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.
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Quantum codes on a lattice with boundary
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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
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 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.
XYZ planar code with pMWPM decoder achieves higher and more stable thresholds under biased noise than standard surface codes, with a 36% improvement in the infinite-bias limit.
Concatenating quantum Reed-Solomon outer codes over the gross code using Galois qudits reaches teraquop regime at 10^{-3} physical noise with lower overhead than prior two-gross-code constructions.
The paper introduces concrete code deformation procedures for dense surface code packing, proposes hook-error-avoiding CNOT scheduling for syndrome extraction, and reports Monte Carlo simulations showing lower logical error rates than standard surface codes at large distances and low physical error,
Local syndrome-based preprocessing accelerates BP decoders for quantum LDPC codes, delivering up to 10x speedup on the [[144,12,12]] code while maintaining or improving logical error rates.
Experimental demonstration of logical |H_L> and |T_L> magic states with fidelities 0.8806 and 0.8665 on IBM superconducting hardware using a qubit-efficient surface code embedding, with reported error thresholds above prior values.
Degenerate BP decoders achieve capacity-achieving or near-capacity performance for quantum erasure correction in linear time on bicycle, product, and topological stabilizer codes.
VGQEC codes embed tunable parameters in Quon graphs to enable noise-tailored quantum error correction, bridging repetition and stabilizer codes and showing experimental results under amplitude damping on a photonic system.
Synchronizable hybrid subsystem codes are built from classical cyclic codes C and D with C^perp subset C subset D via CSS construction to correct Pauli and synchronization errors, tolerate gauge errors, and carry both classical and quantum information, with explicit trade-offs.
Decoherence on abelian topological order is modeled as a temporal defect in double TQFT driving boundary anyon condensation transitions classified by Lagrangian subgroups of the doubled order.
Two new constructions of quantum dual-containing CSS LDPC codes from quasi-dyadic matrices achieve improved finite-length error performance over existing DC codes.
A programmable 2D toric oscillator network enables efficient routing for bivariate bicycle LDPC codes, reducing long-range couplers to O(sqrt(n)) and achieving 3.06% logical error rate per cycle in simulations for the [[18,4,4]] code.
The five-qubit code outperforms Steane and toric codes in preserving fidelity for low-temperature open quantum systems at weak-to-moderate couplings, with a critical time for entangled states beyond which correction helps.
Catalyst towers reduce runtime and spacetime volume for continuous rotations in surface codes at small and medium distances in phase oracle and variational state preparation circuits for option pricing.
Power-law divergence of fidelity susceptibility and logarithmic divergence of an entanglement witness mark the topological-to-non-topological transitions in locally perturbed Kitaev and color codes; critical points are located by finite-size scaling and confirmed by mapping to the 2D Ising model.
New combinatorial proofs and circuit designs for quantum error correction reduce physical qubit overhead by up to 10x and time overhead by 2-6x for codes including Steane, Golay, and surface codes.
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Non-linear Sigma Model for the Surface Code with Coherent Errors
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.