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.
hub Canonical reference
Stabilizer Codes and Quantum Error Correction
Canonical reference. 86% of citing Pith papers cite this work as background.
89
Pith papers citing it
Background
86% of classified citations
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.
hub tools
citation-role summary
background 13
method 1
citation-polarity summary
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
Introduces factorized graph-preserving Clifford operations organized over local-complementation orbits to optimize finite-size multipartite graph-state purification circuits that outperform recurrence protocols under realistic noise.
Constructs an explicit tensor isomorphism establishing that the projective Clifford group C(A) and affine symplectic group ASp(A) are isocategorical, yielding uniform irreps, conjugacy parameters, and identical character tables up to relabeling.
Random cubic qutrit codes in 3D retain no-string logical operators but lack self-similar fractal ones, showing degeneracy exponents k=2 (odd L) and k=4 (even L) with plane-logical operators spanning the space.
For single-logical-qubit surface codes with uniform X rotations, the projected logical ensemble after syndrome extraction and maximum-likelihood decoding is isomorphic to scattering-matrix ensembles of chaotic quantum dots in Altland-Zirnbauer classes D or DIII.
Proves unique stationary law for Clifford random monitored quantum circuits and computes leading asymptotics of steady magic, linear for odd-prime dimension mana and quadratic for qubit 2-stabilizer Rényi entropy.
The stabilizer ZX calculus rule set is minimal because the red/green compact-structure coincidence rule and the bialgebra law are each individually necessary relative to the connectivity meta-rule.
A qIOP protocol for QMA with polylog qubit queries, polynomial communication, exponential completeness, and constant soundness gap using quantum LTCs and classical PCPPs.
The five-cycle graph state |C5> is the unique (up to local Clifford) 1-resistant five-qubit stabilizer state; no seven-qubit stabilizer state is m-resistant for nonzero admissible m.
Neutral atom platform achieves repeated toric code syndrome extraction with qubit reloading, preserving logical information over 90 cycles and showing distance-dependent logical error suppression.
A Set-Transformer architecture with self-attention encodes Pauli-string correlations, optimizes via commutation objective, and finds symmetries with near-deterministic success on physical models like Ising and Toric code.
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.
Introduces correlation functional I that bounds at 2 only for GHZ-equivalent states and yields LU-invariant E_GHZ in [0,1] equaling 1 iff the state is GHZ-type.
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.
citing papers explorer
-
Topological subsystem bivariate bicycle codes with four-qubit check operators
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.
-
An Exponential Advantage for Adaptive Tomography of Structured States under Pauli Basis Measurements
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 and vacuum codes from lattice gauge theories
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.
-
In-Situ Simultaneous Magic State Injection on Arbitrary CSS qLDPC Codes
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
-
Efficient Graph State Purification with Factorized Graph-Preserving Operations across Local Clifford Orbits
Introduces factorized graph-preserving Clifford operations organized over local-complementation orbits to optimize finite-size multipartite graph-state purification circuits that outperform recurrence protocols under realistic noise.
-
Representation theory of projective Clifford groups via isocategoricality
Constructs an explicit tensor isomorphism establishing that the projective Clifford group C(A) and affine symplectic group ASp(A) are isocategorical, yielding uniform irreps, conjugacy parameters, and identical character tables up to relabeling.
-
Random Local Stabilizer Codes in Three Dimensions without String or Self-Similar Fractal Logical Operators
Random cubic qutrit codes in 3D retain no-string logical operators but lack self-similar fractal ones, showing degeneracy exponents k=2 (odd L) and k=4 (even L) with plane-logical operators spanning the space.
-
Projected logical ensembles in surface codes via the random-matrix theory of quantum dots
For single-logical-qubit surface codes with uniform X rotations, the projected logical ensemble after syndrome extraction and maximum-likelihood decoding is isomorphic to scattering-matrix ensembles of chaotic quantum dots in Altland-Zirnbauer classes D or DIII.
-
Invariant Measures and Weak-Magic-Injection Asymptotics in Random Monitored Quantum Circuits
Proves unique stationary law for Clifford random monitored quantum circuits and computes leading asymptotics of steady magic, linear for odd-prime dimension mana and quadratic for qubit 2-stabilizer Rényi entropy.
