Distributing Arbitrary Quantum Graph States by Graph Transformation

Quantum graph state is a special class of nonlocal state among multiple quantum particles, underpinning several nonclassical and promising applications such as quantum computing and quantum secret sharing. Recently, establishing quantum graph states among physically distant nodes has gained increasing popularity owing to its potential in expanding current quantum applications in scale. Existing research on this topic relies on a two-step approach: first distributing low-dimension elementary entanglement to target nodes, and then fusing them into a high-dimension quantum graph state. However, most existing studies focus solely on minimizing costs (e.g., the number of elementary entanglements consumed) to entangle target nodes, while neglecting the structure of the final quantum graph state. This can easily result in weak system entanglement, jeopardizing the graph state under partial measurement or noises. In this paper, we aim to establish any arbitrary quantum graph states of strong entanglement structures at a much lower cost than the state of the art. The method is to search for and establish an alternative state to the target state that is of lowest cost in creation. Subsequently, we transform such an alternative state back to the target state via compressed single-qubit Clifford operations. To verify the performance of our developed algorithm, we conduct comprehensive simulations based on an open dataset containing all graph state structures up to 8 qubits. The results demonstrate fast algorithm convergence, an increased success probability in distributing any graph states, and $53.57\%$ saving in ERP cost compared with the state-of-the-art baseline.