  A critical step in quantum compilation is the transformation of a
technology-independent quantum circuit into a technology-dependent form for a
targeted device. In addition to mapping quantum gates into the supported gate
set, it is necessary to map pseudo qubits in the technology-independent circuit
into physical qubits of the technology-dependent circuit such that coupling
constraints among qubits acting in multiple-qubit gates are satisfied. It is
usually not possible to find such a mapping without adding SWAP gates into the
circuit. To cope with the technical limitations of NISQ-era quantum devices, it
is advantageous to find a mapping that requires as few additional gates as
possible. The large search space of possible mappings makes this task a
difficult combinatorial optimization problem. In this work, we demonstrate how
zero-suppressed decision diagrams (ZDDs) can be used for typical implementation
tasks in quantum mapping algorithms. We show how to maximally partition a
quantum circuit into blocks of adjacent gates, and if adjacent gates within a
circuit do not share common mapping permutations, we attempt to combine them
using parallelized SWAP operations represented in a ZDD. Boundaries for the
partitions are formed where adjacent gates are unable to be combined. Within
each partition block, ZDDs represent all possible mappings of pseudo qubits to
physical qubits.
