  Simulation of quantum systems is challenging due to the exponential size of
the state space. Tensor networks provide a systematically improvable
approximation for quantum states. 2D tensor networks such as Projected
Entangled Pair States (PEPS) are well-suited for key classes of physical
systems and quantum circuits. However, direct contraction of PEPS networks has
exponential cost, while approximate algorithms require computations with large
tensors. We propose new scalable algorithms and software abstractions for
PEPS-based methods, accelerating the bottleneck operation of contraction and
refactorization of a tensor subnetwork. We employ randomized SVD with an
implicit matrix to reduce cost and memory footprint asymptotically. Further, we
develop a distributed-memory PEPS library and study accuracy and efficiency of
alternative algorithms for PEPS contraction and evolution on the Stampede2
supercomputer. We also simulate a popular near-term quantum algorithm, the
Variational Quantum Eigensolver (VQE), and benchmark Imaginary Time Evolution
(ITE), which compute ground states of Hamiltonians.
