01260nas a2200133 4500008004100000245010100041210006900142260001400211490000700225520080900232100002401041700002401065856003701089 2009 eng d00aQuadratic fermionic interactions yield effective Hamiltonians for adiabatic quantum computing
0 aQuadratic fermionic interactions yield effective Hamiltonians fo c2009/3/240 v793 a Polynomially-large ground-state energy gaps are rare in many-body quantum
systems, but useful for adiabatic quantum computing. We show analytically that
the gap is generically polynomially-large for quadratic fermionic Hamiltonians.
We then prove that adiabatic quantum computing can realize the ground states of
Hamiltonians with certain random interactions, as well as the ground states of
one, two, and three-dimensional fermionic interaction lattices, in polynomial
time. Finally, we use the Jordan-Wigner transformation and a related
transformation for spin-3/2 particles to show that our results can be restated
using spin operators in a surprisingly simple manner. A direct consequence is
that the one-dimensional cluster state can be found in polynomial time using
adiabatic quantum computing.
1 aO'Hara, Michael, J.1 aO'Leary, Dianne, P. uhttp://arxiv.org/abs/0808.1768v101156nas a2200133 4500008004100000245005100041210004700092260001400139490000700153520077700160100002400937700002400961856003700985 2008 eng d00aThe adiabatic theorem in the presence of noise0 aadiabatic theorem in the presence of noise c2008/4/220 v773 a We provide rigorous bounds for the error of the adiabatic approximation of
quantum mechanics under four sources of experimental error: perturbations in
the initial condition, systematic time-dependent perturbations in the
Hamiltonian, coupling to low-energy quantum systems, and decoherent
time-dependent perturbations in the Hamiltonian. For decoherent perturbations,
we find both upper and lower bounds on the evolution time to guarantee the
adiabatic approximation performs within a prescribed tolerance. Our new results
include explicit definitions of constants, and we apply them to the spin-1/2
particle in a rotating magnetic field, and to the superconducting flux qubit.
We compare the theoretical bounds on the superconducting flux qubit to
simulation results.
1 aO'Hara, Michael, J.1 aO'Leary, Dianne, P. uhttp://arxiv.org/abs/0801.3872v1