5,553 research outputs found
Calculating energy derivatives for quantum chemistry on a quantum computer
Modeling chemical reactions and complicated molecular systems has been
proposed as the `killer application' of a future quantum computer. Accurate
calculations of derivatives of molecular eigenenergies are essential towards
this end, allowing for geometry optimization, transition state searches,
predictions of the response to an applied electric or magnetic field, and
molecular dynamics simulations. In this work, we survey methods to calculate
energy derivatives, and present two new methods: one based on quantum phase
estimation, the other on a low-order response approximation. We calculate
asymptotic error bounds and approximate computational scalings for the methods
presented. Implementing these methods, we perform the world's first geometry
optimization on an experimental quantum processor, estimating the equilibrium
bond length of the dihydrogen molecule to within 0.014 Angstrom of the full
configuration interaction value. Within the same experiment, we estimate the
polarizability of the H2 molecule, finding agreement at the equilibrium bond
length to within 0.06 a.u. (2% relative error).Comment: 19 pages, 1 page supplemental, 7 figures. v2 - tidied up and added
example to appendice
Ground state features of the Frohlich model
Following the ideas behind the Feynman approach, a variational wave function
is proposed for the Fr\"ohlich model. It is shown that it provides, for any
value of the electron-phonon coupling constant, an estimate of the polaron
ground state energy better than the Feynman method based on path integrals. The
mean number of phonons, the average electronic kinetic and interaction
energies, the ground state spectral weight and the electron-lattice correlation
function are calculated and successfully compared with the best available
results.Comment: 6 figure
Quantum Algorithm for Approximating Maximum Independent Sets
We present a quantum algorithm for approximating maximum independent sets of
a graph based on quantum non-Abelian adiabatic mixing in the sub-Hilbert space
of degenerate ground states, which generates quantum annealing in a secondary
Hamiltonian. For both sparse and dense graphs, our quantum algorithm on average
can find an independent set of size very close to , which is the
size of the maximum independent set of a given graph . Numerical results
indicate that an time complexity quantum algorithm is sufficient for
finding an independent set of size . The best classical
approximation algorithm can produce in polynomial time an independent set of
size about half of
- …