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    "summary": "Kitaev constructed a one-dimensional superconducting chain with unpaired boundary Majorana modes and related their presence to a bulk parity invariant for gapped quadratic fermion systems.\n\nA chain can pair its fermionic degrees of freedom within each site or between neighboring sites. In the second pattern, one effective Majorana mode remains at each end. In the ideal open-chain model, the two associated low-energy states have different total fermion parities; away from a soluble point, their energy splitting becomes exponentially small with separation when the bulk remains gapped. The paper connects this boundary behavior to a bulk invariant, giving a way to identify the nontrivial regime without solving every boundary problem. This made a concrete theoretical route toward protected fermionic information. Protection relies on locality, separation, a gap and the permitted noise model. Parity-preserving interactions can still cause excitation, and a nonlocal coupling between the ends can split the low-energy states. The two opposite-parity states alone are not an unrestricted coherent qubit in a closed parity-conserving system. The paper proposes physical realizations and signatures; it does not report an experimentally built protected device or a complete fault-tolerant gate scheme. The contribution was posted in 2000 and published in 2001.",
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        "description": "The model is a specified one-dimensional superconducting fermion chain with parameter and boundary conditions supporting end modes. Finite-length splitting, parity and gap assumptions matter. A theoretical zero mode is not experimental detection or fault-tolerant computation by itself. Interactions, disorder and later devices need their own evidence.",
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      "statement": "# Kitaev: unpaired Majorana modes in quantum wires\n\nKitaev constructed a one-dimensional superconducting chain with unpaired boundary Majorana modes and related their presence to a bulk parity invariant for gapped quadratic fermion systems.\n\nA chain can pair its fermionic degrees of freedom within each site or between neighboring sites. In the second pattern, one effective Majorana mode remains at each end. In the ideal open-chain model, the two associated low-energy states have different total fermion parities; away from a soluble point, their energy splitting becomes exponentially small with separation when the bulk remains gapped. The paper connects this boundary behavior to a bulk invariant, giving a way to identify the nontrivial regime without solving every boundary problem. This made a concrete theoretical route toward protected fermionic information. Protection relies on locality, separation, a gap and the permitted noise model. Parity-preserving interactions can still cause excitation, and a nonlocal coupling between the ends can split the low-energy states. The two opposite-parity states alone are not an unrestricted coherent qubit in a closed parity-conserving system. The paper proposes physical realizations and signatures; it does not report an experimentally built protected device or a complete fault-tolerant gate scheme. The contribution was posted in 2000 and published in 2001.\n\n## Scientific scope\n\nThe model is a specified one-dimensional superconducting fermion chain with parameter and boundary conditions supporting end modes. Finite-length splitting, parity and gap assumptions matter. A theoretical zero mode is not experimental detection or fault-tolerant computation by itself. Interactions, disorder and later devices need their own evidence.\n\n## People and systems\n\nAlexei Yu. Kitaev\n\n\n\n## Original sources\n\n- [Kitaev: unpaired Majorana modes in quantum wires — complete 2000 arXiv v2](https://arxiv.org/pdf/cond-mat/0010440v2)\n- [Kitaev: unpaired Majorana modes in quantum wires — 2001 publisher identity](https://api.crossref.org/works/10.1070%2F1063-7869%2F44%2F10S%2FS29)\n",
      "summary": "Kitaev constructed a one-dimensional superconducting chain with unpaired boundary Majorana modes and related their presence to a bulk parity invariant for gapped quadratic fermion systems.\n\nA chain can pair its fermionic degrees of freedom within each site or between neighboring sites. In the second pattern, one effective Majorana mode remains at each end. In the ideal open-chain model, the two associated low-energy states have different total fermion parities; away from a soluble point, their energy splitting becomes exponentially small with separation when the bulk remains gapped. The paper connects this boundary behavior to a bulk invariant, giving a way to identify the nontrivial regime without solving every boundary problem. This made a concrete theoretical route toward protected fermionic information. Protection relies on locality, separation, a gap and the permitted noise model. Parity-preserving interactions can still cause excitation, and a nonlocal coupling between the ends can split the low-energy states. The two opposite-parity states alone are not an unrestricted coherent qubit in a closed parity-conserving system. The paper proposes physical realizations and signatures; it does not report an experimentally built protected device or a complete fault-tolerant gate scheme. The contribution was posted in 2000 and published in 2001.",
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