  The performance of superconducting quantum circuits is primarily limited by
dielectric loss due to interactions with two-level systems (TLS).
State-of-the-art circuits with engineered material interfaces are approaching a
limit where dielectric loss from bulk substrates plays an important role.
However, a microscopic understanding of dielectric loss in crystalline
substrates is still lacking. In this work, we show that boron acceptors in
silicon constitute a strongly coupled TLS bath for superconducting circuits. We
discuss how the electronic structure of boron acceptors leads to an effective
TLS response in silicon. We sweep the boron concentration in silicon and
demonstrate the bulk dielectric loss limit from boron acceptors. We show that
boron-induced dielectric loss can be reduced in a magnetic field due to the
spin-orbit structure of boron. This work provides the first detailed
microscopic description of a TLS bath for superconducting circuits, and
demonstrates the need for ultrahigh purity substrates for next-generation
superconducting quantum processors.
