Emmanuel Flurin, Berkeley

Jeudi 7 Janvier 2016 14h
Amphi Holweck, Esc C,
1ème etage

Observing Topological Invariants Using Quantum Walks

Classical random walks characterize stochastic phenomena ranging from physics to
economics, and are at the heart of computational tools for medical imaging, social
networking, and beyond. In the quantum analogue, the walker possesses an
additional “spin” degree of freedom and can exist in a coherent superposition of
lattice sites. The resulting spin-dependent interference mirrors evolution under
effective Hamiltonians which, depending on symmetry, can exhibit topological
invariants robust to local perturbations. These invariants are hallmarks of exotic
phenomena including unconventional edge states in topological insulators and
quantized charge transport in the Thouless pump. We present the first measurement
of a topological invariant—the winding number—in a quantum walk where a coherent
state (walker) diffuses through the phase space of a microwave cavity (lattice)
conditioned on the state of a superconducting qubit (spin), thereby realizing a
digital quantum simulation of the canonical Su-Schrieffer-Heeger (SSH) model of
one-dimensional topological phases. Using time-dependent gate operations, we
adiabatically sample momentum space and imprint the underlying topology onto the
relative phase of a cavity Schrodinger cat state, one component of which lies
dormant while the other undergoes the walk. The SSH Hamiltonian possesses two
distinct topological classes corresponding to either zero or unit winding number,
which we simulate via two different quantum walk protocols. Our scheme can readily
be extended to a larger Hilbert space, where quantum walks can effectively
simulate all non-interacting topological phases known in one and two dimensions as
well as potentially unexplored landscapes in three dimensions.

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