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Title:
The interplay of quantum error correction with physics and geometry
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Abstract:
It has been roughly a century since the quantum revolution which led to the establishment of quantum mechanics as a fundamental theory of physics. Today we are in the age of quantum information science which is at the intersection of physics, computer science and mathematics. One big question in quantum information science is how to build a fault-tolerant quantum computer. Since qubits are susceptible to noise from the environment, quantum error correction is essential for building such a computer. In this colloquium, I will show how quantum error correction is a highly interdisciplinary topic having an interplay with physics and geometry. I will demonstrate the interplay of error correction with ideas of topological order, statistical mechanics and geometry using two works as examples. One is about random Clifford-rotated two-dimensional surface codes which outperform the best known-translation invariant surface codes in terms of threshold error rates and subthreshold logical error rates for biased Pauli noise. The second is about universal quantum computation with a two-dimensional code which is obtained by punching a macroscopic hole in the three dimensional surface code. Such a code provides a fault-tolerant implementation of a logical non-Clifford gate. I will summarize by mentioning problems in which error correction has a close interplay with modern developments in quantum dynamics and quantum many-body physics.
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