Abstract: A principal challenge in realizing the potential of quantum computing lies in our ability to perform computations fault-tolerantly, in the presence of the noise inherent to quantum devices. Non-Clifford quantum gates, which are analogous to the classical multiplication (i.e. AND) gate, are particularly difficult to implement fault-tolerantly. We show how to perform such gates with significantly lower asymptotic overhead than was achievable with prior techniques.
For this purpose, we present new constructions of quantum error-correcting codes supporting transversal non-Clifford gates, meaning that the desired logical gates can be executed by applying a constant-depth physical circuit to the code state. In particular, we present the first asymptotically good such codes, as well as the first such codes with low-weight stabilizers that have almost linear dimension and polynomial distance. Our constructions are based on a combination of algebraic and topological techniques.
No prior knowledge of quantum computing will be assumed.
Based on joint works with Venkatesan Guruswami and Ting-Chun Lin