A stacked device including a first substrate that includes a quantum information processing device, a second substrate bonded to the first substrate, and multiple bump bonds and at least one pillar between the first substrate and the second substrate. Each bump bond of the multiple bump bonds provides an electrical connection between the first substrate and the second substrate. At least one pillar defines a separation distance between a first surface of the first substrate and a first surface of the second substrate. A cross-sectional area of each pillar is greater than a cross-sectional area of each bump bond of the multiple bump bonds, where the cross-sectional area of each pillar and of each bump bond is defined along a plane parallel to the first surface of the first substrate or to the first surface of the second substrate.