34 research outputs found
Faddeev random phase approximation for molecules
The many body Green's function is an adequate tool to study the groundstate energy and ionization energies of molecules. The Faddeev Random Phase Approximation (FRPA)[1] makes use of Faddeev equations to couple two-particle - one-hole (2p1h) and two-hole - one-particle (2h1p) excitations to the single-particle spectrum. Solving these equations implies an inite partial summation of the perturbation expansion of the self-energy. This method goes beyond the ADC(3)[2] approximation by treating both the particle-hole and particle-particle interactions at the RPA level. We present the results of our calculations for some diatomic molecules
Faddeev Random Phase Approximation applied to molecules
This Ph.D. thesis derives the equations of the Faddeev Random Phase
Approximation (FRPA) and applies the method to a set of small atoms and
molecules. The occurence of RPA instabilities in the dissociation limit is
addressed in molecules and by the study of the Hubbard molecule as a test
system with reduced dimensionality.Comment: Ph.D. thesi
Faddeev Random Phase Approximation for Molecules
The Faddeev Random Phase Approximation is a Green's function technique that
makes use of Faddeev-equations to couple the motion of a single electron to the
two-particle--one-hole and two-hole--one-particle excitations. This method goes
beyond the frequently used third-order Algebraic Diagrammatic Construction
method: all diagrams involving the exchange of phonons in the particle-hole and
particle-particle channel are retained, but the phonons are described at the
level of the Random Phase Approximation. This paper presents the first results
for diatomic molecules at equilibrium geometry. The behavior of the method in
the dissociation limit is also investigated
Polynomial Similarity Transformation Theory: A smooth interpolation between coupled cluster doubles and projected BCS applied to the reduced BCS Hamiltonian
We present a similarity transformation theory based on a polynomial form of a
particle-hole pair excitation operator. In the weakly correlated limit, this
polynomial becomes an exponential, leading to coupled cluster doubles. In the
opposite strongly correlated limit, the polynomial becomes an extended Bessel
expansion and yields the projected BCS wavefunction. In between, we interpolate
using a single parameter. The effective Hamiltonian is non-hermitian and this
Polynomial Similarity Transformation Theory follows the philosophy of
traditional coupled cluster, left projecting the transformed Hamiltonian onto
subspaces of the Hilbert space in which the wave function variance is forced to
be zero. Similarly, the interpolation parameter is obtained through minimizing
the next residual in the projective hierarchy. We rationalize and demonstrate
how and why coupled cluster doubles is ill suited to the strongly correlated
limit whereas the Bessel expansion remains well behaved. The model provides
accurate wave functions with energy errors that in its best variant are smaller
than 1\% across all interaction stengths. The numerical cost is polynomial in
system size and the theory can be straightforwardly applied to any realistic
Hamiltonian
Transfer matrices and excitations with matrix product states
We use the formalism of tensor network states to investigate the relation between static correlation functions in the ground state of local quantum many-body Hamiltonians and the dispersion relations of the corresponding low-energy excitations. In particular, we show that the matrix product state transfer matrix (MPS-TM)—a central object in the computation of static correlation functions—provides important information about the location and magnitude of the minima of the low-energy dispersion relation(s), and we present supporting numerical data for one-dimensional lattice and continuum models as well as two-dimensional lattice models on a cylinder. We elaborate on the peculiar structure of the MPS-TM's eigenspectrum and give several arguments for the close relation between the structure of the low-energy spectrum of the system and the form of the static correlation functions. Finally, we discuss how the MPS-TM connects to the exact quantum transfer matrix of the model at zero temperature. We present a renormalization group argument for obtaining finite bond dimension approximations of the MPS, which allows one to reinterpret variational MPS techniques (such as the density matrix renormalization group) as an application of Wilson's numerical renormalization group along the virtual (imaginary time) dimension of the system
Improved precision scaling for simulating coupled quantum-classical dynamics
We present a super-polynomial improvement in the precision scaling of quantum
simulations for coupled classical-quantum systems in this paper. Such systems
are found, for example, in molecular dynamics simulations within the
Born-Oppenheimer approximation. By employing a framework based on the
Koopman-von Neumann formalism, we express the Liouville equation of motion as
unitary dynamics and utilize phase kickback from a dynamical quantum simulation
to calculate the quantum forces acting on classical particles. This approach
allows us to simulate the dynamics of these particles without the overheads
associated with measuring gradients and solving the equations of motion on a
classical computer, resulting in a super-polynomial advantage at the price of
increased space complexity. We demonstrate that these simulations can be
performed in both microcanonical and canonical ensembles, enabling the
estimation of thermodynamic properties from the prepared probability density.Comment: 19 + 51 page
Mutual information-assisted Adaptive Variational Quantum Eigensolver
Adaptive construction of ansatz circuits offers a promising route towards
applicable variational quantum eigensolvers (VQE) on near-term quantum
hardware. Those algorithms aim to build up optimal circuits for a certain
problem. Ansatz circuits are adaptively constructed by selecting and adding
entanglers from a predefined pool in those algorithms. In this work, we propose
a way to construct entangler pools with reduced size for those algorithms by
leveraging classical algorithms. Our method uses mutual information (MI)
between the qubits in classically approximated ground state to rank and screen
the entanglers. The density matrix renormalization group (DMRG) is employed for
classical precomputation in this work. We corroborate our method numerically on
small molecules. Our numerical experiments show that a reduced entangler pool
with a small portion of the original entangler pool can achieve same numerical
accuracy. We believe that our method paves a new way for adaptive construction
of ansatz circuits for variational quantum algorithms.Comment: 8 pages, 11 figure