Joint AMO and Condensed Matter Theory Seminar - Eric Akkermans - Technion-Israel Institute of Technology

Entanglement is topological: from graphene defects to quantum gates

Topological protection is usually discussed for extended systems. I will argue that the tenfold classification of condensed matter applies equally to finite-dimensional Hilbert spaces, where it classifies the generators of entanglement. A vacancy in graphene binds a zero mode fixed by an index theorem; for two qubits, time-reversal-symmetric Hamiltonians split into five disconnected topological phases, with Bell states as zero-dimensional analogs of edge states at the phase boundaries. A topological sum rule equates the winding number of any gate to the sum of Berry phases over a complete basis, a tomography-free signature of entangling capability, illustrated by two implementations of SWAP with distinguishable geometric phases. I will close with indistinguishable fermions, where particle–hole symmetry takes over the role of time reversal.

Biography: I did my PhD in Grenoble at the CNRS (Centre de Recherches sur les Tres Basses Temperatures). Then, I moved to the Laue-Langevin institute (Grenoble) to work as a postdoc in the theory group led by Prof. Philippe Nozieres. In 1987, I received a tenured position at the CNRS (Centre de Recherches sur les Tres Basses Temperatures) in Grenoble. In 1991, I joined the physics department at the Technion (Israel Institute of Technology), where I am presently a professor of physics.

Hosts: Nir Navon and Meng Cheng