We describe a family of quantum error-correcting codes which generalize both the quantum hypergraph-product (QHP) codes by Tillich and Zémor, and all families of toric codes on mdimensional hypercubic lattices. Similar to the latter, our codes form m-complexes Km, with m ≥ 2. These are defined recursively, with Km obtained as a tensor product of a complex Km−1 with a 1complex parameterized by a binary matrix. Parameters of the constructed codes are given explicitly in terms of those of binary codes associated with the matrices used in the construction.

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We consider performance of a simple quantum convolutional code in a fault-tolerant regime using several syndrome measurement/decoding strategies and three different error models, including the circuit model.

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