  Nanomechanical circuits for transverse acoustic waves promise to enable new
approaches to computing, precision biochemical sensing and many other
applications. However, progress is hampered by the lack of precise control of
the coupling between nanomechanical elements. Here, we demonstrate
virtual-phonon coupling between transverse mechanical elements, exploiting
tunnelling through a zero-mode acoustic barrier. This allows the construction
of large-scale nanomechanical circuits on a silicon chip, for which we develop
a new scalable fabrication technique. As example applications, we build
mode-selective acoustic mirrors with controllable reflectivity and demonstrate
acoustic spatial mode filtering. Our work paves the way towards applications
such as fully nanomechanical computer processors and distributed nanomechanical
sensors, and to explore the rich landscape of nonlinear nanomechanical
dynamics.
