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Abstract Element isotopes are characterized by distinct atomic masses and nuclear spins, which can significantly influence material properties. Notably, however, isotopes in natural materials are homogenously distributed in space. Here, we propose a method to configure material properties by repositioning isotopes in engineered van der Waals (vdW) isotopic heterostructures. We showcase the properties of hexagonal boron nitride (hBN) isotopic heterostructures in engineering confined photon-lattice waves—hyperbolic phonon polaritons. By varying the composition, stacking order, and thicknesses of h¹⁰BN and h¹¹BN building blocks, hyperbolic phonon polaritons can be engineered into a variety of energy-momentum dispersions. These confined and tailored polaritons are promising for various nanophotonic and thermal functionalities. Due to the universality and importance of isotopes, our vdW isotope heterostructuring method can be applied to engineer the properties of a broad range of materials. 

Abstract Surface acoustic waves are commonly used in classical electronics applications, and their use in quantum systems is beginning to be explored, as evidenced by recent experiments using acoustic Fabry–Pérot resonators. Here we explore their use for quantum communication, where we demonstrate a single-phonon surface acoustic wave transmission line, which links two physically separated qubit nodes. Each node comprises a microwave phonon transducer, an externally controlled superconducting variable coupler, and a superconducting qubit. Using this system, precisely shaped individual itinerant phonons are used to coherently transfer quantum information between the two physically distinct quantum nodes, enabling the high-fidelity node-to-node transfer of quantum states as well as the generation of a two-node Bell state. We further explore the dispersive interactions between an itinerant phonon emitted from one node and interacting with the superconducting qubit in the remote node. The observed interactions between the phonon and the remote qubit promise future quantum-optics-style experiments with itinerant phonons. 

In statistics and machine learning, we are interested in the eigenvectors (or singular vectors) of certain matrices (e.g.\ covariance matrices, data matrices, etc). However, those matrices are usually perturbed by noises or statistical errors, either from random sampling or structural patterns. The Davis-Kahan $$\sin \theta$$ theorem is often used to bound the difference between the eigenvectors of a matrix $$A$$ and those of a perturbed matrix $$\widetilde{A} = A + E$$, in terms of $$\ell_2$$ norm. In this paper, we prove that when $$A$$ is a low-rank and incoherent matrix, the $$\ell_{\infty}$$ norm perturbation bound of singular vectors (or eigenvectors in the symmetric case) is smaller by a factor of $$\sqrt{d_1}$$ or $$\sqrt{d_2}$$ for left and right vectors, where $$d_1$$ and $$d_2$$ are the matrix dimensions. The power of this new perturbation result is shown in robust covariance estimation, particularly when random variables have heavy tails. There, we propose new robust covariance estimators and establish their asymptotic properties using the newly developed perturbation bound. Our theoretical results are verified through extensive numerical experiments.