1,744 research outputs found
A comparison of the Bravyi-Kitaev and Jordan-Wigner transformations for the quantum simulation of quantum chemistry
The ability to perform classically intractable electronic structure
calculations is often cited as one of the principal applications of quantum
computing. A great deal of theoretical algorithmic development has been
performed in support of this goal. Most techniques require a scheme for mapping
electronic states and operations to states of and operations upon qubits. The
two most commonly used techniques for this are the Jordan-Wigner transformation
and the Bravyi-Kitaev transformation. However, comparisons of these schemes
have previously been limited to individual small molecules. In this paper we
discuss resource implications for the use of the Bravyi-Kitaev mapping scheme,
specifically with regard to the number of quantum gates required for
simulation. We consider both small systems which may be simulatable on
near-future quantum devices, and systems sufficiently large for classical
simulation to be intractable. We use 86 molecular systems to demonstrate that
the use of the Bravyi-Kitaev transformation is typically at least approximately
as efficient as the canonical Jordan-Wigner transformation, and results in
substantially reduced gate count estimates when performing limited circuit
optimisations.Comment: 46 pages, 11 figure
Analyzing many-body localization with a quantum computer
Many-body localization, the persistence against electron-electron
interactions of the localization of states with non-zero excitation energy
density, poses a challenge to current methods of theoretical and numerical
analysis. Numerical simulations have so far been limited to a small number of
sites, making it difficult to obtain reliable statements about the
thermodynamic limit. In this paper, we explore the ways in which a relatively
small quantum computer could be leveraged to study many-body localization. We
show that, in addition to studying time-evolution, a quantum computer can, in
polynomial time, obtain eigenstates at arbitrary energies to sufficient
accuracy that localization can be observed. The limitations of quantum
measurement, which preclude the possibility of directly obtaining the
entanglement entropy, make it difficult to apply some of the definitions of
many-body localization used in the recent literature. We discuss alternative
tests of localization that can be implemented on a quantum computer.Comment: 11 pages, 8 figures; slightly revised, published versio
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