Finite Distinction Maintenance in Fault-Tolerant Quantum Computation Logical Distinction Ledgers, Error-Correction Infrastructure, and Architecture-Specific Resource Bounds

Official website: distinctiontheory.orgPublic portal for the start guide, papers, claim status, failure registry, prior-art boundary, and citation resources. Canonical GitHub repository:https://github.com/yiningwu-research/Distinction-Theory FDS-Q2 develops the quantum-computation paper in the Finite Distinction Systems (FDS) / Distinction Theory sequence. It studies fault-tolerant quantum computation as a problem of finite distinction maintenance: logical quantum distinctions must be actively preserved against noise, leakage, decoherence, latency, reset burden, cooling limits, and finite correction infrastructure. This paper is not a no-go theorem for quantum computation. It does not claim that quantum computation is impossible, does not refute the quantum threshold theorem, and does not identify every syndrome measurement with Landauer erasure. Instead, it asks what physical maintenance ledger must be paid in order to instantiate fault-tolerant assumptions at useful scale. The central claim is: Logical error suppression requires finite distinction-maintenance infrastructure. A logical qubit is treated as a protected quantum quotient or code-algebra distinction, QL = q(ρphys), not as a simultaneously readable classical bit. Quantum error correction therefore converts distinction loss into maintenance work: redundancy, syndrome acquisition, decoding, feedback, reset, cooling, routing, reservoir engineering, and control. The main audit object is a vector ledger rather than a scalar cost: Rcorr(τ)(εL; N, C) = ( Bsyn, Bdec, Breset, Llatency, Pmaint ), together with a maintenance-capacity vector Cmaint(τ) = ( Cread, Cdec, Creset, Cfeed, Ccool, Cctrl, Clatency ). The feasibility condition is componentwise: Rcorr(τ) ⪯ Cmaint(τ), meaning that syndrome, decoding, reset, latency, power, cooling, and effective-error components must each fit their corresponding time window, physical location, and engineering capacity. Landauer’s principle enters only as a lower bound on logically irreversible reset, overwrite, or garbage disposal under its standard assumptions: Perase ≥ kBT ln 2 · berase/cycle / τcyc. The paper explicitly distinguishes syndrome acquisition from erasure. It does not assume that every extracted syndrome bit is erased at the same temperature stage where it is measured. Syndrome information may be exported, buffered, decoded elsewhere, processed reversibly for a time, or dissipated through an engineered reservoir. The Q2 requirement is that the entropy-export path, reset burden, latency, cooling load, and failure probability be specified rather than hidden. The paper introduces two audit principles: No-free logical distinction maintenance: if passive protection does not fully suppress noise, then maintaining a logical distinction below error tolerance requires redundancy, syndrome information, feedback, reset or export, engineered dissipation, latency increase, resource growth, task relaxation, or failure. Ledger relocation: maintenance cost can be moved across cold stages, room-temperature electronics, optical channels, autonomous reservoirs, topological gaps, or passive-protection mechanisms, but it cannot be made unaccounted. For surface-code-like architectures, Q2 uses the normal forms Nphys ∼ αnLd2, and pL(d,p) ∼ A(p/pth)(d+1)/2, to illustrate the central tradeoff: logical error decreases as code distance grows, but physical carriers, syndrome load, decoding burden, routing, reset, and maintenance infrastructure also grow. For cryogenic solid-state processors, Q2 defines a cold-stage reset ledger, Presetcold ≳ [ kBTcold ln 2 / τcyc ] χresetβnLd2, and a scaling-wall diagnostic nLmax ∼ [ Pcoolavailτcyc ] / [ ηχresetβ kBTcold ln 2 d2 ]. This diagnostic is not a platform-independent maximum logical-qubit count. It is a way to locate which cooling, reset, control, or latency ledger is being exhausted. The paper also analyzes ledger-relocation latency tax. Moving decoding or syndrome processing to warmer electronics may reduce cold-stage heat, but can increase feedback-loop time, τloop = τmeas + τexport + τdecode + τfeed, which increases idle error and can require larger code distance: τloop ↑ ⇒ peff ↑ ⇒ dreq ↑ ⇒ Nphys, Bsyn, Pmaint ↑. The architecture discussion covers superconducting processors, spin qubits, trapped ions, neutral atoms, photonics, topological protection, bosonic and cat-code approaches, qLDPC codes, LDPC-cat codes, and autonomous or dissipative QEC. These are treated as ledger-shaping or ledger-relocation strategies rather than as ledger-elimination strategies. Q2 further proposes a minimum reporting template for quantum-computing architecture audits: ( nL, d, Nphys, peff, pL*, τcyc, Bsyn, Breset, Pcold, Proom, Ptotal ), together with decoder location, reset location, cooling stage, latency bottleneck, and entropy-export path. This release includes deterministic normal-form demonstrations: surface-code logical-error/load scaling, cold-stage reset-floor sensitivity bands, latency-density feedback, architecture maintenance regimes, and an FDS-Q2 relation map. These figures are conceptual normal forms, not empirical fits, not refrigerator models, and not quantum dynamical simulations. The release includes the paper PDF, LaTeX source, reproducibility code, generated figures, CSV tables, and model-summary outputs.