Global Estimates of Errors in Quantum Computation by the Feynman–Vernon Formalism

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Research units

  • Royal Institute of Technology
  • CAS - Institute of Theoretical Physics


The operation of a quantum computer is considered as a general quantum operation on a mixed state on many qubits followed by a measurement. The general quantum operation is further represented as a Feynman–Vernon double path integral over the histories of the qubits and of an environment, and afterward tracing out the environment. The qubit histories are taken to be paths on the two-sphere (Formula presented.) as in Klauder’s coherent-state path integral of spin, and the environment is assumed to consist of harmonic oscillators initially in thermal equilibrium, and linearly coupled to to qubit operators (Formula presented.). The environment can then be integrated out to give a Feynman–Vernon influence action coupling the forward and backward histories of the qubits. This representation allows to derive in a simple way estimates that the total error of operation of a quantum computer without error correction scales linearly with the number of qubits and the time of operation. It also allows to discuss Kitaev’s toric code interacting with an environment in the same manner.


Original languageEnglish
Pages (from-to)745–767
Number of pages23
JournalJournal of Statistical Physics
Issue number5
Publication statusPublished - 2018
MoE publication typeA1 Journal article-refereed

    Research areas

  • Feynman–Vernon method, Noisy quantum computing

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ID: 19234575