arXiv subjects

P. Wocjan

Publications and source records attributed to P. Wocjan.

2 recordsLinked to original sources

arXiv2019

Carving-width and contraction trees for tensor networks

We study the problem of finding contraction orderings on tensor networks for physical simulations using a syncretic abstract data type, the $\textit{contraction-tree}$, and explain its connection to temporal and spatial measures of tensor contraction computational complexity (nodes express time; arcs express space). We have implemented the Ratcatcher of Seymour and Thomas for determining the carving-width of planar networks, in order to offer experimental evidence that this measure of spatial complexity makes a generally effective heuristic for limiting their total contraction time.

cs.DM↗

arXiv2001

Simulating Arbitrary Pair-Interactions by a Given Hamiltonian: Graph-Theoretical Bounds on the Time Complexity

We use an n-spin system with permutation symmetric zz-interaction for simulating arbitrary pair-interaction Hamiltonians. The calculation of the required time overhead is mathematically equivalent to a separability problem of n-qubit density matrices. We derive lower and upper bounds in terms of chromatic index and the spectrum of the interaction graph. The complexity measure defined by such a computational model is related to gate complexity and a continuous complexity measure introduced in a former paper. We use majorization of graph spectra for classifying Hamiltonians with respect to their computational power.

quant-ph↗