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Error correction papers 75 papers
Error correction. Codes, fault tolerance, logical qubits Tagged papers: 75.
Joint Bruhat–Tits Tree Product as a Testable Cross‑Domain Structure for Standard‑Model Mass Ratios, Quantum‑Error‑Correction Lattices, and Efimov Scaling
The Standard‑Model mass spectrum, Gottesman–Kitaev–Preskill (GKP) lattice spacings, and Efimov discrete‑scaling factor are each treated as empirical inputs, limiting predictive power. A conjectured universal geometry—the diagonal embedding of the product of Bruhat–Tits trees…
Ultrametric Quantum Computation for Direct Integer Factorization: A Resource Analysis with a Largely Negative Verdict
Factoring large integers underpins RSA, and the best-known polynomial-time quantum method, Shor's algorithm, extracts the period of modular exponentiation through a quantum phase-estimation detour that dominates circuit depth. A conjecture in the ultrametric research program holds that a quantum…
Leakage as the Price of Binary Truncation: A Scaling Law for Transmon Leakage, Removal Capacity, and Its Ontological Reading
Superconducting transmon processors lose population from the computational $\{|0\rangle,|1\rangle\}$ subspace into higher levels of an anharmonic oscillator, and this leakage is normally treated as an engineering defect to be suppressed pulse by pulse. The gap addressed here is conceptual and…
Joint Bruhat–Tits Tree Product as a Candidate Universal Structure for Standard Model Mass Ratios, Quantum Error-Correction Lattices, and Efimov Scaling: Formalization, Arithmetic Consequences, and a Partial Falsification
The Standard Model (SM) treats particle masses as free parameters, quantum-error-correction (QEC) lattice designs are chosen by heuristic optimization, and the Efimov discrete scaling factor lacks a structural explanation; a single mathematical object generating all three would change how each…
Passive Error Rejection via Cryo-Fluidic Topological Phases: A Feasibility Analysis of the Topological Matter Engine
Active quantum error correction imposes a large and growing overhead of physical qubits, control electronics, and entropy-exporting measurement cycles on every scalable quantum processor. This paper examines a proposed alternative: a "Topological Matter Engine" in which errors are rejected…
Two-Level System Defects as a Random Ensemble: Counting and Dephasing Estimates for Superconducting Qubits
Parasitic two-level system (TLS) defects in the amorphous tunnel barriers of superconducting qubits are a major identified source of decoherence, yet device designers lack closed-form estimates linking defect density and junction geometry to the probability that a device is degraded and to the…
Scaling of the Hadamard Deformation Space in Concatenated 4,1,2 Iceberg Codes: Exact Counts, Skew Amplification, and Search Reduction
Concatenated quantum error-correcting codes raise the effective distance of a joint code without requiring the discovery of new codes with desirable parameters, and the $[[4,1,2]]$ Iceberg code is the smallest error-detecting building block and therefore the one with the lowest resource overhead.…
What Must a Quantum-Memory Decoder Know About Temporally Correlated Noise? A Reconciled Exposition and Cost Accounting
Temporal correlations in quantum-memory noise create a calibration problem that is invisible to syndrome statistics alone. We reconstruct, in expository form, the central results of a study of fixed stabilizer memory experiments with known system-environment interactions [1],[2]. The study's main…
Thermodynamic Divergence of Active Quantum Error Correction Overhead: A Kapitza-Limited Feasibility Threshold for Gate-Based Architectures
Active quantum error correction (QEC) is conventionally analyzed as an algorithmic resource problem: how many physical qubits and gate cycles are needed per logical qubit. We propose a complementary thermodynamic feasibility criterion. In a gate-based architecture, every QEC cycle is driven by…
Ultrametric Quantum Error Correction on Bruhat–Tits Trees: Energy Barriers, Classical Evidence, and the Quantization Question
We study a conjectured passive fault-tolerance scheme in which logical qubits are encoded on a Bruhat–Tits tree, the infinite homogeneous tree associated with a non-Archimedean local field, whose natural metric satisfies the strong (ultrametric) triangle inequality. The conjecture states that the…
Holographic Quantum Error Correction on Bruhat–Tits Trees: A Conditional Threshold and Resource Analysis at $10^{-4}$
We assess, quantitatively and conditionally, whether a quantum error correction (QEC) architecture in which the encoding map is realized as renormalization-group (RG) flow on a Bruhat–Tits tree $\mathcal{T}_p$ — the $p$-adic analogue of hyperbolic anti-de Sitter space — can achieve a QEC threshold…
