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

Loading...
Thumbnail Image

Access rights

openAccess
publishedVersion

URL

Journal Title

Journal ISSN

Volume Title

A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

Date

2018

Major/Subject

Mcode

Degree programme

Language

en

Pages

23

Series

Journal of Statistical Physics, Volume 171, issue 5, pp. 745–767

Abstract

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.

Description

Keywords

Feynman–Vernon method, Noisy quantum computing

Other note

Citation

Aurell, E 2018, ' Global Estimates of Errors in Quantum Computation by the Feynman–Vernon Formalism ', Journal of Statistical Physics, vol. 171, no. 5, pp. 745–767 . https://doi.org/10.1007/s10955-018-2037-6