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Results for “error correction” 15 papers
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…
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…
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…
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…
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…
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…
Alpha Pi Project
The Alpha Pi project begins with a practical engineering challenge: quantum states are exquisitely fragile, decohering rapidly due to environmental noise. This fragility stems not merely from technical limitations but from a deeper mathematical vulnerability: the continuous real‑number field that…
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…
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…
CRYOGENICALLY STABILIZED SYNTHETIC LATTICE
We present the design and physical operating principles of a rack-mountable photonic hardware platform designed to instantiate a synthetic vacuum capable of passive quantum error rejection. Unlike conventional quantum processors that rely on algorithmic error correction, this architecture utilizes…
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