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The Bravyi-Kitaev transformation: Properties and applications

International journal of quantum chemistry, 2015-10, Vol.115 (19), p.1431-1441 [Peer Reviewed Journal]

2015 Wiley Periodicals, Inc. ;ISSN: 0020-7608 ;EISSN: 1097-461X ;DOI: 10.1002/qua.24969 ;CODEN: IJQCB2

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  • Title:
    The Bravyi-Kitaev transformation: Properties and applications
  • Author: Tranter, Andrew ; Sofia, Sarah ; Seeley, Jake ; Kaicher, Michael ; McClean, Jarrod ; Babbush, Ryan ; Coveney, Peter V. ; Mintert, Florian ; Wilhelm, Frank ; Love, Peter J.
  • Subjects: quantum chemistry ; quantum computing ; quantum simulation
  • Is Part Of: International journal of quantum chemistry, 2015-10, Vol.115 (19), p.1431-1441
  • Description: Quantum chemistry is an important area of application for quantum computation. In particular, quantum algorithms applied to the electronic structure problem promise exact, efficient methods for determination of the electronic energy of atoms and molecules. The Bravyi–Kitaev transformation is a method of mapping the occupation state of a fermionic system onto qubits. This transformation maps the Hamiltonian of n interacting fermions to an O(log⁡n)‐local Hamiltonian of n qubits. This is an improvement in locality over the Jordan–Wigner transformation, which results in an O(n)‐local qubit Hamiltonian. We present the Bravyi–Kitaev transformation in detail, introducing the sets of qubits which must be acted on to change occupancy and parity of states in the occupation number basis. We give recursive definitions of these sets and of the transformation and inverse transformation matrices, which relate the occupation number basis and the Bravyi–Kitaev basis. We then compare the use of the Jordan–Wigner and Bravyi–Kitaev Hamiltonians for the quantum simulation of methane using the STO‐6G basis. © 2015 Wiley Periodicals, Inc. Quantum chemistry is a promising application of quantum computation. Calculating the energy of electrons in molecules exactly and efficiently will be possible on future quantum computers. The quantum algorithms developed for this purpose include new methods for handling the antisymmetry of the electron wavefunction. This article discusses one such method in detail together with the results of its application to the simulation of methane.
  • Publisher: Hoboken: Blackwell Publishing Ltd
  • Language: English;French;German
  • Identifier: ISSN: 0020-7608
    EISSN: 1097-461X
    DOI: 10.1002/qua.24969
    CODEN: IJQCB2
  • Source: Alma/SFX Local Collection
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