Topological Order and Quantum Computation
Joel Moore, University of California, Berkeley
Many areas of modern science are concerned with the emergence of complex behavior from relatively simple interactions between many simple constituents. The physics of electrons in solids, which underlies the transistor and the information age, includes several dramatic examples of this emergence. Electrons are point-like particles that interact through long-understood forces, but new examples of collective electron behavior continue to be discovered, even as superconductivity, one dramatic example of emergence, marks its 100th anniversary this year.
The introduction to the session will review some examples of emergent physics in electronic materials and discuss the relevance of solid-state physics to current societal challenges. Two examples of the latter are efforts to improve the efficiency of solar energy conversion and the speed of microprocessors. The talks in this session discuss recent discoveries of physics at the intersection of quantum mechanics and topology, the branch of mathematics dealing with properties that are invariant under continuous deformations. Quantum mechanics and topology can combine to allow the emergence of macroscopic perfection despite microscopic imperfections.
Chetan Nayak will speak about using topological phases of electrons to create a quantum computer. A quantum computer will allow some important algorithms to run enormously faster than current classical computers. Topological phases offer a route to novel quantum computer architectures that are essentially immune to errors induced by local defects or noise. Krishnendu Sengupta will speak about the discovery in 2008 that some materials have protected metallic conduction at any surface despite being bulk insulators. These topological surface states, in addition to having many possible applications that are currently being investigated, show that our basic knowledge of electrons in solids is far from complete.
Non-technical review: G. P. Collins, “Computing with Quantum Knots”, Scientific American, 2006 (attached).