Publications by Michael Lubasch

Variational quantum algorithms for nonlinear problems

Physical Review A American Physical Society 101 (2020) 010301(R)

M Lubasch, J Joo, P Moinier, M Kiffner, D Jaksch

We show that nonlinear problems including nonlinear partial di↵erential equations can be e- ciently solved by variational quantum computing. We achieve this by utilizing multiple copies of variational quantum states to treat nonlinearities eciently and by introducing tensor networks as a programming paradigm. The key concepts of the algorithm are demonstrated for the nonlinear Schr¨odinger equation as a canonical example. We numerically show that the variational quantum ansatz can be exponentially more ecient than matrix product states and present experimental proof-of-principle results obtained on an IBM Q device.

Bosonic fractional quantum hall states on a finite cylinder

Physical Review A American Physical Society 99 (2019) 033603-

P Rosson, M Lubasch, M Kiffner, D Jaksch

We investigate the ground-state properties of a bosonic Harper-Hofstadter model with local interactions on a finite cylindrical lattice with filling fraction ν = 1/2. We find that our system supports topologically ordered states by calculating the topological entanglement entropy, and its value is in good agreement with the theoretical value for the ν = 1/2 Laughlin state. By exploring the behavior of the density profiles, edge currents, and singleparticle correlation functions, we find that the ground state on the cylinder shows all signatures of a fractional quantum Hall state even for large values of the magnetic flux density. Furthermore, we determine the dependence of the correlation functions and edge currents on the interaction strength. We find that depending on the magnetic flux density, the transition toward Laughlin-like behavior can be either smooth or it can happen abruptly for some critical interaction strength

Multigrid renormalization

Journal of Computational Physics 372 (2018) 587-602

M Lubasch, P Moinier, D Jaksch

© 2018 Elsevier Inc. We combine the multigrid (MG) method with state-of-the-art concepts from the variational formulation of the numerical renormalization group. The resulting MG renormalization (MGR) method is a natural generalization of the MG method for solving partial differential equations. When the solution on a grid of N points is sought, our MGR method has a computational cost scaling as O(log⁡(N)), as opposed to O(N) for the best standard MG method. Therefore MGR can exponentially speed up standard MG computations. To illustrate our method, we develop a novel algorithm for the ground state computation of the nonlinear Schrödinger equation. Our algorithm acts variationally on tensor products and updates the tensors one after another by solving a local nonlinear optimization problem. We compare several different methods for the nonlinear tensor update and find that the Newton method is the most efficient as well as precise. The combination of MGR with our nonlinear ground state algorithm produces accurate results for the nonlinear Schrödinger equation on N=1018grid points in three spatial dimensions.

Tensor network states in time-bin quantum optics

PHYSICAL REVIEW A 97 (2018) ARTN 062304

M Lubasch, AA Valido, JJ Renema, WS Kolthammer, D Jaksch, MS Kim, I Walmsley, R Garcia-Patron

Diagonalization of complex symmetric matrices: Generalized Householder reflections, iterative deflation and implicit shifts


JH Noble, M Lubasch, J Stevens, UD Jentschura

Systematic construction of density functionals based on matrix product state computations

New Journal of Physics IOP Publishing (2016)

M Lubasch, JI Fuks, H Appel, A Rubio, JI Cirac, M-C Bañuls

We propose a systematic procedure for the approximation of density functionals in density functional theory that consists of two parts. First, for the efficient approximation of a general density functional, we introduce an efficient ansatz whose non-locality can be increased systematically. Second, we present a fitting strategy that is based on systematically increasing a reasonably chosen set of training densities. We investigate our procedure in the context of strongly correlated fermions on a onedimensional lattice in which we compute accurate training densities with the help of matrix product states. Focusing on the exchange-correlation energy, we demonstrate how an efficient approximation can be found that includes and systematically improves beyond the local density approximation. Importantly, this systematic improvement is shown for target densities that are quite different from the training densities.