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Topological Codes Gained a Proven Coherent-Error Threshold

A cluster-expansion proof covers bounded logical-qubit quantum LDPC codes, including the surface code.

Published Updated Story ID: mp-2026-09-18-016
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Summary

A cluster-expansion proof covers bounded logical-qubit quantum LDPC codes, including the surface code.

Unlike random Pauli faults, coherent rotations can interfere across many error paths. The proof retains those amplitudes with Fourier analysis and combines them with a polymer-model cluster expansion. Below a code-size-independent rotation bound, maximum-likelihood Pauli recovery suppresses entanglement infidelity exponentially in distance, up to a prefactor linear in physical qubits.

Why it matters

A cluster-expansion proof covers bounded logical-qubit quantum LDPC codes, including the surface code.

Limits and context

No additional limitation was separately recorded.

Key claims

  1. A cluster-expansion proof covers bounded logical-qubit quantum LDPC codes, including the surface code.

    Evidence: source-2026-09-18-018

Sources

  1. arXiv preprint 2609.20708arXiv · primary research

Corrections

No corrections have been recorded for this story.