  Low-loss cavities are important in building high-coherence superconducting
quantum computers. Generating high quality joints between parts is crucial to
the realization of a scalable quantum computer using the circuit quantum
electrodynamics (cQED) framework. In this paper, we adapt the technique of
indium bump bonding to the cQED architecture to realize high quality
superconducting microwave joints between chips. We use this technique to
fabricate compact superconducting cavities in the multilayer microwave
integrated quantum circuits (MMIQC) architecture and achieve single photon
quality factor over 300 million or single-photon lifetimes approaching 5 ms. To
quantify the performance of the resulting seam, we fabricate microwave
stripline resonators in multiple sections connected by different numbers of
bonds, resulting in a wide range of seam admittances. The measured quality
factors combined with the designed seam admittances allow us to bound the
conductance of the seam at $g_\text{seam} \ge 2\times 10^{10} /(\Omega
\text{m})$. Such a conductance should enable construction of micromachined
superconducting cavities with quality factor of at least a billion. These
results demonstrate the capability to construct very high quality microwave
structures within the MMIQC architecture.
