Abstract: Techniques for encoding quantum circuit mapping problems as SAT solver optimization problems are disclosed. Quantum circuit mapping often requires the use of SWAP gates in order to configure logical quantum computations to be executed using fixed quantum hardware device layouts. A quantum compilation service takes a logical quantum circuit, a physical qubit connectivity graph, and a requested number of SWAP gates to solve the mapping using and encodes the information into a Conjunctive Normal Form (CNF) equation using a layout-transition-based encoding scheme. The CNF equation is then provided to a SAT solver which attempts to determine an assignment for the mapping using the set number of SWAP gates requested. Multiple CNF equations corresponding to different requested numbers of SWAP gates may be solved for in parallel using multiple SAT solving instances.