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)
4 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.
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.
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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.