The B ravyi– K itaev transformation: Properties and applications
Andrew Tranter, Sarah E. Sofia, Jake Seeley, Michael Kaicher, Jarrod R. McClean, Ryan Babbush, Peter V. Coveney, Florian Mintert, Frank K. Wilhelm, Peter J. Love · International Journal of Quantum Chemistry · 2015
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 ofninteracting fermions to an ‐local Hamiltonian ofnqubits. This is an improvement in locality over the Jordan–Wigner transformation, which results in anO(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.