Between Dec. 16th and Dec. 20th, 2013, Scott Aaronson (MIT) delivered a 5-lecture mini-course at the Physics Institute of Universidade Federal Fluminense. This was part of an academic visit to our Quantum Optics and Quantum Information group. The visit was organized by Ernesto Galvão and Thiago de Oliveira, and Ernesto and Fernando Melo took some notes about the course, which are available below. We also list a few references which were mentioned in the course. We'd like to thank Scott for a wonderful course, and all the participants for attending.

Course title: Complexity theory and quantum optics Speaker: Scott Aaronson (MIT) Summary: This mini-course will start with the fundamentals of classical and quantum computational complexity theory. It will then progress to an exciting area where computational complexity is now interacting with quantum information science and even experimental quantum optics: namely, the quest to understand the computational power of beamsplitter networks, and to build a device capable of solving the so-called BosonSampling problem exponentially faster than a classical computer.

Topics to be addressed:

• P versus NP, the Extended Church-Turing Thesis, and Quantum Mechanics.
• Quantum Computing, Counting, Sampling, and Postselection.
• BosonSampling, the Permanent, the KLM Scheme, and the AA Approximate

Hardness Result.

• Physical Implementation Issues, Classical Verification of BosonSampling Devices,

and FermionSampling.

• Possible extra topics: equivalence of sampling and searching, BQP versus the polynomial hierarchy, linear-optical

proof that the permanent is #P-hard.

Informal notes taken by Ernesto and Fernando:

Lecture 1 Lecture 2