When designing quantum algorithms, we typically abstract away the full capabilities
of the underlying hardware. For near-term applications of quantum hardware, it is
not clear that this is justified. In this thesis, I develop techniques to exploit the greater
underlying control over qubit interactions available in principle in most quantum
hardware. I derive analytic circuit identities for efficiently synthesising multi-qubit
evolutions from two-qubit interactions. I apply these techniques to Hamiltonian
simulation and quantum phase estimation, two of the most important algorithms
within the field of quantum computing. I analyse these techniques under a standard
error model where errors occur per gate, and an error model with a constant error
rate per unit time. For both Hamiltonian simulation and quantum phase estimation I
explore a concrete numerical example: the 2D spin Fermi-Hubbard model.