Beni Yoshida (Perimeter) “Fault-tolerant quantum computation meets symmetry-protected topological phases” SPECIAL LOCATION: 1 Le Conte Hall

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Abstract: The goal of fault-tolerant quantum computation is to operate a large-scale quantum computer reliably by encoding the quantum computer’s state in the blocks of quantum error-correcting code. As such, finding and classifying fault-tolerantly implementable logical gates in a quantum error-correcting code has been a long-standing important problem in quantum information science. In this talk, I will argue that a solution to this problem may come from theory of symmetry-protected topological (SPT) phases, a recent breakthrough in condensed matter physics community. Namely, I will demonstrate how to construct fault-tolerant logical gates in a d-dimensional topological quantum code by using path-integral formulation of (d-1)-dimensional bosonic SPT order. Building on this idea, I will speculate about how to build a robust quantum computing architecture via a certain class of SPT order which is stable even at nonzero temperature. Our results also have surprising bonuses, such as systematic construction of gapped domain walls/boundaries in the Dijkgraaf-Witten topological gauge theories as well as a new family of higher-form SPT phases on a lattice.