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Error correction papers 19 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.
Stabilizer formalism. Stabilizer, decoder and code constructions Tagged papers: 40.
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 $p\ge 3$…
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…
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…
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…
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…
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…
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…
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…
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…
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.
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.
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…
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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