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710 papers from the QNFO program, filed on nine shelves by the reader each one is written for: energy per answer, error correction, physics, numbers and p-adics, logic and formalism, AI and knowledge, autonomous systems, assessments, and cross-cutting essays. Every page renders its mathematics and can be questioned in place. How a living paper works.
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Error correction papers 11 papers
Error-correction researchers and quantum hardware teams. Codes, decoders and the cost of keeping a logical qubit alive: stabilizer, surface, LDPC, concatenated and ultrametric constructions, fault-tolerance thresholds, leakage, syndromes and circuit mapping onto real hardware.
Bruhat–Tits trees. Bruhat-Tits trees used as the model space Tagged papers: 61.
Passive Fault Tolerance via Bruhat–Tits Tree Codes: Exact Ball-Code Error Rates, Energy Barriers, and the Cooling Wall of Active Quantum Error Correction
Large-scale quantum computation is gated by active error correction: stabilizer codes such as the surface code require physical-to-logical overheads of $10^{2}$–$10^{4}$, continuous syndrome measurement, and millikelvin refrigeration whose thermodynamic cost grows as the operating temperature falls.…
Passive Quantum Error Correction via Ultrametric Geometry on Bruhat–Tits Trees
Scalable quantum computing is limited by the thermodynamic overhead of active error‑correction cycles, which require repeated syndrome extraction, low‑latency decoding, and large ancilla resources. A quantitative gap exists: no fully derived account shows how non‑Archimedean (ultrametric) geometry…
Ultrametric Passive Fault Tolerance on Bruhat–Tits Trees: Analytic Derivation and Quantitative Projections
Quantum computing today is limited by the large physical‑to‑logical qubit overhead required for active error correction, which demands frequent syndrome extraction, low‑latency decoding, and extensive ancilla resources. A proposed alternative encodes logical information on the vertices of a $p$‑adic…
Ultrametric Passive Fault Tolerance on Bruhat–Tits Trees: Analytic Derivation and Numerical Projections
Fault‑tolerant quantum computation currently demands a physical‑to‑logical qubit overhead of $10^{2}$–$10^{4}$, a cost that limits near‑term scalability. A major gap is the lack of a passive protection mechanism that does not require syndrome extraction or additional ancilla qubits. We analytically…
Regular Ternary Tree Codes and Symmetric Exponential Energy Barriers for Passive Quantum Error Correction
Quantum error correction (QEC) currently relies on active syndrome extraction, which incurs large qubit overheads. A conjectured passive scheme encodes logical information on the vertices of a regular ternary Bruhat–Tits tree, exploiting the ultrametric triangle inequality to create an energy…
Ultrametric Passive Error Correction on \(p\)-ary Bruhat–Tits Trees: Barrier Analysis and Recursive Thresholds
Fault‑tolerant quantum computation presently depends on active stabilizer codes such as the surface code, which require repeated syndrome extraction, low‑latency decoding, and large ancilla overhead. A fundamentally different approach would encode logical qubits on the vertices of a regular…
Ultrametric Quantum Error Correction on Bruhat–Tits Trees: Energy Barriers, Classical Evidence, and the Quantization Question
Passive fault tolerance — protection of logical qubits by encoding geometry alone, without repeated syndrome measurement — would remove the dominant overhead in scalable quantum computing if it could be made to work for quantum information rather than only for classical bits. We study a conjectured…
Holographic Quantum Error Correction on Bruhat–Tits Trees: A Conditional Threshold and Resource Analysis at $10^{-4}$
The holographic quantum error‑correction (QEC) architecture that implements encoding as a renormalization‑group (RG) flow on a Bruhat–Tits tree $\mathcal{T}_p$ claims a physical error‑rate threshold $\epsilon_{th}\ge10^{-4}$. No hardware data accompany the proposal, so we construct a fully explicit…
Ultrametric Geometry as Passive Quantum Error Correction: Bruhat–Tits Qudit Codes and the Non-Archimedean Bound
We formalize a proposal for passive quantum error correction (QEC) in which logical qudits are encoded on the vertices of a ball of the Bruhat–Tits tree $T_{p+1}$, the incidence geometry of the $p$‑adic numbers $\mathbb{Q}_p$, with Hecke‑type operators acting as the natural gate set. The…
Holographic Quantum Error Correction as AdS/CFT Renormalization‑Group Flow on Bruhat–Tits Trees: A Conditional Threshold Analysis at $10^{-4}$
Quantum error‑correction (QEC) thresholds determine whether physical error rates can be suppressed to arbitrarily low logical error probabilities. A recent proposal encodes logical information as a renormalization‑group (RG) flow on a $p$‑adic Bruhat–Tits tree $\mathcal{T}_p$, with a bosonic…
Holographic QEC as AdS/CFT RG Flow on Bruhat–Tits Trees
Tasks X3.1 and X3.2 established bosonic QEC as RG fixed-point subspaces on Bruhat–Tits trees. Task X3.3 completes the trilogy by showing that this structure is holographic: the Bruhat–Tits tree $\mathcal{T}_p$ is the $p$-adic analog of anti-de Sitter space, tensor networks on $\mathcal{T}_p$ are…
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