Talks

Many quantum platforms naturally host Hamiltonians with power-law or even all-to-all connectivity, which may potentially process quantum information in a way much faster than conventional gate-based models. For such non-geometrically-local Hamiltonians, it is then important to both come up with fast protocols and understand the ultimate limit for realizing various information processing tasks. In this talk, I will first overview this quantum speed limit topic, and then dive into the particular task of quantum routing, i.e. permuting unknown quantum states on the qubits. I aim to show [1] a provably optimal Hamiltonian routing protocol on the star graph that is asymptotically faster than gate-based routing; [2] a lower bound on the time to realize the shift unitary using 1d power-law interactions which, perhaps surprisingly, can be much slower than the time for the conventional Lieb-Robinson light cone to spread across the whole system. The latter result shares interesting connections to the classification of 1d quantum cellular automata and symmetry-protected topological order.

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The state-sum invariants of 4d manifolds obtained from spherical fusion 2-categories due to Douglas-Reutter offer an exciting entrypoint to the study of 4d TQFTs. In this talk we will argue that these invariants arise from a TQFT, obtained by filling the trivial 4d TQFT with a defect foam. Such construction is known as a generalised orbifold, the Turaev-Viro-Barrett-Westbury (i.e. 3d state-sum) models are also known to arise in this way from the defects in the trivial 3d TQFT (a result by Carqueville-Runkel-Schaumann). Advantages of this point of view offer e.g. realisations of state-spaces, examples of domain walls and commuting-projector realisations of (3+1)-dimensional topological phases. Based on a joint project with Nils Carqueville and Lukas Müller.

In this presentation, I will discuss our latest efforts to classify and characterize insulators in two spatial dimensions in the presence of interactions. I will focus on two examples, both on the square lattice. The first example is of bosonic insulators with symmetry G = p4m x K, where K is an internal symmetry group taken to be U(1), SO(3) or Z_N. The second example is of fermionic insulators with G= p4 x U(1)^f. In both scenarios, we propose a set of invariants that reproduce the classification anticipated through real space constructions and topological field theory (TFT). In doing so, we relate these invariants to coefficients appearing in the response action obtained from TFT. For the fermionic case, we propose a map from the non-interacting classification to the interacting classification.

This talk is based on work done with Naren Manjunath and Maissam Barkeshli.

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