Quantum error correction and topology
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Speaker: Michele Pacenti, Electrical and Computer Engineering, University of Arizona
Title: Quantum error correction and topology
Abstract: Quantum error correction is the study of techniques to correct errors on quantum bits (qubits), and it’s a necessary step to achieve fault-tolerant quantum computation. Calderbank, Shor and Steane (CSS) have shown that it’s possible to design quantum error correcting codes starting from a dual containing classical code and its dual. The most promising CSS codes are called quantum low-density parity-check (QLDPC) codes, which can be seen as the quantum counterpart of the classical LDPC codes. The most successful designs of such codes start from geometrical manifolds, e.g., surface codes, 2D and 3D toric codes or hyperbolic surface codes. These approaches were further generalized using abstract algebraic structures: we now know that a quantum CSS code is a 2-terms chain complex, such that the two (co)-boundary maps are sparse binary matrices. In this talk, I will introduce the fundamental concepts of classical and quantum error correction and highlight the connections with topology, focusing on some of the major open problems.