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Error correction papers 50 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.
Fault‑Tolerant Quantum Memory as a Thermodynamic Phase in a 4‑D Topological Photonic Lattice
Passive protection of quantum information can be achieved when a material phase possesses a bulk energy gap that exceeds the ambient thermal energy. Existing self‑correcting memory proposals rely on many‑body Hamiltonians that are difficult to engineer. We propose a concrete photonic implementation…
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.…
Error Confinement Theorem for Ultrametric Decoders and Its Implications for Quantum Error Correction
Fault‑tolerant quantum computing is impeded by the large qubit overhead required for active quantum error correction (QEC). Existing decoders either lack rigorous hierarchical guarantees or incur computational costs that scale with the full syndrome volume. We model a symmetric decoder with $p\ge 3$…
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…
Cross‑Ratio Invariants of Braids as Fault‑Tolerant Quantum Computation Resources
Fault‑tolerant quantum computation currently relies on stabilizer codes whose physical‑to‑logical qubit ratios are on the order of $10^{3}\!:\!1$, far exceeding the ten‑qubit devices demonstrated today. This work closes the gap by introducing cross‑ratio invariants of anyon worldlines as…
Falsifying Geometrically Inspired Quantum Error‑Correcting Codes via Distinct Logical‑Error Scaling
Geometric constructions of quantum error‑correcting codes (QECCs) have been proposed as alternatives to standard topological codes, yet their physical relevance remains ambiguous. Existing proposals lack a testable prediction that distinguishes them from surface‑code scaling of logical error rates.…
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 Computing as the Natural Realization of Adelic Factoring
Integer factorisation underpins modern public‑key cryptography, yet classical algorithms such as the General Number Field Sieve (GNFS) scale sub‑exponentially and quantum Shor’s algorithm requires fault‑tolerant hardware that remains unavailable. A gap therefore exists between the theoretical…
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…
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…
The Price of the Digital Abstraction: Entropy and Encoding Overhead When Discrete Error Models Meet Continuous Quantum Hardware
Quantum processors built from superconducting transmons operate as anharmonic oscillators with many energy levels, yet fault‑tolerant architectures model each device as a two‑level qubit subject to a discrete Pauli error set. This mismatch forces a continuous bosonic error model into a discrete…
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…
Deductive Verification of Discrete‑Time Quantum‑Walk Simulators: Contracts, Cost Bounds, and Extensions to Graph‑Generalized and Open‑System Walks
Discrete‑time quantum walks are a universal model of quantum computation, a platform for topological phases, and a testbed for quantum algorithms, yet the simulators used to study them are rarely checked with the rigor applied to classical library code. This paper frames quantum‑walk simulator…
Planar Fluxonium‑Controlled Bosonic Error Correction: A Quantitative Error‑Budget Reassessment
Bosonic quantum error correction (QEC) encodes a logical qubit in a single harmonic oscillator, promising fault tolerance with far fewer physical components than qubit‑based surface codes. Recent planar demonstrations using a heavy fluxonium ancilla report a bit‑flip lifetime of…
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…
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…
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,…
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,…
Measurement-and-Feedforward Quantum Circuits as Code Design: Detectability, Branch Counting, and the Location of Nonstabilizerness
Shallow quantum circuits augmented by mid-circuit measurements and classical feedforward can deterministically prepare long-range entangled states and implement global unitaries that no comparable-depth unitary circuit can reach. Recent work established a general correspondence between all such…
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…
Adaptivity Closes the Stabilizer Learning Gap: An Analytical Account of Optimal Single-Copy Stabilizer State Learning
Stabilizer states underpin quantum error correction, device benchmarking, and the classical simulation of quantum circuits, yet their learnability shows a sample-complexity gap: an $n$-qubit stabilizer state can be identified from $\Theta(n)$ copies using joint two-copy Bell measurements, while…
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…
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…
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…
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 traditionally been tied to specific code families through their input representations. The POLYMECHANON decoder [1, 2] proposes a contract in which the sole input is the detection error model (DEM)—a tripartite graph of detectors,…
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…
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…
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…
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…
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…
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.
Passive Error Resilience Through Ultrametric Geometry: A Proposal for p-Adic Quantum Metrology
Active quantum error correction is the dominant paradigm for achieving fault-tolerant quantum computation, but its thermodynamic cost at utility scale remains unaddressed. Each round of syndrome extraction, decoding, and feedback erases information — and under Landauer's principle, that erasure…
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…
Adelic Quantum Error Correction: Code Constructions Beyond the Stabilizer Formalism
Adelic generalization of Heydeman holographic QEC. v0.1.1 adds professionally rendered PDF.
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.
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…
Adelic Quantum Error Correction: Intrinsic Qubit Protection from Ostrowski
We propose a quantum error-correcting code whose protection derives from Ostrowski's theorem. The code leverages the classification of non-trivial absolute values on Q to achieve intrinsic fault tolerance without active syndrome extraction.
Computational Simulation of Geometric Orientation Codes
Fault-tolerant quantum computing requires robust error correction traditionally met using planar topologies that assume noise is perfectly isotropic. However, recent astrophysical measurements suggest the universe possesses fundamental anisotropic properties. This paper challenges the isotropic…
Computational Toy Model of Non-Local Information Storage in a Quantum Cellular Automaton
Can local, unitary dynamics generate the kind of non-local information storage that holographic quantum error correction requires? This paper revisits that question with a fully reproducible, exact state-vector simulation of a twelve-qubit quantum cellular automaton (QCA) evolving under the…
Hybrid Gate Decomposition and Vector-Norm Analysis for Quantum PDE Solvers
The simulation of high-Reynolds number fluid turbulence remains a grand challenge in computational physics, where the “Curse of Dimensionality” imposes an \(O(N^4)\) complexity scaling on classical solvers (Zylberman, 2025). Quantum algorithms offer a theoretical logarithmic pathway, but their…
Phase Transitions of Logic
The realization of fault-tolerant universal quantum computation is currently hindered by a fundamental dichotomy between substrate controllability and intrinsic robustness. This paper introduces the “Universal Hamiltonian Computational Substrate” (UHCS) framework to quantitatively compare two…
Qudit Quantum Error Correction
Extends the Ultrametric Foundation thesis into quantum computing. Formalizes geometric error confinement on tree-topology quantum processors.
Lifecycle of a Fault-Tolerant Quantum Computer
The operational lifetime of a fault-tolerant quantum computer is fundamentally a race between the inevitable, continuous degradation of its physical hardware and the escalating resource cost of the classical computation required for the error correction to compensate. This dynamic process defines a…
Stabilization of Gottesman-Kitaev-Preskill States
Harmonic oscillators enable hardware-efficient quantum error correction through the redundancy of infinite-dimensional Hilbert spaces. Conventional stabilization relies on measurement-based feedback, which is limited by detection latency and recoil heating in trapped ion systems. We propose an…
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