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Perfect Quantum Error Correction Code

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arxiv quant-ph/9602019 v1 pith:DPWQEKNT submitted 1996-02-27 quant-ph

Raymond Laflamme , Cesar Miquel , Juan Pablo Paz , Wojciech Hubert Zurek This is my paper · ORCID
classification quant-ph
keywords stateerrorquantumqubitqubitscircuitcodecorrection
verification ladder T0 review T1 audit T2 compute T3 formal
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We present a quantum error correction code which protects a qubit of information against general one qubit errors which maybe caused by the interaction with the environment. To accomplish this, we encode the original state by distributing quantum information over five qubits, the minimal number required for this task. We give a simple circuit which takes the initial state with four extra qubits in the state |0> to the encoded state. The circuit can be converted into a decoding one by simply running it backward. Reading the extra four qubits at the decoder's output we learn which one of the sixteen alternatives (no error plus all fifteen possible 1-bit errors) was realized. The original state of the encoded qubit can then be restored by a simple unitary transformation.

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Forward citations

Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Preparation Circuits for Matrix Product States by Classical Variational Disentanglement

    quant-ph 2025-04 unverdicted novelty 7.0 of 10

    A layer-by-layer classical variational disentanglement algorithm compiles preparation circuits for matrix product states by minimizing bipartite entanglement to reduce bond dimensions.

  2. Quantum Error Correction Codes for Truncated SU(2) Lattice Gauge Theories

    quant-ph 2025-11 conditional novelty 6.0 of 10

    Gauss's law constraints in jmax=1/2 SU(2) lattice gauge theory are converted into stabilizer codes that correct single-qubit errors using about 9N or 12N physical qubits per N plaquettes.

  3. Quantum codes do not fix isotropic errors

    quant-ph 2025-01 reject novelty 6.0 of 10

    For a family of spherically symmetric quantum errors, any non-degenerate quantum code leaves the corrected state no closer to the ideal, and any detected syndrome randomizes the logical qubits.

  4. Tensor-network decoders for process tensor descriptions of non-Markovian noise

    quant-ph 2024-12 conditional novelty 6.0 of 10

    A tensor-network-based maximum likelihood decoder is constructed for quantum error correction under process-tensor noise, with an MPS approximation demonstrated on the five-qubit and Steane codes.

  5. Certified boundary-magic witness for state-dependent proto-area in a holographic code

    hep-th 2026-07 conditional novelty 5.5 of 10

    Only matter-controlled bond motion yields state-dependent proto-area in a four-qubit holographic code, and a projected stabilizer-Rényi quadratic witness certifies it while total magic does not.

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