Friday, 13 July 2012, 4:00 pm
Room G.07, School of Informatics
10 Crichton Street, Edinburgh EH8 9AB
and afterwards for a drinks and canapé reception
Quantum Computing and the Limits of the Efficiently Computable
I’ll discuss what can and can’t be feasibly computed according to physical law. I’ll argue that this is a fundamental question, not only for mathematics and computer science, but also for physics; and that the infeasibility of certain computational problems (such as NP-complete problems) could plausibly be taken as a physical principle, analogous to the Second Law or the impossibility of superluminal signalling. I’ll first explain the basics of computational complexity, including the infamous P versus NP problem and the Extended Church-Turing Thesis. Then I’ll discuss quantum computers: what they are, whether they can be scalably built, and what’s known today about their capabilities and limitations.
Lastly, I’ll touch on speculative models of computation that would go even beyond quantum computers, using (for example) closed timelike curves or nonlinearities in the Schrodinger equation. I’ll emphasize that, even if “intractable” computations occur in a particular description of a physical system, what really matters is whether those computations have observable consequences.
Venue: School of Informatics, University of Edinburgh, Room 4.33/4.31
Times: 15:00 till 16:30
New Computational Insights from Quantum Optics
In work with Aleksandr Arkhipov, we proposed a rudimentary form of quantum computing, based on linear optics with nonadaptive measurements; and used a connection between linear optics and the permanent function to show that even this limited model could solve sampling and search problems that are intractable for classical computers under plausible complexity assumptions. In this talk, I’ll discuss this work in a self-contained way, and mention some of its implications for quantum computing experiments. I’ll also discuss some more general results that emerged from our work. These include a new equivalence between sampling problems and search problems based on Kolmogorov complexity; a new, linear-optics-based proof of Valiant’s famous theorem that the permanent is #P-complete; and a new classical approximation algorithm for the permanent.
The Computational Complexity of Linear Optics
The Equivalence of Sampling and Searching
A Linear-Optical Proof that the Permanent is #P-Hard
How Much Information Is In A Quantum State?
People often talk about the quantum state of n entangled particles as if it contained an amount of information exponential in n. In this talk, I’ll discuss three results that suggest that, in various senses relevant for computation, prediction, and learning, quantum states
actually *don’t* behave as if they contained exponential amounts of information. Specifically, I’ll discuss the limitations of “quantum advice states,”the approximate “learnability” of quantum states from random measurement results, and the simulation of arbitrary quantum state preparation tasks by the preparation of ground states of local Hamiltonians (joint work with Andrew Drucker).
Limitations of Quantum Advice and One-Way Communication
The Learnability of Quantum States
A Full Characterization of Quantum Advice
Talk #3 will be determined based on audience interest.
We’re delighted to announce that Prof. Aaronson will be visiting us from July 9 till July 13 and will present a series of lectures on quantum complexity theory covering topics on complexity of linear optics and information content of quantum states.
The venue is the School of Informatics, University of Edinburgh, Room 4.33/4.31 on Tuesday, Wednesday and Thursday July 10, 11 and 12 from 15:00 till 16:30.
We hope you can all attend this unique rejuvenating QUISCO meetings.
Scott Aaronson is an Associate Professor of Electrical Engineering and Computer Science at MIT. He received his PhD in computer science from University of California, Berkeley and did postdocs at the Institute for Advanced Study and the University of Waterloo. Scott’s research interests center around fundamental limits on what can efficiently be computed in the physical world. This has entailed studying quantum computing, the most powerful model of computation we have based on known physical theory. He also writes a popular blog, and is the creator of the Complexity Zoo, an online encyclopedia of computational complexity theory. He is the recipient of NSF’s Alan T. Waterman Award for 2012.