Generating Compilers for Qubit Mapping and Routing

Abstract: Quantum computers promise to solve important problems faster than classical computers, potentially unlocking breakthroughs in materials science, chemistry, and beyond. Optimizing compilers are key to realizing this potential, as they minimize expensive resource usage and limit error rates. A critical compilation step is qubit mapping and routing (QMR), which finds mappings from circuit qubits to qubits on a target device and plans instruction execution while satisfying the device's connectivity constraints. The challenge is that the landscape of quantum architectures is incredibly diverse and fast-evolving. Given this diversity, hundreds of papers have addressed the QMR problem for different qubit hardware, connectivity constraints, and quantum error correction schemes. We present an approach for automatically generating qubit mapping and routing compilers for arbitrary quantum architectures. Though each QMR problem is different, we identify a common core structure-device state machine-that we use to formulate an abstract QMR problem. Our formulation naturally leads to a domain-specific language, Marol, for specifying QMR problems-for example, the well-studied NISQ mapping and routing problem requires only 12 lines of Marol. We demonstrate that QMR problems, defined in Marol, can be solved with a powerful parametric solver that can be instantiated for any Marol program. We evaluate our approach through case studies of important QMR problems from prior and recent work, covering noisy and fault-tolerant quantum architectures on all major hardware platforms. Our thorough evaluation shows that generated compilers are competitive with handwritten, specialized compilers in terms of runtime and solution quality. We envision that our approach will simplify development of future quantum compilers as new quantum architectures continue to emerge.