Perimeter Institute Quantum Discussions

In this talk I'll discuss recent joint work with Raymond Laflamme, David Poulin and Maia Lesosky in which a unified approach to quantum error correction is presented, called "operator quantum error correction". This scheme relies on a generalized notion of noiseless subsystems and includes the known techniques for the error correction of quantum operations --i.e., the standard model, the method of decoherence-free subspaces, and the noiseless subsystem method--as special cases. Correctable codes in this approach take the form of operator algebras and operator semigroups. The condition from the standard model is shown to be necessary for all of the known methods of error correction, and we'll see this as part of a discussion on conditions that characterize correctability for the general case.

One of the central critical results in the theory of fault-tolerant quantum computation is that arbitrarily long reliable computation is possible provided the error rate per gate and per time step is below some threshold value. This was proved by a number of groups, but the detailed published proofs are complex and furthermore only hold for concatenation of quantum error-correcting codes able to correct 2 errors per block, while typically the best estimates of the threshold value are based on the 7-qubit code, which only corrects 1 error per block. I will describe recent work by Panos Aliferis, John Preskill, and myself which substantially simplifies existing proofs and applies as well to the concatenated 7-qubit code. The new proof also provides a nice framework in which to attempt to prove relatively high values of the threshold, which so far have only emerged as estimates from simulations

Understanding how galaxies form is a major current goal in physical cosmology: although a basic picture is well-accepted, there are outstanding mysteries to be solved. First, what is the origin of the heavy elements seen outside of galaxies? Given that these elements are created only inside galaxies, there must be a process whereby galaxies can expel gas rather than accrete it. Second, galaxy properties are somewhat different from theory predicts, yet extremely regular -- to the extent that it has been seriously argued that modified gravity, rather than dark matter, explains them. I will discuss these mysteries and the possibility that the same culprit -- galactic winds -- may play a key role in solving both.