Talks

The LHC bear great potential in seeking for hidden sector particles, such as a high-quality QCD axion, glueballs, and heavy neutrinos. 

In this talk, I will present my recent studies on how to probe these hidden sector particles through the novel but challenging long-lived particle searches.

The color code is a topological quantum code with many valuable fault-tolerant logical gates. Its two-dimensional version may soon be realized with currently available superconducting hardware despite constrained qubit connectivity. In the talk, I will focus on how to perform error correction with the color code in d ≥ 2 dimensions. I will describe an efficient color code decoder, the Restriction Decoder, which uses as a subroutine any toric code decoder. I will also present numerical estimates of the storage threshold of the Restriction Decoder for the triangular color code against circuit-level depolarizing noise. Based on arXiv:1905.07393 and arXiv:1911.00355.

In the AdS/CFT correspondence, global symmetries of the CFT are realized as local symmetries of AdS; this feature underlies the error-correcting property of AdS. I will explain how this allows AdS3 to realize multiple redundant computations of any CFT2 correlation function in the form of networks of Wilson lines. The main motivation is to rigorously define the CFT at a cutoff and study it as a model of computational complexity; in that regard we will find agreement with the holographic "Complexity = Volume" proposal. But the framework might be useful more generally.

In a continuum field theory the Hilbert space does not factorize into local tensor products. How then can we define entanglement and the basic protocols of quantum information theory? In this talk we will show how the factorization problem can be solved in a class of 2D conformal field theories by directly appealing to the fusion rules. The solution suggests a tensor network description of a CFT path integral using the OPE data.

I will report on an ongoing project to work out and exploit an analogue of Schur-Weyl duality for the Clifford group. Schur-Weyl establishes a one-one correspondence between irreps of the unitary group and those of the symmetric group. A similar program can be carried out for Cliffords. The permutations are then replaced by certain discrete orthogonal maps. As is the case for Schur-Weyl, this duality has many applications for problems in quantum information. It can be used, e.g., to derive quantum property tests for stabilizerness and Cliffordness, a new direct interpretation of the sum-negativity of Wigner functions, bounds on stabilizer rank, the construction of designs using few non-Clifford resources, etc. [arXiv:1609.08172, arXiv:1712.08628, arXiv:1906.07230, arXiv:out.soon].