Type-Based Verification of Connectivity Constraints in Lattice Surgery

TL;DR

This paper introduces a type-based static verification method for lattice surgery in fault-tolerant quantum computing, ensuring programs execute without invalid connectivity operations, formalized through a new quantum programming language.

Contribution

It presents the first type-based verification approach for lattice surgery connectivity constraints and a new quantum language, $ ext{Q}_{LS}$, for modeling these operations.

Findings

Type checking reduces to offline dynamic connectivity problem.

Method guarantees safe execution of quantum programs involving lattice surgery.

Formalization with $ ext{Q}_{LS}$ language supports verification process.

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.