Subsystem bivariate bicycle codes achieve high-rate BB logical qubits with local four-qubit gauge checks, yielding examples such as [[108,12,6]] that outperform surface-code alternatives.
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Stabilizer Codes and Quantum Error Correction
Canonical reference. 86% of citing Pith papers cite this work as background.
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abstract
Controlling operational errors and decoherence is one of the major challenges facing the field of quantum computation and other attempts to create specified many-particle entangled states. The field of quantum error correction has developed to meet this challenge. A group-theoretical structure and associated subclass of quantum codes, the stabilizer codes, has proved particularly fruitful in producing codes and in understanding the structure of both specific codes and classes of codes. I will give an overview of the field of quantum error correction and the formalism of stabilizer codes. In the context of stabilizer codes, I will discuss a number of known codes, the capacity of a quantum channel, bounds on quantum codes, and fault-tolerant quantum computation.
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representative citing papers
For an explicit prefix/tree family of quantum states, adaptive local Pauli tomography achieves polynomial copy complexity while non-adaptive strategies require exponentially many copies.
Gauss law codes identify the full gauge-invariant sector as the code space while vacuum codes restrict to the matter vacuum, with the two shown to be unitarily equivalent for finite gauge groups.
A new in-situ scheme prepares logical magic states inside arbitrary CSS qLDPC codes using only syndrome-extraction ancillas, with simulations on the [[144,12,12]] BB code and [[225,9,4]] hypergraph-product code showing injection error rates around 10^{-3} or lower under depolarizing and asymmetric噪声
Univariate bicycle codes give an explicit basis for logical operators and distance upper bounds in a restricted class of quantum LDPC codes while matching the performance of less constrained generalized and bivariate bicycle codes in simulations.
Using post-selection to map physical noise to a weaker accepted logical channel and then applying order-K perturbative PEC reduces sampling overhead by 3-4 orders of magnitude for logical GHZ preparation on up to 200 qubits with the Iceberg code.
Punctured surface codes map disjoint or overlapping Z-couplings to a single logical Z for protected distributed estimation of many-body Hamiltonian parameters.
Dual-species Na-Cs Rydberg array enables simultaneous non-destructive readout of multiple Pauli-Z stabilizers on four-qubit plaquettes using a single global pulse sequence after compensating geometric phase errors.
I(n1, n2) is a correlation functional with |I| ≤ 2 for any three-qubit state, saturated only for GHZ-equivalent states under mutually unbiased measurements.
Adding an ancilla qubit to GKP-stabilizer codes reduces Gaussian displacement noise standard deviation from σ to O(σ²) for universal hybrid CV-DV gates.
Harmoniq approximates a quantum-harmonic-analysis data augmentation operator as a mixture of at most quadratic-depth n-qubit circuits, enabling modular combination with other quantum subroutines for signal denoising.
Multi-entropy exhibits a structural obstruction to replica symmetry breaking in random tensor networks due to incompatible boundary permutations in the replica hypercube, unlike entanglement negativity.
Closed-form sector length distributions for recursively definable graph states (paths, cycles, stars, grids) via generating functions, yielding analytical concentratable entanglement, depolarizing fidelity bounds, and multipartite entanglement criteria.
Dismagicker is a non-Clifford unitary that suppresses non-stabilizerness in quantum states, improving simulation accuracy when combined with Clifford disentanglers.
A code-switching protocol in the [[8,3,2]] code yields a universal scheme for postselected fault-tolerant quantum computation with quadratic logical error suppression.
Introduces gauge-invariant QMETTS using mutually unbiased physical bases derived from stabilizer formalism for Z2 LGT at finite T and density, with single-shot sampling shown near-optimal and numerical validation in 1+1D.
Knill error correction reduces circuit-level decoding for quantum LDPC codes to the simpler code-capacity decoder while remaining fault-tolerant under locally decaying noise.
A new Sparse Stabilizer Tensor cost function enables hyper-optimized contraction schedules for Quantum LEGO WEP calculations, delivering orders-of-magnitude improvements over dense tensor baselines for stabilizer codes.
A new framework certifies global quantum properties including multipartite entanglement, circuit complexity, and quantum magic on small subsystems with constant sample complexity via local Pauli measurements.
Introduces a minimal matchgate circuit representation for fermionic Gaussian states together with a Yang-Baxter update algorithm, then maps out entanglement transitions in unitary circuit games under braiding and generic matchgate rules.
Wire codes are a construction that converts any stabilizer code into a local weight-3 subsystem code on an arbitrary graph via low-density Tanner-graph embedding, with overhead governed by the embedding quality.
Magic state cultivation prepares high-fidelity T states with an order of magnitude fewer qubit-rounds than prior distillation methods by gradually growing them within a surface code under depolarizing noise.
Defines a resource theory of GPT-contextuality whose free operations are classical systems and univalent simulations, yielding monotones including classical excess (minimal embedding error into infinite classical systems) and parity-oblivious multiplexing success probability, with noncontextual GPTs
Compactification of a single higher-dimensional hypergraph-product fracton model yields a broad family of translation-invariant quantum LDPC codes that includes fracton models and all A2BGA codes such as BB codes.
citing papers explorer
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Error Correction in Lattice Quantum Electrodynamics with Quantum Reference Frames
Lattice QED is established as a quantum error-correcting code beyond stabilizers, with explicit recovery operations constructed via quantum reference frames for gauge and fermionic sectors.