From Founders at Work: Stories of Startups' Early Days by Jessica Livingston, we find a gem of quantum computer's capabilities in an interview with Max Levchin, cofounder of Paypal:
...Its one of those things where, in the end, fraud is so nondeterministic that you need a human or a quantum computer to look at it and sort of make a final decision...Fight determinism with determinism, but fight nondeterminism with nondeterminism! I like it! But can you fight determinism with nondeterminism? Why am I now singing "I shot the nondeterminism, and the nondeterminism won?"
(I'm pretty sure Max is waxing poetic here, cus from all I've read about him he's a pretty sharp cookie.)

Dave Bacon is a theoretical ski bum who is also an assistant research
Comments
Dave, your post does illustrate that computational complexity issues are at the heart of modern economic theory ... and moral philosophy too.
Because does the notion of "free market" made sense---practically or morally---in a world in which Nash equilibria (for example) are expensive to compute?
The answer pretty obviously is "no" ... and this mathematical truth upsets some pretty-well established economic and philosophical ideologies.
Posted by: John Sidles | July 23, 2008 2:54 PM
Why am I now singing "I shot the nondeterminism, and the nondeterminism won?"
Because your brain is in a superposition of Eric Clapton and the Clash? (Or maybe Bob Marley and Bobby Fuller?)
Posted by: Sean Carroll | July 23, 2008 4:02 PM
Ha, I'd totally forgotten how many times that song had been covered.
Posted by: Dave Bacon | July 23, 2008 4:06 PM
Which song? You combined two: I Shot the Sheriff and I Fought the Law
Posted by: JohnQPublic | July 23, 2008 4:49 PM
Doh, how did "shot" get in there?
Posted by: Dave Bacon | July 23, 2008 4:59 PM
I should just quit while I'm behind.
Posted by: Dave Bacon | July 23, 2008 5:01 PM
Dave, do you believe in the Hawking $-matrix? Do you think that the Hawking radiation true?
Posted by: JohnQPublic | July 23, 2008 5:50 PM
Do I believe Max Levchin or not? Let mt flip a quantum coin.
Let A = "I shot the sheriff" and
B= "I shot the deputy."
Then 1-A = "I did not shoot the sheriff"
and 1-B = "but I did not shoot the deputy".
Assume mxing angle theta. Now, for the mixed state, we prepare the singer at "I shot the singer but I did not shoot the deputy" and use inclusion-exclusion as follows...
By the way, does Alice shoot Bob, thinking that he'd been seduced by Carla?
Posted by: Jonathan Vos Post | July 25, 2008 11:08 AM