The Price of the Digital Abstraction: Entropy and Encoding Overhead When Discrete Error Models Meet Continuous Quantum Hardware
A working assumption of much quantum error correction (QEC) is that noise can be modeled as a discrete set of Pauli errors acting on two-level systems. We ask what it costs, in information-theoretic terms, to impose this digital abstraction on hardware whose native dynamics are continuous. Using the…
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 central…
Planck Fidelity: The Fundamental Leakage Cost of Binary Truncation of Bosonic Ladders
Superconducting transmon qubits are weakly anharmonic oscillators whose spectra form discrete but unbounded ladders of energy eigenstates; the binary register $n \in \{0,1\}$ is imposed on this ladder by truncation, not by physics. Because every physical drive contains the raising operator…
Booklet Cosmological States as Random-Tensor Codes: Recovery Bounds and Entropic Diagnostics for Multi-Boundary Baby Universes
Cosmological states in holography can contain closed "baby" universes inaccessible to any single asymptotic boundary, raising the question of whether the information they carry is recoverable, and from where. The booklet cosmology construction extends the two-boundary cosmological-state proposal of…
The Resource Burden of Active Quantum Error Correction: A Scaling Analysis of Qubit, Bandwidth, and Energy Overheads
Active quantum error correction (QEC) protects quantum information only by continuously consuming physical resources: qubits, measurement bandwidth, classical processing, and energy. While the theoretical foundations of QEC are mature, the resource burden of running a code—rather than constructing…
The Scaling Paradox of Surface-Code Quantum Error Correction: Exponential Suppression, Logarithmic Overhead, and a Landauer Floor That Grows with Reliability
Surface-code quantum error correction (QEC) is widely regarded as the leading route to fault-tolerant quantum computation, yet its resource story contains an under-examined tension we call the scaling paradox: the code suppresses logical errors exponentially in code distance $d$, so the…
Error Correction Properties of Covariant Bosonic Encodings: A Quantitative Assessment
Bosonic modes provide a hardware‑efficient substrate for quantum error correction (QEC) because logical information can be encoded in continuous‑variable states with built‑in symmetries. Recent work introduced a representation‑theoretic framework in which a physical representation of a finite group,…
Distinguishability-Induced Degradation of Monolithic Quantum Error Correction: A Reconciled Analytic Study of Syndrome-Checking Constraints
Quantum error-correcting codes rely on the assumption that the environment cannot distinguish which error occurred on which codeword. Residual Zeeman, Stark, and anharmonic shifts in physical platforms break this assumption by imprinting error-dependent photon frequencies on the environment,…
CSS Codes for Quantum Metrology with Discrete-Time Error Correction: A Reconciled Quantitative Analysis
Quantum metrology promises estimation precision scaling as the Heisenberg limit $\Delta\omega \sim 1/(NT)$ rather than the standard quantum limit (SQL) $\Delta\omega \sim 1/\sqrt{NT}$, but noise typically destroys this advantage. Recent work showed that when the noise is perpendicular to the sensing…
Planar Bosonic Error Correction with Heavy Fluxonium: A Quantitative Reassessment of Hardware-Efficient GKP Stabilization
Bosonic quantum error correction (QEC) encodes one logical qubit into an oscillator mode, promising fault tolerance with far fewer physical components than qubit-based surface codes. Until recently, however, all superconducting demonstrations of bosonic QEC relied on centimeter-scale…
Exact Maximum-Likelihood Quantum Decoding beyond Treewidth: A Structural Analysis of Rank-Decomposition Dynamic Programming
Maximum-likelihood (ML) decoding is the optimal decoding rule for quantum error correction under stochastic Pauli noise, but exact evaluation of logical-class probabilities has required tensor-network contraction whose cost grows exponentially in the treewidth of the syndrome graph, blocking…
Low-Overhead Quantum Error Correction with Boundary-Connected Planar Modules: A Reconciled Quantitative Assessment
The planar surface code protects quantum information robustly but pays for its two-dimensional layout with an encoding rate that vanishes as the distance grows, so fault-tolerant memories require hundreds to thousands of physical qubits per logical qubit. A recent proposal constructs modular…
Error Attribution as a Resource-Allocation Principle for Quantum Error Correction: Sensitivity-Guided Noise Reduction and Its Analytic Limits
Logical error rate is the standard benchmark for quantum error correction (QEC), but it is an aggregate quantity: it says nothing about which circuit components actually drive logical failure. Recent work introduced an error attribution scheme that computes per-component sensitivities…
