  Vigorous optimization of quantum gates has led to bipotent quantum
architectures, where the optimized gates are available for some qubits but not
for others. However, such gate-level improvements limit the application of
user-side pulse-level optimizations, which have proven effective for quantum
circuits with a high level of regularity, such as the ansatz circuit of the
Quantum Approximate Optimization Algorithm (QAOA). In this paper, we
investigate the trade-off between hardware-level and algorithm-level
improvements on bipotent quantum architectures. Our results for various QAOA
instances on two quantum computers offered by IBM indicate that the benefits of
pulse-level optimizations currently outweigh the improvements due to vigorously
optimized monolithic gates. Furthermore, our data indicate that the fidelity of
circuit primitives is not always the best indicator for the overall algorithm
performance; also their gate type and schedule duration should be taken into
account. This effect is particularly pronounced for QAOA on dense portfolio
optimization problems, since their transpilation requires many SWAP gates, for
which efficient pulse-level optimization exists. Our findings provide practical
guidance on optimal qubit selection on bipotent quantum architectures and
suggest the need for improvements of those architectures, ultimately making
pulse-level optimization available for all gate types.
