Abstract
We develop an algorithmic framework for contracting tensor networks and demonstrate its power by classically simulating quantum computation of sizes previously deemed out of reach. Our main contribution, index slicing, is a method that efficiently parallelizes the contraction by breaking it down into much smaller and identically structured subtasks, which can then be executed in parallel without dependencies. We benchmark our algorithm on a class of random quantum circuits, achieving greater than 105 times acceleration over the original estimate of the simulation cost. We then demonstrate applications of the simulation framework for aiding the development of quantum algorithms and quantum error correction. As tensor networks are widely used in computational science, our simulation framework may find further applications.
Highlights
We develop an algorithmic framework for contracting tensor networks and demonstrate its power by classically simulating quantum computation of sizes previously deemed out of reach
The computational task associated with a tensor network—called the tensor network contraction—is to compute an output tensor given the values of the tensor nodes and the hypergraph structure
The index slicing framework proposed in our paper establishes an interpolation between the sequential pairwise contraction and the Feynman path integral algorithm, which correspond to the cases in which no index is sliced and in which all indices are sliced, respectively
Summary
We develop an algorithmic framework for contracting tensor networks and demonstrate its power by classically simulating quantum computation of sizes previously deemed out of reach. Index slicing decomposes a tensor network contraction task into many subtasks that have identical shapes and can be executed in an embarrassingly parallel way, that is, there is no dependency or communication required between the execution of the subtasks Such an algorithm can be readily deployed on modern computational clusters and experimental evidence shows that such parallelization introduces little overhead to the total running time. As tensor networks are ubiquitous in quantum information science (with applications including benchmarking quantum devices[2], probing quantum many-body systems[10,11,12,13] and decoding quantum error-correcting codes14–17), our simulator represents a useful tool to aid in the development of quantum technologies
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