Qubit circuits with deep, in-substrate components

A circuit for quantum computing, the circuit comprising:

• a silicon substrate;
• a qubit comprising:
• a Josephson junction formed on the silicon substrate;
• and
• a capacitive element comprising a first conductor deposited in a first cavity and electrically connected to the Josephson junction, wherein the first cavity extends into the silicon substrate and has an aspect ratio between 5:1 and 100:1, and wherein the aspect ratio is a ratio of a depth of the first cavity into the silicon substrate to a smallest transverse dimension of the first cavity;
• and
• a readout resonator comprising a second conductor deposited in a second cavity that extends into the silicon substrate and has an aspect ratio between 5:1 and 100:1, and wherein the second conductor capacitively couples to the first conductor when the circuit is operating and wherein the first conductor and second conductor are formed from a superconducting material.