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In Layout Synthesis, the logical qubits of a quantum circuit are mapped tothe physical qubits of a given quantum hardware platform, taking into accountthe connectivity of physical qubits. This involves inserting SWAP gates beforean operation is applied on distant qubits. Optimal Layout Synthesis is crucialfor practical Quantum Computing on current error-prone hardware: Minimizing thenumber of SWAP gates directly mitigates the error rates when running quantumcircuits. In recent years, several approaches have been proposed for minimizingthe required SWAP insertions. The proposed exact approaches can only scale to asmall number of qubits. Proving that a number of swap insertions is optimal ismuch harder than producing near optimal mappings. In this paper, we provide twoencodings for Optimal Layout Synthesis as a classical planning problem. We useoptimal classical planners to synthesize the optimal layout for a standard setof benchmarks. Our results show the scalability of our approach compared toprevious leading approaches. We can optimally map circuits with 9 qubits onto a14 qubit platform, which could not be handled before by exact methods.

Optimal Layout Synthesis for Quantum Circuits as Classical Planning (full version)