IQIM Postdoctoral and Graduate Student Seminar

Abstract: Two-dimensional topological stabilizer codes are among the most practical code families for fault-tolerant quantum computation.
However, they suffer fundamental limitations, as there is no such code with a protected non-Clifford gate, which is needed for a universal quantum computation. To mitigate these limitations, non-native schemes such as magic-state distillation or non-scalable schemes that rely on post-selection have been developed.

In this talk, I will present a new scheme to perform reliable non-Clifford logic in 2D topological codes [1]. They are realized by fault-tolerant non-Clifford circuits augmented with a just-in-time decoding strategy. In fact, the circuits implement a non-Abelian topologically ordered state. Using a path-integral tensor-network representation of the circuits, we can identify errors as defects of the underlying topological phase and prove thresholds against arbitrary p-bounded noise. The construction allows for a large flexibility in both the physical circuits used to implement the gates as well as the specific logic gates that are implemented.
I will focus on an example presented in [2] that performs a fault-tolerant Clifford measurement on a 2D color code using a low-overhead planar circuit with the only non-Clifford component being physical T gates. They can realize a wealth of logical diagonal non-Clifford gates such as T, CS, CCZ, or measurements of logical XS or CZ gates.
This work extends the common approach to topologically protected computation with Abelian phases using Clifford circuits to non-Abelian phases using non-Clifford circuits and highlights the spacetime perspective to quantum error correction.

[1]: https://arxiv.org/pdf/2503.15751
[2]: https://arxiv.org/pdf/2505.05175

Following the talk, lunch will be provided on the lawn outside East Bridge.