The authors formalize tensor-network contraction orders as contraction trees, link the space and time bottlenecks to carving-width and treewidth, and show experimentally that a Ratcatcher-based planner produces near-optimal orders on planar grid networks.
Simulation of Quantum Many-Body Systems on Amazon Cloud
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Quantum many-body systems (QMBs) are some of the most challenging physical systems to simulate numerically. Methods involving approximations for tensor network (TN) contractions have proven to be viable alternatives to algorithms such as quantum Monte Carlo or simulated annealing. However, these methods are cumbersome, difficult to implement, and often have significant limitations in their accuracy and efficiency when considering systems in more than one dimension. In this paper, we explore the exact computation of TN contractions on two-dimensional geometries and present a heuristic improvement of TN contraction that reduces the computing time, the amount of memory, and the communication time. We run our algorithm for the Ising model using memory optimized x1.32x large instances on Amazon Web Services (AWS) Elastic Compute Cloud (EC2). Our results show that cloud computing is a viable alternative to supercomputers for this class of scientific applications.
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Carving-width and contraction trees for tensor networks
The authors formalize tensor-network contraction orders as contraction trees, link the space and time bottlenecks to carving-width and treewidth, and show experimentally that a Ratcatcher-based planner produces near-optimal orders on planar grid networks.