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
Purification of weakly monitored Clifford circuits on prime-dimensional qudits reduces exactly to a pure-death Markov process on the density-matrix rank, producing compact universal scaling functions for all Rényi entropies.
MGT protocols encode the input into a measurement-heralded stabilizer code then apply a logical non-Clifford gate; useful resource states are Clifford-equivalent to diagonal states, and feedforward can often be Pauli.
High-rate CSS codes compile nonlocal Clifford and non-Clifford logical circuits into onsite phases and classical permutations, so MPS bond dimension stays fixed by the encoder while logical entanglement, magic, and non-Gaussianity grow.
Two covariance-matrix-derived entropy families are proven to be fermionic non-Gaussianity monotones, yielding SWAP-gate lower bounds and classical-simulation upper bounds.
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.
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.
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.
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.
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
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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.