Parallel tensor network contraction algorithms have emerged as the pivotal benchmarks for assessing the classical limits of computation, exemplified by Google's demonstration of quantum supremacy through random circuit sampling. However, the massive parallelization of the algorithm makes it vulnerable to computer node failures. In this work, we apply coded computing to a practical parallel tensor network contraction algorithm. To the best of our knowledge, this is the first attempt to code tensor network contractions. Inspired by matrix multiplication codes, we provide two coding schemes: 2-node code for practicality in quantum simulation and hyperedge code for generality. Our 2-node code successfully achieves significant gain for f-resilient number compared to naive replication, proportional to both the number of node failures and the dimension product of sliced indices. Our hyperedge code can cover tensor networks out of the scope of quantum, with degraded gain in the exchange of its generality.
Tensor-network simulation of quantum circuits depends on contraction orders with low computational cost and small intermediate tensors, found without excessive planning time. We present ArcTN, a contraction-order optimization framework with two search presets. Light keeps planning overhead low, and Heavy spends more effort on refinement. Both combine randomized-greedy construction, subtree reconfiguration, and parallel tempering with stage-specific stopping rules. ArcTN also provides Fixed and Dynamic slicing to meet tensor-size limits and executes the returned orders. On the 30 QC32 quantum-circuit networks completed by all eight compared configurations, Light reduces FLOPs by 61.32% and plans 1.62
× faster than Cotengra Auto/CMA-ES, and Heavy reduces FLOPs by 43.83% and plans 7.21
× faster than Cotengra AutoHQ/Optuna. Heavy also needs 11.85% fewer FLOPs than OMECO TreeSA-8 and plans 1.33
× faster. Dynamic slicing meets the size limits in all 90 runs on 18 scalar-output networks and reduces total sliced FLOPs by 31.99% relative to Fixed slicing, at the cost of longer planning. With a common NumPy executor, Heavy has the lowest combined planning and execution time among five configurations on the runs that all of them completed. On 672 networks built from 320 MQT Bench circuits, Heavy obtains the lowest geometric-mean FLOPs on the 142 large networks while planning 3.1
× and 31
× faster than Cotengra AutoHQ and Hyper128.
Tensors are a natural generalization of matrices, and tensor networks are a natural generalization of matrix products. Despite the simple definition of tensor networks, they are versatile enough to represent many different kinds of "products" that arise in various theoretical and practical problems. In particular, the powerful computational model of quantum computation can be defined almost entirely in terms of matrix products and tensor products, both of which are special cases of tensor networks. As such, (classical) algorithms for evaluating tensor networks have profound importance in the study of quantum computation. In this thesis, we design and implement a parallel algorithm for tensor network contraction. In addition to finding efficient contraction orders for a tensor network, we also dynamically slice it into multiple sub-tasks with lower space and time costs, in order to evaluate the tensor network in parallel. We refer to such an evaluation strategy as a contraction scheme for the tensor network. In addition, we introduce a local optimization procedure that improves the efficiency of the contraction schemes we find. We also investigate the applications of our parallel tensor network contraction algorithm in quantum computation. The most ready application is the simulation of random quantum supremacy circuits, where we benchmark our algorithm to demonstrate its advantage over other similar tensor network based simulators. Other applications we found include evaluating the energy function of a Quantum Approximate Optimization Algorithm (QAOA), and simulating surface codes under a realistic error model with crosstalk.