Scott AaronsonAssociate Professor, EECS

Quantum Computers and Beyond

Moore’s Law

Extrapolating: Robot uprising?

But even a killer robot would still be “merely” a Turing machine, operating on

principles laid down in the 1930s…

=

Is there any feasible way to solve these problems, consistent with

the laws of physics?

And it’s conjectured that thousands of interesting problems are inherently

intractable for Turing machines…

Relativity Computer

DONE

Zeno’s Computer

STEP 1

STEP 2

STEP 3STEP 4

STEP 5

Tim

e (s

econ

ds)

Time Travel Computer

R CTC R CR

C

0 0 0

Answer

“Causality-Respecting Register”

“Closed Timelike

Curve Register”

Polynomial Size Circuit

S. Aaronson and J. Watrous. Closed Timelike Curves Make Quantum and Classical Computing Equivalent, Proceedings of the Royal Society A 465:631-647, 2009. arXiv:0808.2669.

What we’ve learned from quantum computers so far:

15 = 3 × 5(with high probability)

Linear-Optical Quantum Computingwww.scottaaronson.com/papers/optics.pdf

My student Alex Arkhipov and I recently proposed an experiment, which involves generating n identical photons, passing them through a network of beamsplitters, then measuring where they end up

Our proposal almost certainly wouldn’t yield a universal quantum computer—and indeed, it seems a lot easier to implement

Nevertheless, we give complexity-theoretic evidence that our experiment would solve some sampling problem that’s classically intractable

Groups in Brisbane, Australia and Imperial College London are currently working to implement our experiment

Summary1. From a theoretical standpoint, modern

computers are “all the same slop”: polynomial-time Turing machines

2. We can imagine computers that vastly exceed those (by using closed timelike curves, etc.)

3. But going even a tiny bit beyond polynomial-time Turing machines (say, with linear-optical quantum computers) is a great experimental challenge