32 research outputs found
Extending relax-and-round combinatorial optimization solvers with quantum correlations
We introduce a relax-and-round approach embedding the quantum approximate
optimization algorithm (QAOA) with layers. We show for many problems,
including Sherrington-Kirkpatrick spin glasses, that at , it is as
accurate as its classical counterpart, and maintains the infinite-depth optimal
performance guarantee of the QAOA. Employing a different rounding scheme, we
prove the method shares the performance of the Goemans-Williamson algorithm for
the maximum cut problem on certain graphs. We pave the way for an overarching
quantum relax-and-round framework with performance on par with some of the best
classical algorithms.Comment: 17 pages (10 figures
Synthetic dimensions in ultracold molecules: quantum strings and membranes
Synthetic dimensions alter one of the most fundamental properties in nature,
the dimension of space. They allow, for example, a real three-dimensional
system to act as effectively four-dimensional. Driven by such possibilities,
synthetic dimensions have been engineered in ongoing experiments with ultracold
matter. We show that rotational states of ultracold molecules can be used as
synthetic dimensions extending to many - potentially hundreds of - synthetic
lattice sites. Microwaves coupling rotational states drive fully controllable
synthetic inter-site tunnelings, enabling, for example, topological band
structures. Interactions leads to even richer behavior: when molecules are
frozen in a real space lattice with uniform synthetic tunnelings, dipole
interactions cause the molecules to aggregate to a narrow strip in the
synthetic direction beyond a critical interaction strength, resulting in a
quantum string or a membrane, with an emergent condensate that lives on this
string or membrane. All these phases can be detected using measurements of
rotational state populations.Comment: 5-page article + 4 figures + references; 7 pages + 4 figures in
Supplemen
Fermat's principle with complex refractive indices and local light-ray rotation
We describe local light-ray rotation in terms of complex refractive indices.
We show that Fermat's principle holds, and we derive an extended Snell's law.
The change in the angle of a light ray with respect to the normal to a
refractive-index interface is described by the modulus of the refractive-index
ratio, the rotation around the interface normal is described by the argument of
the refractive-index ratio.Comment: 3 pages, 2 figure
Entanglement Spectroscopy and probing the Li-Haldane Conjecture in Topological Quantum Matter
Topological phases are characterized by their entanglement properties, which
is manifest in a direct relation between entanglement spectra and edge states
discovered by Li and Haldane. We propose to leverage the power of synthetic
quantum systems for measuring entanglement via the Entanglement Hamiltonian to
probe this relationship experimentally. This is made possible by exploiting the
quasi-local structure of Entanglement Hamiltonians. The feasibility of this
proposal is illustrated for two paradigmatic examples realizable with current
technology, an integer quantum Hall state of non-interacting fermions on a 2D
lattice and a symmetry protected topological state of interacting fermions on a
1D chain. Our results pave the road towards an experimental identification of
topological order in strongly correlated quantum many-body systems.Comment: 11+11 pages, 7+3 figure