Vine codes generalize directional codes to open planar boundaries, delivering up to 28% fewer data/measure qubits at circuit distance 7 and better simulated performance than the surface code at 10^{-3} noise while using fewer total qubits.
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Quantum codes on a lattice with boundary
Mixed citation behavior. Most common role is background (67%).
48
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67% of classified citations
abstract
A new type of local-check additive quantum code is presented. Qubits are associated with edges of a 2-dimensional lattice whereas the stabilizer operators correspond to the faces and the vertices. The boundary of the lattice consists of alternating pieces with two different types of boundary conditions. Logical operators are described in terms of relative homology groups.
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representative citing papers
Proves that minimum-weight decoding of 2D TTI stabilizer codes admits a PTAS by reducing the problem to Euclidean geometric approximation tasks such as TSP when errors are modeled as point-like excitations connected by strings.
Averaging symmetric Z_N quantum circuits over random noise produces a noisy surface code whose logical information is protected against symmetric errors up to a threshold, with charge-sharpening transitions coinciding with bulk confinement transitions that differ for N≤4 versus N>4.
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 LLM-guided search method called structured concept evolution discovers competitive lifted-product qLDPC code families including non-abelian constructions.
Coset-based generalization of 2BGA codes produces new quantum LDPC codes with parameters such as [[48,8,6]] and competitive noise thresholds under BP-OSD decoding.
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.
Experimental realization of lattice surgery on two d=3 surface-code logical qubits in superconducting hardware, with logical Bell state, Deutsch-Jozsa algorithm, and conditioned non-Clifford gate fidelity of 0.943.
Experimental breakeven demonstration of a qLDPC code encoding 4 logical qubits in 18 physical qubits on trapped ions, with up to 9x lower logical error rate than prior superconducting implementations.
Partial QEC on superpositions of code states suppresses parallel weight-l noise by p^floor((l+1)/2) while preserving super-SQL metrology performance using local operators and an adaptive imprinter strategy.
LightStim automates DEM construction for QEC protocols via a record-augmented Pauli tableau tracker, validated across memory, logical operations, distillation, and a novel cross-code lattice surgery design.
A non-linear sigma model maps surface-code decoding under coherent errors to distinct replica limits, exposing a thermal-metal phase for suboptimal decoders that is absent in optimal decoding.
Circle graphs are closed under r-local complementation and bipartite circle graph states correspond one-to-one with planar code states whose MBQC is classically simulable.
Lattice-surgery scheduling is mapped to 3D path embedding and solved with look-ahead Dijkstra projection, yielding 3.8x lower execution time on quantum phase estimation benchmarks versus greedy scheduling.
Higher gauging of 1-form symmetries on surfaces in 2+1d QFT yields condensation defects whose fusion rules involve 1+1d TQFTs and realizes every 0-form symmetry in TQFTs.
Parameterized families of toric code Hamiltonians realize em-duality pumping and higher-order anyon pumping, diagnosed by topological pumping into tensor-network bond spaces and corner modes.
KOVAL-Q uses SAT solving to optimize and verify surface-code logical operations with general encodings, finding d-cycle CNOTs and 2d-cycle rotations that reduce FTQC application runtime by about 10 percent.
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.
Hardware experiment on IBM devices shows reset-free LUCI achieves logical X and Z error suppression ratios of 1.75(10) and 1.93(12), competitive with surface code despite halved syndrome density.
A calibration workflow using ELEA and CAFE circuits achieves CZ gate fidelity above 99.9% on an 84-qubit superconducting processor with 0.007% coherent error and median 99.25% across 72 gates.
Under circuit-level noise the predicted advantage of bias-optimized rectangular surface codes over XZZX codes vanishes, while a new bias-filtering CNOT gadget recovers only a few-percent threshold improvement for XZZX codes.
BBS code dimension equals the algebraic multiplicity of finite nonzero common roots of the defining bivariate polynomials, enabling a root-based prescription for arbitrary boundary shapes that avoids corner corrections when edge conditions hold.
Barbell codes are a family of qLDPC codes with a matching superconducting chip layout enabling constant hardware complexity, simulated to preserve logical information over trillions of QEC cycles at 10^{-4} physical noise with under 30 data qubits per logical qubit.
Establishes necessary and sufficient criterion for [[n,1,d]] stabilizer codes to preserve code space under restricted transversal block-Pauli masking U_enc(a,b)=(X^a Z^b)^⊗n for homomorphic quantum error correction.
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LightStim automates DEM construction for QEC protocols via a record-augmented Pauli tableau tracker, validated across memory, logical operations, distillation, and a novel cross-code lattice surgery design.