1. Bio
Scott Aaronson is David J. Bruton Centennial Professor of Computer Science at the University of Texas at Austin.  He received his bachelor's from Cornell University and his PhD from UC Berkeley, and did postdoctoral fellowships at the Institute for Advanced Study as well as the University of Waterloo.  Before coming to UT Austin, he spent nine years as a professor in Electrical Engineering and Computer Science at MIT.  Aaronson's research in theoretical computer science has focused mainly on the capabilities and limits of quantum computers.  His first book, Quantum Computing Since Democritus, was published in 2013 by Cambridge University Press.  He’s received the National Science Foundation’s Alan T. Waterman Award, the United States PECASE Award, the Vannevar Bush Fellowship, the Simons Investigator Award, and MIT's Junior Bose Award for Excellence in Teaching.

2. Scott Aaronson (UT Austin) Papers and slides at www.scottaaronson.com
Quantum Computing
ZOOM THRU ZOOM THRU Thanks so much for inviting me! When I typed “quantum computer” into Google Image Search, that’s the first picture that came up. That’s apparently what they look like. (I should warn you that I’m a theorist rather than an engineer.)
Scott Aaronson (UT Austin)
Papers and slides at
October 17, 2017

3. This must break down…
Moore’s Law. I’m sure you’ve all seen this before: the number of transistors per computer has doubled pretty much every two years. This is arguably the main thing that’s driven the progress of human civilization since World War II.
To go further, challenge the (polynomial-time) Church-Turing Thesis itself?

4. Relativity Computer DONE
But while we’re waiting for scalable quantum computers, we can also base computers on that other great theory of the 20th century, relativity! The idea here is simple: you start your computer working on some really hard problem, and leave it on earth. Then you get on a spaceship and accelerate to close to the speed of light. When you get back to earth, billions of years have passed on Earth and all your friends are long dead, but at least you’ve got the answer to your computational problem. I don’t know why more people don’t try it!

5. STEP 1 Zeno’s Computer STEP 2 Time (seconds) STEP 3 STEP 4
Another of my favorites is Zeno’s computer. The idea here is also simple: this is a computer that would execute the first step in one second, the next step in half a second, the next in a quarter second, and so on, so that after two seconds it’s done an infinite amount of computation. Incidentally, do any of you know why that WOULDN’T work?
The problem is that, once you get down to the Planck time of 10^{-43} seconds, you’d need so much energy to run your computer that fast that, according to our best current theories, you’d exceed what’s called the Schwarzschild radius, and your computer would collapse to a black hole. You don’t want that to happen.
STEP 3
STEP 4
STEP 5

6. Ah, but what about quantum computing? (you knew it was coming)
Quantum mechanics: “Probability theory with minus signs” (Nature seems to prefer it that way)

7. THE RULES: If a system can be in two distinguishable states, labeled |0 and |1, it can also be in a superposition, written
|0 + |1
Here  and  are complex numbers called amplitudes, which satisfy ||2+||2=1. A 2-state superposition is called a qubit.
If we observe, we see |0 with probability ||2 and |1 with probability ||2. But if the qubit is isolated, it evolves by rules different from those of classical probability.
In the 1980s, Feynman, Deutsch, and others noticed that a system of n qubits seems to take ~2n steps to simulate on a classical computer, because of the phenomenon of entanglement between the qubits. They had the amazing idea of building a quantum computer to overcome that problem

8. Quantum Simulation “What a QC does in its sleep”
The “original” application of QCs!
My personal view: still the most important one
Major applications (high-Tc superconductivity, protein folding, nanofabrication, photovoltaics…)
High confidence in possibility of a quantum speedup
Can plausibly realize even before universal QCs are available

9. What else could QCs do? Beware: A quantum computer is NOT like a massively-parallel classical computer!
Exponentially many possible answers, but you only get to observe one of them
Any hope for a speedup rides on choreographing an interference pattern that boosts the amplitude of the right answer

10. BQP (Bounded-Error Quantum Polynomial-Time): The class of problems solvable efficiently by a quantum computer, defined by Bernstein and Vazirani in 1993
Interesting
Shor 1994: Factoring integers is in BQP NP
NP-complete P
Factoring
BQP

11. Key point: Factoring is not believed to be NP-complete!
And today, we don’t believe quantum computers can solve NP-complete problems in polynomial time in general (though not surprisingly, we can’t prove it)
Bennett et al. 1997: “Quantum magic” won’t be enough
If you throw away the problem structure, and just consider an abstract “landscape” of N possible solutions, then a quantum computer can find a solution in ~N steps, using Grover’s algorithm—but that’s optimal
If there’s a fast quantum algorithm for NP-complete problems, it will have to exploit their structure somehow

12. Quantum Adiabatic Algorithm (Farhi et al. 2000)Hf
Hamiltonian with easily-prepared ground state
Ground state encodes solution to NP-complete problem
Problem: “Eigenvalue gap” can be exponentially small

13. Landscapeology
Adiabatic algorithm can find global minimum exponentially faster than simulated annealing (though maybe other classical algorithms do better)
Simulated annealing can find global minimum exponentially faster than adiabatic algorithm (!)
Simulated annealing and adiabatic algorithm both need exponential time to find global minimum

14. Quantum Machine Learning Algorithms
‘Exponential quantum speedups’ for solving linear systems, support vector machines, Google PageRank, computing Betti numbers, recommendation systems…
THE FINE PRINT:
Don’t get solution vector explicitly, but only as vector of amplitudes. Need to measure to learn anything!
Dependence on condition number
Need a way of loading huge amounts of data into quantum state
Are there fast randomized algorithms to learn the same information? Current research topic!

15. Some of My Recent Research
“QUANTUM SUPREMACY”: Getting a clear quantum speedup for some task—not necessarily a useful one
BosonSampling (with Alex Arkhipov): A proposal for a simple optical quantum computer to sample a distribution that (we think) can’t be sampled efficiently classically
Experimentally demonstrated with 6 photons by group at Bristol
Random Quantum Circuit Sampling: Martinis group at Google is building a system with 49 high-quality superconducting qubits this year. Lijie Chen and I studied the hardness of sampling its output distribution

16. “Executive Summary” Exponential quantum speedups depend on structure
Sometimes we can find such structure in problems of practical interest (quantum simulation, codebreaking, data analysis??)
We can also get smaller, “Grover-like” speedups for a much wider range of practical problems: optimization, planning, constraint satisfaction…
Single most important reason to build QCs (for me): To disprove the people who said QC is impossible!
Second most important reason: A new tool for simulating Nature