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arXiv · 2409.00529

Type-Based Verification of Connectivity Constraints in Lattice Surgery

Ryo Wakizaka·Yasunari Suzuki·Atsushi Igarashi
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Abstract

Fault-tolerant quantum computation using lattice surgery can be abstracted as operations on graphs, wherein each logical qubit corresponds to a vertex of the graph, and multi-qubit measurements are accomplished by connecting the vertices with paths between them. Operations attempting to connect vertices without a valid path will result in abnormal termination. As the permissible paths may evolve during execution, it is necessary to statically verify that the execution of a quantum program can be completed. This paper introduces a type-based method to statically verify that well-typed programs can be executed without encountering halts induced by surgery operations. Alongside, we present $\mathcal{Q}_{LS}$, a first-order quantum programming language to formalize the execution model of surgery operations. Furthermore, we provide a type checking algorithm by reducing the type checking problem to the offline dynamic connectivity problem.

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Ryo Wakizaka, Yasunari Suzuki, Atsushi Igarashi. 2024-08-31. Type-Based Verification of Connectivity Constraints in Lattice Surgery. https://doi.org/10.1007/978-981-97-8943-6_11

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