  While mapping a quantum circuit to the physical layer one has to consider the
numerous constraints imposed by the underlying hardware architecture.
Connectivity of the physical qubits is one such constraint that restricts
two-qubit operations, such as CNOT, to "connected" qubits. SWAP gates can be
used to place the logical qubits on admissible physical qubits, but they entail
a significant increase in CNOT-count. In this paper we consider the problem of
reducing the CNOT-count in Clifford+T circuits on connectivity constrained
architectures, like noisy intermediate-scale quantum (NISQ) computing devices.
We "slice" the circuit at the position of Hadamard gates and "build" the
intermediate {CNOT,T} sub-circuits using Steiner trees, significantly improving
on previous methods. We compared the performance of our algorithms while
mapping different benchmark and random circuits to some well-known
architectures such as 9-qubit square grid, 16-qubit square grid, Rigetti
16-qubit Aspen, 16-qubit IBM QX5 and 20-qubit IBM Tokyo. Our methods give less
CNOT-count compared to Qiskit and TKET transpiler as well as using SWAP gates.
Assuming most of the errors in a NISQ circuit implementation are due to CNOT
errors, then our method would allow circuits with few times more CNOT gates be
reliably implemented than the previous methods would permit.
