TY  - JOUR
A1  - Hübener, Robert
A1  - Kruszynska, Caroline
A1  - Hartmann, Lorenz
A1  - Duer, Wolfgang
A1  - Verstraete, Frank
A1  - Eisert, Jens
A1  - Plenio, Martin B.
T1  - Renormalization algorithm with graph enhancement
N2  - We introduce a class of variational states to describe quantum many-body systems. This class generalizes matrix product states which underlie the density-matrix renormalization-group approach by combining them with weighted graph states. States within this class may (i) possess arbitrarily long-ranged two-point correlations, (ii) exhibit an arbitrary degree of block entanglement entropy up to a volume law, (iii) be taken translationally invariant, while at the same time (iv) local properties and two-point correlations can be computed efficiently. This variational class of states can be thought of as being prepared from matrix product states, followed by commuting unitaries on arbitrary constituents, hence truly generalizing both matrix product and weighted graph states. We use this class of states to formulate a renormalization algorithm with graph enhancement and present numerical examples, demonstrating that improvements over density-matrix renormalization-group simulations can be achieved in the simulation of ground states and quantum algorithms. Further generalizations, e.g., to higher spatial dimensions, are outlined.
Y1  - 2009
UR  - http://pra.aps.org/
U6  - https://doi.org/10.1103/Physreva.79.022317
SN  - 1050-2947
ER  - 
TY  - JOUR
A1  - Hübener, Robert
A1  - Kruszynska, Caroline
A1  - Hartmann, Lorenz
A1  - Duer, Wolfgang
A1  - Plenio, Martin B.
A1  - Eisert, Jens
T1  - Tensor network methods with graph enhancement
JF  - Physical review : B, Condensed matter and materials physics
N2  - We present applications of the renormalization algorithm with graph enhancement (RAGE). This analysis extends the algorithms and applications given for approaches based on matrix product states introduced in [Phys. Rev. A 79, 022317 (2009)] to other tensor-network states such as the tensor tree states (TTS) and projected entangled pair states. We investigate the suitability of the bare TTS to describe ground states, showing that the description of certain graph states and condensed-matter models improves. We investigate graph-enhanced tensor-network states, demonstrating that in some cases (disturbed graph states and for certain quantum circuits) the combination of weighted graph states with TTS can greatly improve the accuracy of the description of ground states and time-evolved states. We comment on delineating the boundary of the classically efficiently simulatable states of quantum many-body systems.
Y1  - 2011
U6  - https://doi.org/10.1103/PhysRevB.84.125103
SN  - 1098-0121
VL  - 84
IS  - 12
PB  - American Physical Society
CY  - College Park
ER  -