The stabilizer code formalism is presented as a powerful group-theoretic tool for quantum error correction, enabling code construction, analysis of quantum channel capacity, bounds on codes, and fault-tolerant computation.
Quantum Error Correction via Codes over GF(4)
5 Pith papers cite this work. Polarity classification is still indexing.
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abstract
The problem of finding quantum error-correcting codes is transformed into the problem of finding additive codes over the field GF(4) which are self-orthogonal with respect to a certain trace inner product. Many new codes and new bounds are presented, as well as a table of upper and lower bounds on such codes of length up to 30 qubits.
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A layer-by-layer classical variational disentanglement algorithm compiles preparation circuits for matrix product states by minimizing bipartite entanglement to reduce bond dimensions.
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.
LDGM codes enable syndrome measurement for QLDPC codes with controlled constant-weight stabilizers, yielding lower logical error rates than repeated extraction on a distance-5 surface code.
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.
citing papers explorer
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Preparation Circuits for Matrix Product States by Classical Variational Disentanglement
A layer-by-layer classical variational disentanglement algorithm compiles preparation circuits for matrix product states by minimizing bipartite entanglement to reduce bond dimensions.
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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.
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Fault-Tolerant QLDPC Syndrome Measurement via LDGM Encoding
LDGM codes enable syndrome measurement for QLDPC codes with controlled constant-weight stabilizers, yielding lower logical error rates than repeated extraction on a distance-5 surface code.
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Lower overhead fault-tolerant building blocks for noisy quantum computers
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.