-
Minimality of the Stabilizer ZX Calculus
The stabilizer ZX calculus rule set is minimal because the red/green compact-structure coincidence rule and the bialgebra law are each individually necessary relative to the connectivity meta-rule.
-
Probabilistically Checking Quantum Proofs, with Interaction
A qIOP protocol for QMA with polylog qubit queries, polynomial communication, exponential completeness, and constant soundness gap using quantum LTCs and classical PCPPs.
-
A five-qubit 1-resistant graph state and stabilizer marginal certificates
The five-cycle graph state |C5> is the unique (up to local Clifford) 1-resistant five-qubit stabilizer state; no seven-qubit stabilizer state is m-resistant for nonzero admissible m.
-
Quantum error correction with the toric code
Neutral atom platform achieves repeated toric code syndrome extraction with qubit reloading, preserving logical information over 90 cycles and showing distance-dependent logical error suppression.
-
Attention-based optimizer for symmetry finding
A Set-Transformer architecture with self-attention encodes Pauli-string correlations, optimizes via commutation objective, and finds symmetries with near-deterministic success on physical models like Ising and Toric code.
-
Univariate Bicycle Quantum LDPC Codes: Explicit Logical Structure and Distance Bounds
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.
-
Zeno-Enhanced Probabilistic Error Cancellation with Quantum Error Detection Codes
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.
-
Distributed estimation of many-body Hamiltonians via punctured surface code
Punctured surface codes map disjoint or overlapping Z-couplings to a single logical Z for protected distributed estimation of many-body Hamiltonian parameters.
-
Multi-Qubit Stabilizer Readout on a Dual-Species Rydberg Array
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.
-
Noise Reduction for Universal Hybrid Oscillator-Qubit Quantum Computation
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: Efficient Data Augmentation on a Quantum Computer Inspired by Harmonic Analysis
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.
-
Structural Obstruction to Replica Symmetry Breaking for Multi-Entropy in Random Tensor Networks
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.
-
Sector length distributions of recursively definable graph states through analytic combinatorics
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: Unitary Gate for Non-Stabilizerness Reduction
Dismagicker is a non-Clifford unitary that suppresses non-stabilizerness in quantum states, improving simulation accuracy when combined with Clifford disentanglers.
-
Universal Weakly Fault-Tolerant Quantum Computation via Code Switching in the [[8,3,2]] Code
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.
-
Certifying localizable quantum properties with constant sample complexity
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.
-
Disentangling strategies and entanglement transitions in unitary circuit games with matchgates
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
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: growing T states as cheap as CNOT gates
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.
-
Resource-theoretic hierarchy of contextuality for general probabilistic theories
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
-
Computable measures of fermionic non-Gaussianity from the covariance matrix
Introduces occupation number entropies (Tsallis) and natural-orbital participation entropies (Renyi) as computable convex resource monotones for fermionic non-Gaussianity from the covariance matrix.
-
Cavity-mediated probabilistic magic $T$-gate injection
Proposes a cavity-mediated probabilistic protocol to prepare and teleport magic T-states into atoms with 0.74 success probability using Rydberg atom-cavity interactions.
-
Fast and Parallel High-Rate STAR Architecture for Megaquop Quantum Simulation
A symmetry-co-designed high-rate QEC architecture with parallel STAR injection on bivariate bicycle codes achieves ~5.5x space savings for TFIM and Fermi-Hubbard simulations versus surface-code STAR.
-
Infinite-Level Hierarchy of Solvable Quantum Circuits
An infinite hierarchy of solvability conditions is presented that combines with generalized dual-unitary conditions to enable exact analysis of correlation functions and entanglement dynamics in quantum circuits, with non-trivial solutions at every level.
-
Scaling-optimal purification of noisy qubit unitary channels
A U(2)-covariant parallel protocol based on a novel entanglement-assisted QECC purifies noisy qubit unitaries with O(1/n) noise scaling shown to be asymptotically optimal in the low-noise regime.
