surface code 1%), reducing overhead by 90-96% for target logical error rates of 10^-10 to 10^-24. (reviewer:will-blair 2025) ## Contested - Surface code threshold for depolarizing noise ranges from 0.57% to 1.40% per gate, with consensus around 1% optimal threshold depending on decoding algorithm and syndrome extraction model. - LDPC codes (including bivariate bicycle codes) reduce overhead to ~4x fewer physical qubits per logical qubit vs. surface codes, enabling 50+ logical qubits on current hardware scales.