International Workshop on Quantum LDPC Codes
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.