-
An iterative Ising decoder for quantum error correction codes
ILOD approximates X-Z error correlations in Ising-based quantum decoding via iterative Bayesian reweighting, halving maximum interaction order and restoring convergence at larger code distances.
-
Coset Ensemble Decoder for Quantum Error Correction with Algorithm-Hardware Co-Design
Presents a coset ensemble decoder with algorithm-hardware co-design that claims better accuracy-latency trade-off and lower FPGA resource use than MWPM and UF baselines under depolarizing noise.
-
Quantum resources in non-stoquastic quantum annealing
Numerical evidence that non-stoquastic terms in quantum annealing maintain or increase entanglement and non-stabilizerness, aligning quantum performance gains with classical intractability for tensor networks and stabilizer methods.
-
Constructions of Quantum $(r,\delta)$-LRCs from cyclic codes
Three explicit families of quantum (r,δ)-LRCs are built from cyclic codes, two optimal under the quantum Singleton-like bound when pure, with no length bound relative to field size for constructions 2 and 3.
-
Adaptive Stabilizer State Fidelity Certification
Adaptive gauge selection protocol for stabilizer state fidelity certification that reports full intervals with monotonic tightening and exact recovery on full coverage.
-
Towards Scalable Quaternary Message-Passing Decoding for Quantum Error Correction
Dilution method for quaternary Min-Sum decoder yields 16% apparent depolarizing threshold up to d=20, outperforms MWPM in finite regimes, and for X-noise beats BP-OSD at d=65 with O(N log² d) complexity.
-
Translation-invariant quantum low-density parity-check codes from compactified fracton models
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.
-
Spatial overhead reduction for 2D hypergraph product codes
A qubit-reduction method for hypergraph product codes preserves dimension, distance, and fault-tolerance properties, producing smaller codes such as [[441,64,6]] from [[610,64,6]] with comparable noise performance and compatibility with logical gates.
-
Protocol for Efficient Generation of Fusion-Based Quantum Computing Resource States from Quantum Emitters
Logically encoded 24-photon FBQC resource states can be deterministically produced from 3 quantum emitters and 11 CNOT gates by using symmetries to reduce the search over photon emission orderings.
-
Quantum Magic in early FTQC: From Diagonal Clifford Hierarchy No-Go Theorems to Architecture Design Blueprints
No-go theorems prove hierarchy level and state-independent sequences cannot maximize operational magic in early FTQC, requiring state-aware differentiable optimization and nonlinear phases for scalable magic generation.
-
Design and Analysis of Quantum Dual-Containing CSS LDPC Codes based on Quasi-Dyadic Matrices
Two new constructions of quantum dual-containing CSS LDPC codes from quasi-dyadic matrices achieve improved finite-length error performance over existing DC codes.
-
Interplay of Nonstabilizerness and Ergotropy in Quantum Batteries
Ergotropy in the battery corresponds one-to-one with total nonstabilizerness under U(1)-symmetric charger-battery interactions, while maximum average charging power in Clifford evolution is achievable even with zero initial magic.
-
Defect-Adaptive Lattice Surgery on Irregular Boundary Surface-Code Patches
A defect-adaptive lattice surgery technique reconstructs joint logical parities on irregular surface-code patches via GF(2) binary synthesis from seam measurements and pre-merge constraints, yielding executable rules or failure certificates while preserving effective distance.
-
A graph-aware bounded distance decoder for all stabilizer codes
A graph-based bounded distance decoder corrects all errors up to a chosen weight in arbitrary stabilizer codes by representing stabilizers and syndromes as graphs and pruning the search space with a feed-forward structure.
-
Coherence dynamics in quantum many-body systems with conservation laws
Conservation laws in quantum circuits and Hamiltonians replace logarithmic coherence saturation with slow hydrodynamic relaxation globally and produce algebraic peak-time growth locally, unlike ergodic cases.
-
Deterministic generation of grid states with programmable nonlinear bosonic circuits
Programmable nonlinear bosonic circuits can deterministically produce phased-comb states that serve as a scalable bosonic quantum error-correcting code with near-optimal performance against boson loss.