%0 PDF
%T The Bravyi-Kitaev transformation for quantum computation of electronic structure.
%A Seeley, Jacob T.; Richard, Martin J.; Love, Peter J.
%D 2018-02-06T10:36:22.563-05:00
%8 2018-02-06
%I Tufts University. Tisch Library.
%R http://localhost/files/n009wd46g
%X Quantum simulation is an important application of future quantum computers with applications in quantum chemistry, condensed matter, and beyond. Quantum simulation of fermionic systems presents a specific challenge. The Jordan-Wigner transformation allows for representation of a fermionic operator by O(n) qubit operations. Here, we develop an alternative method of simulating fermions with qubits, first proposed by Bravyi and Kitaev [Ann. Phys. 298, 210 (2002)10.1006/aphy.2002.6254; e-print arXiv:quant-ph/0003137v2], that reduces the simulation cost to O(logn) qubit operations for one fermionic operation. We apply this new Bravyi-Kitaev transformation to the task of simulating quantum chemical Hamiltonians, and give a detailed example for the simplest possible case of molecular hydrogen in a minimal basis. We show that the quantum circuit for simulating a single Trotter time step of the Bravyi-Kitaev derived Hamiltonian for H2 requires fewer gate applications than the equivalent circuit derived from the Jordan-Wigner transformation. Since the scaling of the Bravyi-Kitaev method is asymptotically better than the Jordan-Wigner method, this result for molecular hydrogen in a minimal basis demonstrates the superior efficiency of the Bravyi-Kitaev method for all quantum computations of electronic structure. © 2012 American Institute of Physics.
%[ 2018-10-10
%9 Text
%~ Tufts Digital Library
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