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Results for “error correction” 79 papers
Ultrametric Tree Encoding for Passive Quantum Error Confinement: Support Confinement, Barrier Models, and the Limits of the Strong Triangle Inequality
Scalable quantum computing is blocked by the overhead of active error correction: surface-code implementations require on the order of $10^{3}$ physical qubits per logical qubit, repeated syndrome extraction, and low-latency decoding. A recent proposal claims that encoding logical information on a…
The Zitterbewegung Current Correlator as a $\mathbb{Z}_2$ Invariant: Vanishing ZBW Signal as a Hardware-Level Diagnostic of the Majorana Condition
Certifying that a candidate excitation in a topological-qubit device is a true Majorana zero mode rather than an ordinary Dirac fermion or a trivial Andreev bound state remains an unsolved hardware-level problem, and the same Dirac-versus-Majorana question has consumed decades of effort in neutrino…
BQP_physical: Bounding Universal Quantum Computation under Correlated Noise and Causality Constraints
Universal gate‑based quantum computers promise exponential speed‑ups for problems such as integer factorisation, yet commercial‑scale devices remain absent. The gap originates from physical limits that are not captured by the abstract class BQP. We formalise a new class BQP_physical that…
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.…
Thermodynamic Feedback Limits on the Scalability of Surface‑Code Quantum Error Correction
Quantum error correction (QEC) is essential for fault‑tolerant quantum computation, yet the control electronics, wiring, and cryogenic heat load required for each correction cycle generate heat that raises the qubit temperature and thereby increases the intrinsic physical error rate. This creates a…
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…
p‑Adic Lift‑and‑Shift: Transplanting Elementary Calculus to the 2‑adic Tree and a Primary‑Education Blueprint
Elementary analysis is taught exclusively on the Archimedean real line, yet many scientific domains—hierarchical data mining, ultrametric phylogenetics, and quantum error correction—operate naturally on non‑Archimedean structures. This paper closes the gap by (i) formally identifying the points at…
Thermodynamic Scaling Limit of Active Quantum Error Correction
Active quantum error correction (QEC) underpins fault‑tolerant quantum computation, yet its control circuitry dissipates heat that must be removed by cryogenic infrastructure. A hard scalability limit arises when the localized power density generated by control pulses exceeds the Kapitza thermal…
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…
Differential Einthoven‑Inspired Readout for Superconducting Qubit Measurement: Theory and Projected Fidelity Gains
Readout error dominates the overhead of quantum error correction in superconducting processors, limiting logical error rates and scaling prospects. Existing dispersive readout chains suffer from common‑mode disturbances such as amplifier drift, thermal fluctuations, and stray coupling, which add…
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…
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…
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…
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 Geometry as Passive Quantum Error Correction: Bruhat–Tits Qudit Codes and the Non-Archimedean Bound
Active quantum error correction (QEC) dominates the overhead of scalable quantum processors, requiring repeated syndrome extraction, low-latency decoding, and large ancilla counts that inflate hardware cost and energy consumption. A passive alternative that eliminates measurement cycles would reduce…
Planar Fluxonium‑Controlled Bosonic Error Correction: A Quantitative Error‑Budget Reassessment (Corrected Version)
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…
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…
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,…
Entanglement Wedge Reconstruction Beyond the Large \(N\) Limit via the Twirled Petz Map
Entanglement wedge reconstruction (EWR) furnishes the most precise holographic statement of bulk locality: the bulk region bounded by the quantum extremal surface is recoverable from a chosen boundary subregion. At leading order in the large‑\(N\) expansion this statement is underpinned by modular…
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,…
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…
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…
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…
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…
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…
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…
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…
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.…
Error Correction Is a Landauer Machine: The Thermodynamic Floor of Quantum Error-Correction Overhead
Quantum error correction is priced almost exclusively in combinatorial currency: rate, distance, threshold. The physical bill — the energy paid for performing the correction itself — goes unpriced by the field's headline metrics. This paper prices it. Every cycle of active (measurement-based) error…
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…
The Qudit Advantage: System-Level Joules-per-Solution Comparison of a Qudit Architecture Against 17 Conventional Qubit Quantum Computing Platforms
Prior work benchmarked 17 qubit-based quantum computing platforms across the joules-per-solution (JPCUB) energy-efficiency metric. All 17 platforms use two-level quantum systems (qubits). This paper extends the JPCUB framework to qudit architectures — d-level quantum systems — and computes a…
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…
The Adelic Cross-Domain Program: From the Fine-Structure Constant to the Standard Model Mass Spectrum via Bruhat-Tits Trees
We present a unified synthesis of a six-avenue research program revealing that the renormalization group, bosonic quantum error correction, holographic AdS/CFT, Efimov physics, and the Standard Model mass spectrum share a common geometric substrate: the Bruhat–Tits tree $\mathcal{T}_p$ of $p$-adic…
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…
The Adelic Physics Program: Epistemological Foundations and Communications Framework
The QNFO Adelic Physics Program proposes that the physically accessible base field of physics is ℚ (the rational numbers), not ℝ (the real numbers). Ostrowski's theorem — a proven result in number theory — then demands that all p-adic completions of ℚ be physically meaningful, transforming the…
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
Heydeman, Marcolli, Parikh, and Saberi (2018) demonstrated that holographic quantum error-correcting codes can be constructed on a single $p$-adic Bruhat-Tits tree using perfect tensor networks. This paper extends their result to the adelic setting: the simultaneous use of ALL $p$-adic…
Consilience Between Physics and Number Theory: Convergent Theses from Ostrowski's Theorem to Adelic Quantum Mechanics
We synthesize convergent evidence from physics (quantum mechanics, quantum field theory, zitterbewegung, quantum error correction, the Standard Model mass spectrum) and number theory (Ostrowski's theorem, Tate's thesis, the Riemann zeta function, Bruhat-Tits buildings, the adele ring) into a unified…
The Adelic ZBW Programme: ZBW-Majorana Hypothesis, Ostrowski-QEC Synthesis, and Cross-Programme Consilience
The ZBW-Majorana hypothesis, developed across four companion papers (P1--P4), establishes that Zitterbewegung (ZBW) --- the rapid trembling motion of Dirac fermions at the Compton scale --- is a $\mathbb{Z}_2$ topological observable that distinguishes Dirac from Majorana fermions at the hardware…
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