Short of an herbicide a good barrier will keep it out. While I do not have anything that sends its rhizomes that deep I do contend with Quack Grass (aka Couch Grass, and several other sometimes not printable names) and I have found the best means of keeping it out of my planting beds is with barriers and I use 10 inch aluminum flashing for that. Janet Macunovich ("Easy Garden Design", "Caring For Perennials") uses that plastic carpet runner when she installs gardens to keep the Quack Grass out of them.

What is "plastic carpet runner"? Does this mean the thick clear plastic that some people put down on top of the carpet in a hall or on a stair? or ...?

Yes, that is what it is.

You buy a roll of it and split it down the middle. I haven't used it yet and only recently found out about it used for rhizome control. I had been using those plastic strips that garden centers sell, and those do not work. The rhizomes just run right under it and come up the other side. Carpet runner when split will give you 9" of barrier. Hopefully that will do the trick.