  Engineering nano-mechanical quantum systems possessing ultra-long motional
coherence times allow for applications in ultra-sensitive quantum sensing,
motional quantum memories and motional interfaces between other carriers of
quantum information such as photons, quantum dots and superconducting systems.
To achieve ultra-high motional Q one must work hard to remove all forms of
motional noise and heating. We examine a magneto-nanomechanical quantum system
that consists of a 3D arrangement of miniature superconducting loops which is
stably levitated in a static inhomogenous magnetic field. The resulting
motional Q is limited by the tiny decay of the supercurrent in the loops and
may reach up to Q~10^(10). We examine the classical and quantum dynamics of the
levitating superconducting system and prove that it is stably trapped and can
achieve motional oscillation frequencies of several tens of MHz. By inductively
coupling this levitating object to a nearby flux qubit we further show that by
driving the qubit one can cool the motion of the levitated object and in the
case of resonance, this can cool the vertical motion of the object close to
it's ground state.