Beyond Pure Dephasing: A Quantitative Analysis of Two-Level Error Correction for Multi-Spin Molecular Qubits
Molecular spin systems exhibit a natural hierarchy of decoherence channels: fast pure dephasing (characterized by the transverse relaxation time T₂) and comparatively slow energy relaxation (characterized by T₁). A recent proposal argues that fault-tolerant quantum computing with molecules requires…
BARC Codes as Algebraically Restricted Coherent-State Constellations: Geometry, Separation Bounds, and a Worked Single-Mode Benchmark
Bosonic algebraically-restricted constellation (BARC) codes encode quantum information in finite superpositions of coherent states whose constellation points are solution sets of multivariate complex polynomial systems, with the polynomial constraints chosen to reflect photon-gain and photon-loss…
Ensemble Dependence of Critical Exponents at Quantum Error Correction Thresholds: Analytic Mechanisms and Statistical Consequences
Ensemble equivalence — the expectation that microcanonical, canonical, and grand-canonical descriptions of a system agree in the thermodynamic limit — is a cornerstone of statistical mechanics, yet it can fail for observables that probe exponentially rare events. Recent work on a simplified quantum…
Code-Agnostic Graph Neural Network Decoding from Detection Error Models: A Reconciled Quantitative and Structural Assessment
Graph neural network (GNN) decoders for quantum error correction have historically been locked to specific code families. The POLYMECHANON preprint [1,2] proposes a decoder whose sole input is the detection error model (DEM) — a tripartite graph of detectors, error mechanisms, and logical…
From Random Quantum Codes to Explicit qLD Codes: A Reconciled Threshold Analysis of the Quantum-LCL Framework
A recent preprint (arXiv:2609.40252) extends the local coordinate-wise linear (LCL) witness framework of Levi, Mosheiff, and Shagrithaya from classical linear codes to CSS quantum codes. The central structural difficulty is that a CSS code is a nested pair of spaces S ⊆ C, so a local witness has two…
Coherence-Assisted Error Correction for Deep Learning: A Reconciled Feasibility Analysis of a Hybrid Quantum-Classical Architecture
Deep learning inference and training are increasingly limited not by raw throughput but by the energy cost of protecting computation against bit-level faults arising from aggressive low-voltage operation, near-threshold computing, or radiation-prone deployment environments. This paper reconciles…
Constant-Sized-Support Magic State Distillation with Qubit Recycling: A Reconciled Resource, Footprint, and Energy Analysis
Magic state distillation (MSD) is the canonical route to non-Clifford gates in fault-tolerant quantum computation, but conventional nested factories exhibit qubit occupancy that grows multiplicatively with the number of distillation rounds. Recent work on constant-sized-support distillation…
Holographic Quantum Error Correction as AdS/CFT Renormalization-Group Flow on Bruhat–Tits Trees: A Conditional Threshold Analysis at 10⁻⁴
We analyze a proposal in which quantum error correction (QEC) is organized as renormalization-group (RG) flow on a Bruhat–Tits tree $\mathcal{T}_p$ — the $p$-adic analogue of hyperbolic anti-de Sitter (AdS) space — so that the encoding map of a holographic code is literally an RG trajectory from…
Braid Group Representations and Modular Data: Non-Uniqueness, Finite Images, and the Ising Test Case
A central question in the theory of topological order asks whether the braid group representation $B_N$ carried by $N$ non-Abelian anyons uniquely determines the modular data — the $S$ and $T$ matrices — of the underlying topological quantum field theory. We reconcile three lines of analysis into a…
Braid Group Representations, Modular Data, and the Classification of Majorana Zero Mode Fusion Rules in 2D Topological Superconductors
Majorana zero modes (MZMs) localized on vortices of a two-dimensional topological superconductor carry a projective representation of the braid group, and the associated anyon theory is encoded in a modular tensor category whose fusion rules and modular data ($S$ and $T$ matrices) determine the…
TETRIS-Q: Tiling-based Effective Transient-fault Reduction and Parallelism Optimizations for Quantum Circuit Mapping
Quantum circuit mapping on Noisy Intermediate-Scale Quantum (NISQ) devices must satisfy physical connectivity constraints while minimizing both SWAP overhead and exposure to transient faults like decoherence. Existing compilers typically optimize qubit routing and noise-aware placement…
Braid Group Representations, Modular Data, and the Classification of Majorana Zero Mode Fusion Rules in 2D Topological Superconductors
