Paper Title
Optimal any-Circuit QUBIT Mapping for ODRA 5 Quantum Computer

Abstract
Qubit mapping is a discrete optimization problem in transpilation of quantum circuits. It asks for a logical-to-physical mapping of qubits and insertion points for SWAP gates to make the quantum circuit possible to execute while minimizing the number of 2-qubit quantum gates used. Despite some attention, there are no approaches that qubit mapping that consider largest circuits that can be executed with high-enough fidelity for a given quantum computer. In this paper we consider an optimal qubit mapping for any reasonable quantum circuit for Odra 5, a 5 qubit quantum computer installed at Wrocław University of Science and Technology. We proposed two exact algorithms: an Integer Linear Programming formulation and a Branch-and-Bound method (with four variants), while using an existing SABRE heuristic for reference. We performed computer experiments using both random and benchmark problem instances and measured the obtained gate counts, method running times and how often no solution was found. Results indicate that random and benchmark instances behave differently and different algorithms are viable for different ranges of instance sizes.In particular, the proposed algorithms managed to obtain up to 10% smaller gate count that SABRE. We observe that for higher sizes (60–70 initial gates) some circuits are impossible to be transpiled under our assumptions, proving that larger circuits are unreasonable for Odra 5. We also highlight the overall effectiveness of the Integer Linear Programming method and lack of high-difficulty instance benchmark sets. Keywords - Branch and Bound, Discrete Optimization, Integer Linear Programming, Operations Research, Quantum Transpilation, Qubit Mapping, SABRE.