Entanglement goes large: The success of quantum computing relies on the ability to entangle large-scale systems. Various platforms are being pursued, with architectures based on superconducting qubits and trapped atoms being the most advanced. By entangling up to 20 qubits, Omran et al. and Song et al. —working with Rydberg atom qubits and superconducting qubits, respectively—demonstrate how far these platforms have reached. The demonstrated controllable generation and detection of entanglement on such quantum systems is promising for the development of large-scale quantum processors. Science , this issue p. 570 , p. 574

We use micro-Raman and photoluminescence (PL) spectroscopy at 300 K to investigate the influence of uniaxial tensile strain on the vibrational and optoelectronic properties of monolayer and bilayer MoS${}_2$ on a flexible substrate. The initially degenerate $E^{\prime }$ monolayer Raman mode is split into a doublet as a direct consequence of the strain applied to MoS${}_2$ through Van der Waals coupling at the sample-substrate interface. We observe a strong shift of the direct band gap of 48 meV/(% of strain) for the monolayer and 46 meV/% for the bilayer, whose indirect gap shifts by 86 meV/%. We find a strong decrease of the PL polarization linked to optical valley initialization for both monolayer and bilayer samples, indicating that scattering to the spin-degenerate $\Gamma$ valley plays a key role.

Generative modeling, which learns joint probability distribution from data and generates samples according to it, is an important task in machine learning and artificial intelligence. Inspired by probabilistic interpretation of quantum physics, we propose a generative model using matrix product states, which is a tensor network originally proposed for describing (particularly one-dimensional) entangled quantum states. Our model enjoys efficient learning analogous to the density matrix renormalization group method, which allows dynamically adjusting dimensions of the tensors and offers an efficient direct sampling approach for generative tasks. We apply our method to generative modeling of several standard data sets including the Bars and Stripes random binary patterns and the MNIST handwritten digits to illustrate the abilities, features, and drawbacks of our model over popular generative models such as the Hopfield model, Boltzmann machines, and generative adversarial networks. Our work sheds light on many interesting directions of future exploration in the development of quantum-inspired algorithms for unsupervised machine learning, which are promisingly possible to realize on quantum devices.

The law of statistical physics dictates that generic closed quantum many-body systems initialized in nonequilibrium will thermalize under their own dynamics. However, the emergence of many-body localization (MBL) owing to the interplay between interaction and disorder, which is in stark contrast to Anderson localization, which only addresses noninteracting particles in the presence of disorder, greatly challenges this concept, because it prevents the systems from evolving to the ergodic thermalized state. One critical evidence of MBL is the long-time logarithmic growth of entanglement entropy, and a direct observation of it is still elusive due to the experimental challenges in multiqubit single-shot measurement and quantum state tomography. Here we present an experiment fully emulating the MBL dynamics with a 10-qubit superconducting quantum processor, which represents a spin-$1/2$ $XY$ model featuring programmable disorder and long-range spin-spin interactions. We provide essential signatures of MBL, such as the imbalance due to the initial nonequilibrium, the violation of eigenstate thermalization hypothesis, and, more importantly, the direct evidence of the long-time logarithmic growth of entanglement entropy. Our results lay solid foundations for precisely simulating the intriguing physics of quantum many-body systems on the platform of large-scale multiqubit superconducting quantum processors.

Quantum walks on a superconducting circuit: Quantum walks generate large-scale quantum superposed states. This allows for classically unavailable applications, such as simulating many-body quantum systems, and also yields quantum algorithms exponentially faster than classical computation. Yan et al. demonstrate quantum walks of one and two strongly correlated microwave photons in a one-dimensional array of 12 superconducting qubits with short-range interactions. The scalability of the superconducting platform could lead to large-scale implementations and the quantum simulation of complex systems. Science , this issue p. 753