Since 2002 Perimeter Institute has been recording seminars, conference talks, and public outreach events using video cameras installed in our lecture theatres. Perimeter now has 7 formal presentation spaces for its many scientific conferences, seminars, workshops and educational outreach activities, all with advanced audio-visual technical capabilities. Recordings of events in these areas are all available On-Demand from this Video Library and on Perimeter Institute Recorded Seminar Archive (PIRSA). PIRSA is a permanent, free, searchable, and citable archive of recorded seminars from relevant bodies in physics. This resource has been partially modelled after Cornell University's arXiv.org.
The threshold theorem for fault tolerance tells us that it is possible to build arbitrarily large reliable quantum computers provided the error rate per physical gate or time step is below some threshold value. Most research on the threshold theorem so far has gone into optimizing the tolerable error rate under various assumptions, with other considerations being secondary. However, for the foreseeable future, the number of qubits may be an even greater restriction than error rates.
We introduce space-time quantum code construction which is based on repeating the layers of an arbitrary quantum error correcting code. The error threshold of such space-time construction is shown to be related to the fault tolerant error threshold of the original quantum error correcting code in the presence of errors in syndrome measurements. The decoding transition for space-time codes can be further mapped to random-bond Wegner spin models.
In maximum likelihood (ML) decoding, we are trying to find the most likely error given the measured syndrome. While this is hardly ever practical, such a decoder is expected to have the highest threshold.
I will review the theory of spin glasses with an emphasis on gauge symmetry. A number of exact results will be shown to be derived, some of which are useful to discuss the properties of quantum LDPC codes. Also will be explained is the combination of gauge symmetry, replica method, and duality argument to predict the precise location of a multicritical point, which is equivalent to the error-tolerance limit of toric code.
In this talk, I will cover some basic notions of quantum LDPC codes, focusing on the similarities and distinctions with their classical cousins. Topics will include definitions of stabilizer quantum LDPC codes (CSS and general), iterative decoding algorithms, dual spin models, and obstructions caused by error degeneracy. The talk will be informal and a good occasion to ask questions.
The singularity theorems of general relativity tell us that spacetime singularities form in gravitational collapse, but tell us very little about the precise nature of these singularities. More information can be found using analytic approximations and numerical simulations. It is conjectured that inside black holes are two types of singularities: one that is spacelike, local, and oscillatory, and the other that is null and weak.
One of the most basic but intriguing properties of quantum systems is their ability to `tunnel' between configurations which are classically disconnected. That is, processes which are classically impossible, are quantum allowed. In this talk I will outline a new, first-principles approach combining the semiclassical approximation with the concepts of post-selection and weak measurement.