  Fixed-frequency superconducting quantum processors are one of the most mature
quantum computing architectures with high-coherence qubits and simple controls.
However, high-fidelity multi-qubit gates pose tight requirements on individual
qubit frequencies in these processors , and these constraints are difficult to
satisfy when constructing larger processors due to the large dispersion in the
fabrication of Josephson junctions. In this article, we propose a
mixed-integer-programming-based optimization approach that determines qubit
frequencies to maximize the fabrication yield of quantum processors. We study
traditional qubit and qutrit (three-level) architectures with cross-resonance
interaction processors. We compare these architectures to a differential
AC-Stark shift based on entanglement gates and show that our approach greatly
improves the fabrication yield and also increases the scalability of these
devices. Our approach is general and can be adapted to problems where one must
avoid specific frequency collisions.
