This talks about bits. It is my understanding that qbits are significantly different from bits. Sorry that I can't illuminate further.
"...until computers are built from something other than matter..."
We can get semantically cute and argue both sides, but in my book a quantum computer passes this definition.
Armchair scientist here, but - the differentiating criterion of a quantum computer is the existence of these chained qbits.
A problem with 2^8 possibilities has 256 solutions. Our normal computers take that O(n^2) problem and solves it by traversing all n^2 solutions.
Computer science demonstrates we can solve big-O problems in less than the brute force number of times. However, we cannot reduce Big-O-COMPLEX problems into a problem set that is small enough for a regular computer to solve.
A quantum computer would look at this problem and say, okay, I need 8 qbits. One to store each of the two possible outcomes for each of the 8 possibilities.
Having those, the solution is O(1) - it is already solved. Each qbit holds BOTH states, so a 2^8 problem requires 8 qbits. A 2^512 problem requires 512 qbits and it is solved. A standard computer could never solve it.
The writer of that quote understood that notion. He understood that a fundamentally different process must occur than the one we use today to make the next evolutionary leap in processing.
I would argue that since the 'core' of the machine relies not on a measurement that is physical, but on the underpinnings of quantum theory which rather fly in the face of matter...that the quote is quite correct.