Related papers: Functional completeness of planar Rydberg blockade…

We develop a bubble tree construction and prove compactness results for $W^{2,2}$ branched conformal immersions of closed Riemann surfaces, with varying conformal structures whose limit may degenerate, in a compact Riemannian manifold with…

Neighborhood regression has been a successful approach in graphical and structural equation modeling, with applications to learning undirected and directed graphical models. We extend these ideas by defining and studying an algebraic…

In this chapter, we present an overview of experiments with trapped Rydberg ions and outline the advantages and challenges of developing applications of this new platform for quantum computing, sensing and simulation. Trapped Rydberg ions…

Strongly Rydberg-blockaded two-level atoms form a Rydberg superatom, which is excited only to a collective symmetrical Dicke state. However, emerging often in the alkali-earth atoms, the spontaneous decay from the Rydberg state to an…

Many quantum hardware platforms natively support either phase or exchange operations, yet converting between these two forms of control typically incurs substantial overhead. Rydberg-blockade neutral-atom arrays are highly developed for…

We study the appearance of correlated many-body phenomena in an ensemble of atoms driven resonantly into a strongly interacting Rydberg state. The ground state of the Hamiltonian describing the driven system exhibits a second order quantum…

Within the reduced basis methods approach, an effective low-dimensional subspace of a quantum many-body Hilbert space is constructed in order to investigate, e.g., the ground-state phase diagram. The basis of this subspace is built from…

Cold Rydberg atoms, known for their long lifetimes and strong dipole-dipole interactions that lead to the Rydberg blockade phenomenon, are among the most promising platforms for quantum simulations, quantum computation and quantum networks.…

Coherent states in a projected Hilbert space have many useful properties. When there are conserved quantities, a representation of the entire Hilbert space is not necessary. The same issue arises when conditional observations are made with…

Man-made environments typically comprise planar structures that exhibit numerous geometric relationships, such as parallelism, coplanarity, and orthogonality. Making full use of these relationships can considerably improve the robustness of…

The concept of topological phases is a powerful framework to characterize ground states of quantum many-body systems that goes beyond the paradigm of symmetry breaking. While a few topological phases appear in condensed matter systems, a…

We propose a quantum sensor for electric fields based on networks of Rydberg atoms. The sensing mechanism exploits the strong dependence of the Rydberg blockade on the applied electric field near a F\"orster resonance. In this regime,…

We solve the quantum mechanical problem of a charged particle on S^2 in the background of a magnetic monopole for both bosonic and supersymmetric cases by constructing Hilbert space and realizing the fundamental operators obeying…

Elaborating on our joint work with Abramsky in quant-ph/0402130 we further unravel the linear structure of Hilbert spaces into several constituents. Some prove to be very crucial for particular features of quantum theory while others…

Non-semisimple extensions of the Ising anyon model developed in our previous work enable universal topological quantum computation via braiding alone, overcoming the Clifford-only limitation of semisimple theories. The non-semisimple theory…

A hierarchical, reversible mapping between levels of tree structured computation, applicable for structuring the Quantum Computation algorithm for NP-complete problem is presented. It is proven that confining the state of a quantum computer…

We show how a broad class of lattice spin-1/2 models with angular- and distance-dependent couplings can be realized with cold alkali atoms stored in optical or magnetic trap arrays. The effective spin-1/2 is represented by a pair of atomic…

Rydberg atom arrays are powerful platforms for studying quantum many-body systems. We consider the Rydberg-Ising Hamiltonian on periodic chains and numerically study ensembles of states generated by random global pulse sequences subject to…

Atoms excited into high-lying Rydberg states and under strong dipole-dipole interactions exhibit phenomena associated with highly correlated and complex systems. We perform first principles numerical simulations on the dynamics of such…

There is a significant ongoing effort in realizing quantum annealing with different physical platforms. The challenge is to achieve a fully programmable quantum device featuring coherent adiabatic quantum dynamics. Here we show that…