  Quantum algorithms promise quadratic or exponential speedups for applications
in cryptography, chemistry and material sciences. The topologies of today's
quantum computers offer limited connectivity, leading to significant overheads
for implementing such quantum algorithms. One-dimensional topology
displacements that remedy these limits have been recently demonstrated for
architectures based on Rydberg atoms, and they are possible in principle in
photonic and ion trap architectures. We present the first optimal quantum
circuit-to-architecture mapping algorithm that exploits such one-dimensional
topology displacements. We benchmark our method on quantum circuits with up to
15 qubits and investigate the improvements compared with conventional mapping
based on inserting swap gates into the quantum circuits. Depending on
underlying technology parameters, our approach can decrease the quantum circuit
depth by up to 58% and increase the fidelity by up to 29%. We also study
runtime and fidelity requirements on one-dimensional displacements and swap
gates to derive conditions under which one-dimensional topology displacements
provide benefits.