We investigate whether the braid group representation on $N$ anyons uniquely determines the modular data ($S$ and $T$ matrices) of a non-Abelian topological order, and whether this framework classifies all fusion rules for Majorana zero modes (MZMs) in 2D topological superconductors. We show that…
Majorana Zero-Mode Parity, the Hexagon Equation, and Chiral Edge Modes in 2D Topological Superconductors
In a two-dimensional topological superconductor hosting vortices with Majorana zero modes (MZMs), the exchange of vortices yields a projective representation of the braid group. We investigate whether the full anyonic exchange matrix is uniquely determined by the MZM parity operators and whether…
Quantum Computation Latency-Energy Tradeoff and the JPCUB Metric
Fault-tolerant quantum computation trades latency against energy through the code distance: a larger distance d costs more syndrome rounds and more physical gates per logical operation, lengthening every operation and raising its energy. This paper computes that tradeoff for the rotated surface code…
Revising the Joules-per-Compute (JPCUB) Benchmark: Normalizing Energy Efficiency by Logical-Qubit Operations
Energy benchmarks for quantum processors are usually quoted per physical gate or per physical qubit, figures that hide the dominant cost of a fault-tolerant machine: the error-correction overhead that multiplies physical work by a distance-dependent factor before any logical operation is delivered.…
A Lower Bound on Energy Cost per Logical-Qubit Operation in Surface-Code Quantum Error Correction
Surface-code quantum error correction translates one logical qubit into a two-dimensional array of physical qubits, and the energy cost of that translation is rarely quantified at the level of a logical operation. This paper specifies a minimal, convention-explicit energy model for a rotated…
Error Correction Is a Landauer Machine: The Thermodynamic Floor of Quantum Error-Correction Overhead
Every cycle of active (measurement-based) quantum error correction is an erasure process priced by Landauer's principle at no less than kT ln 2 per erased bit; correction overhead therefore converges to a positive thermodynamic floor, (n-k)/k * kT ln 2 per logical qubit per round for an n,k…
Implications for Computing and Quantum Error Correction
The anchor paper introduced the branch-depth reading: the p-adic valuation $v_p(n)$ is a measure of depth along a prime branch of the integer factorization tree (not a measure of size), and because the tensor product multiplies Hilbert-space dimensions, $v_2(\dim H) = n$ counts tensor-branch depth…
Archimedean Shadows: The QEC-Darwinism Tradeoff in Ultrametric Spaces
Maity et al. (arXiv:2608.03944, 2026) proved that quantum error correction and Quantum Darwinism cannot coexist above a critical logical fidelity $F_L > 0.874$ — a tight, model-independent no-go theorem establishing an exact tradeoff between protected quantum information and emergent classical…
Extending v_p^max Code Classification: Testing the Mahler Spectral Conjecture on Additional Stabilizer Code Families
ACRP-06: Tests UF paper C7.3 on 8 additional codes. Golay CSS confirmed v_p^max=28; all other stabilizer codes cluster at random baseline (1-6). C7.3 bound to Golay-type self-dual codes.
Ultrametric Consilience Atlas: Cross-Domain Applications of p-Adic Mathematical Structure
A single mathematical structure — the p-adic ultrametric topology — appears in apparently unrelated domains: quantum error correction (stabilizer codes), protein folding (energy landscapes), neural coding (population activity clustering), financial markets (hierarchical correlation), climate…
Adelic Quantum Error Correction: A Synthesis Across All Primes v1.0.0
The $p$-adic quantum error correction program has developed three independent but connected strands: a mathematical theory of $p$-adic stabilizer codes (Phase A), an experimental protocol to test for ultrametric error structure (Phase B), and a hardware co-design proposal for tree-structured qubit…
HM-LWE v3.0
Hidden-modulus LWE: novel hardness assumption
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…
Bosonic Codes as the Native Encoding: Resource-Commensurable Comparison of Cat, GKP, Binomial, and Surface Codes
X3.3 — Resource-commensurable comparison of bosonic codes vs surface codes using photons/logical-qubit metric at p_L=10^-6. Bosonic codes require 5-40x fewer photons and ~100x fewer modes. Novel claim: HO as QM IR attractor implies bosonic codes are the native encoding.
Shor's Algorithm and the Unproven Premise: An Assumption Audit of the Quantum Factoring Narrative
Shor's 1994 algorithm proves FACTORING ∈ BQP, but the claim that this constitutes a quantum advantage requires the additional unproven premise FACTORING ∉ BPP. This paper decomposes Shor's claim architecture into nine assumptions spanning number theory, computational complexity, and quantum physics.…
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