Random quantum states serve as a powerful tool in various scientific fields, including quantum supremacy and black hole physics. It has been theoretically predicted that entanglement transitions may happen for different partitions of multipartite random quantum states; however, the experimental observation of these transitions is still absent. Here, we experimentally demonstrate the entanglement transitions witnessed by negativity on a fully connected superconducting processor. We apply parallel entangling operations, that significantly decrease the depth of the pseudo-random circuits, to generate pseudo-random pure states of up to 15 qubits. By quantum state tomography of the reduced density matrix of six qubits, we measure the negativity spectra. Then, by changing the sizes of the environment and subsystems, we observe the entanglement transitions that are directly identified by logarithmic entanglement negativities based on the negativity spectra. In addition, we characterize the randomness of our circuits by measuring the distance between the distribution of output bit-string probabilities and the Porter-Thomas distribution. Our results show that superconducting processors with all-to-all connectivity constitute a promising platform for generating random states and understanding the entanglement structure of multipartite quantum systems.
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Abstract -
Kim, Juyeong ; Song, Xiaohui ; Kim, Ahyoung ; Luo, Binbin ; Smith, John W. ; Ou, Zihao ; Wu, Zixuan ; Chen, Qian ( , Macromolecular Rapid Communications)
Abstract Reconfigurable hybrid nanoparticles made by decorating flexible polymer shells on rigid inorganic nanoparticle cores can provide a unique means to build stimuli‐responsive functional materials. The polymer shell reconfiguration has been expected to depend on the local core shape details, but limited systematic investigations have been undertaken. Here, two literature methods are adapted to coat either thiol‐terminated polystyrene (PS) or polystyrene‐poly(acrylic acid) (PS‐
b ‐PAA) shells onto a series of anisotropic gold nanoparticles of shapes not studied previously, including octahedron, concave cube, and bipyramid. These core shapes are complex, rendering shell contours with nanoscale details (e.g., local surface curvature, shell thickness) that are imaged and analyzed quantitatively using the authors' customized analysis codes. It is found that the hybrid nanoparticles based on the chosen core shapes, when coated with the above two polymer shells, exhibit distinct shell segregations upon a variation in solvent polarity or temperature. It is demonstrated for the PS‐b ‐PAA‐coated hybrid nanoparticles, the shell segregation is maintained even after a further decoration of the shell periphery with gold seeds; these seeds can potentially facilitate subsequent deposition of other nanostructures to enrich structural and functional diversity. These synthesis, imaging, and analysis methods for the hybrid nanoparticles of anisotropically shaped cores can potentially aid in their predictive design for materials reconfigurable from the bottom up.