An algorithm converts topological data of 2D bulk stabilizer codes into 1D boundary subsystem codes via operator algebra and normal forms, enabling automatic generation of boundaries and defects demonstrated on toric, color, and other codes.
and Martin-Delgado, M
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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.
Mutual information between non-contractible regions on the torus fully classifies long-range nonstabilizerness for toric-code states but leaves a finite subset undetected in the doubled-Fibonacci string-net model.
Gauging enables constant-depth logical XS dagger measurements for color-code magic state cultivation, achieving 10^{-12} logical error rates at 0.05% physical error for distance-7 codes while retaining over 1% of shots via post-selection.
Ancilla-mediated protocols enable deterministic universal logical gates on any stabilizer code without ancilla consumption or code modification.
Introduces a gauging-based method for fault-tolerant logical measurement achieving qubit overhead linear in operator weight up to polylog factors, adaptable to arbitrary codes.
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.
A distributed (6.6.6) color code is realized by interconnecting patches via entangled pairs, with simulations showing the concatenated MWPM decoder maintains error threshold under asymmetric seam noise while tensor-network decoder shows slight reduction.
A topical review unifying statistical mechanics, tensor network, and AI approaches to approximate maximum likelihood decoding for quantum error correction codes.
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Operator algebra and algorithmic construction of boundaries and defects in (2+1)D topological Pauli stabilizer codes
An algorithm converts topological data of 2D bulk stabilizer codes into 1D boundary subsystem codes via operator algebra and normal forms, enabling automatic generation of boundaries and defects demonstrated on toric, color, and other codes.
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Low-overhead fault-tolerant quantum computation by gauging logical operators
Introduces a gauging-based method for fault-tolerant logical measurement achieving qubit overhead linear in operator weight up to polylog factors, adaptable to arbitrary codes.