  Quantum computing is a promising technology that harnesses the peculiarities
of quantum mechanics to deliver computational speedups for some problems that
are intractable to solve on a classical computer. Current generation noisy
intermediate-scale quantum (NISQ) computers are severely limited in terms of
chip size and error rates. Shallow quantum circuits with uncomplicated
topologies are essential for successful applications in the NISQ era. Based on
matrix analysis, we derive localized circuit transformations to efficiently
compress quantum circuits for simulation of certain spin Hamiltonians known as
free fermions. The depth of the compressed circuits is independent of
simulation time and grows linearly with the number of spins. The proposed
numerical circuit compression algorithm behaves backward stable and scales
cubically in the number of spins enabling circuit synthesis beyond
$\mathcal{O}(10^3)$ spins. The resulting quantum circuits have a simple
nearest-neighbor topology, which makes them ideally suited for NISQ devices.
