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Alexei Kitaev proposes the toric code and topological quantum computing

Jul 9, 1997

Alexei Kitaev describes how a two-dimensional quantum system hosting exotic particle-like excitations called anyons could work as a quantum computer that resists errors by its physical nature. The paper introduces the toric code, a model of qubits arranged on a 2D lattice.

Why it matters

It laid the groundwork for topological quantum computing, and its grid-based toric code became a classic model whose states Google has since created on its quantum processor.

Alexei Kitaev

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Sources (3)

  • arXiv (A. Yu. Kitaev) Fault-tolerant quantum computation by anyons
    Primary sourceJul 9, 1997
    “A two-dimensional quantum system with anyonic excitations can be considered as a quantum computer. Unitary transformations can be performed by moving the excitations around each other. Measurements can be performed by joining excitations in pairs and observing the result of fusion. Such computation is fault-tolerant by its physical nature.”
  • Google Quantum AI Toric Code (Cirq experiments)
    Independent coverage
    “The toric code is an "instant classic" model of interacting qubits on a 2D lattice first proposed by Alexei Kitaev in 1997 ( A. Y. Kitaev, Ann. Phys. 303, 2–30 (2003) ). In K. J. Satzinger et al., Science 374 6572, 1237-1241 (2021) , we create toric code eigenstates on our quantum processor”
  • Breakthrough Prize Foundation Alexei Kitaev – 2012 Breakthrough Prize in Fundamental Physics
    Independent coverage
    “Alexei Kitaev formulated a proposal for a quantum computer that could correct errors through its intrinsic physical properties. This laid the mathematical groundwork for a new type of quantum computer that uses macroscopic-scale matter in exotic states to simulate the behavior of atomic-scale particles.”

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