The availability of the first prototypes of quantum computers, in 2016, with free access through the cloud, brought much enthusiasm to the research community. Yet, programming said computers is difficult. One core challenge is the so called qubit allocation problem. This problem consists in mapping the virtual qubits that make up a logical quantum program onto the physical qubits that exist in the target quantum architecture. To deal with this challenge, we have proposed one of the first algorithms to solve qubit allocation. This algorithm, together with its ensuing formulations, is today available in the Enfield compilera concrete product of this work. Our first paper in this field, titled Qubit Allocation, has inspired much research, and our latest qubit allocation design, called Bounded Mapping Tree, stands out today as one of the most effective qubit allocators in the world.

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In 2016, the first quantum processors have been made available to the general public. The possibility of programming an actual quantum device has elicited much enthusiasm. Yet, such possibility also brought challenges. One challenge is the so called Qubit Allocation problem: the mapping of a virtual quantum circuit into an actual quantum architecture. There exist solutions to this problem; however, in our opinion, they fail to capitalize on decades of improvements on graph theory. In contrast, this paper shows how to model qubit allocation as the combination of Subgraph Isomorphism and Token Swapping. This idea has been made possible by the publication of an approximative solution to the latter problem in 2016. We have compared our algorithm against five other qubit allocators, all independently designed in the last two years, including the winner of the IBM Challenge. When evaluated in łTokyo", a quantum architecture with 20 qubits, our technique outperforms these state-of-the-art approaches in terms of the quality of the solutions that it finds and the amount of memory that it uses, while showing practical runtime. CCS Concepts: • Computer systems organization → Quantum computing; • Software and its engineering → Compilers; • Theory of computation → Parameterized complexity and exact algorithms.