  We simulate and experimentally demonstrate the existence of an orientation of
quartz which minimizes diffraction losses in surface acoustic wave (SAW)
resonators at ultra-low temperatures. The orientation is optimized for
applications to quantum technologies which benefit from high mechanical quality
factors, strong electromechanical coupling, and narrow acoustic apertures. We
fabricate narrow aperture SAW resonators on this substrate and measure internal
quality factors greater than 100,000 at mK temperatures.
