By testing the classical correlation violation between two systems, true random numbers can be generated and certified without applying classical statistical method. In this work, we propose a true random-number expansion protocol without entanglement, where the randomness can be guaranteed only by the two-dimensional quantum witness violation. Furthermore, we only assume that the dimensionality of the system used in the protocol has a tight bound, and the whole protocol can be regarded as a semi-device-independent black-box scenario. Compared with the device-independent random-number expansion protocol based on entanglement, our protocol is much easier to implement and test.

In this paper we derived a necessary and sufficient condition for classical correlated states and proposed a norm-based measurement Q of quantum correlation. Using the max norm of operators, we gave the expression of the quantum correlation measurement Q and investigated the dynamics of Q in Markovian and non-Markovian cases, respectively. Q decays exponentially and vanishes only asymptotically in the Markovian case and causes periodical death and rebirth in the non-Markovian case. In the pure state, the quantum correlation Q is always larger than the entanglement, which was different from other known measurements. In addition, we showed that locally broadcastable and broadcastable are equivalent and reproved the density of quantum correlated states.

One of the main challenges of quantum many‐body physics is the exponential growth in the dimensionality of the Hilbert space with system size. This growth makes solving the Schrödinger equation of the system extremely difficult. Nonetheless, many physical systems have a simplified internal structure that typically makes the parameters needed to characterize their ground states exponentially smaller. Many numerical methods then become available to capture the physics of the system. Among modern numerical techniques, neural networks, which show great power in approximating functions and extracting features of big data, are now attracting much interest. In this work, the progress in using artificial neural networks to build quantum many‐body states is reviewed. The Boltzmann machine representation is taken as a prototypical example to illustrate various aspects of the neural network states. The classical neural networks are also briefly reviewed, and it is illustrated how to use neural networks to represent quantum states and density operators. Some physical properties of the neural network states are discussed. For applications, the progress in many‐body calculations based on neural network states, the neural network state approach to tomography, and the classical simulation of quantum computing based on Boltzmann machine states are briefly reviewed.

The quantum-classical hybrid algorithm is a promising algorithm with respect to demonstrating the quantum advantage in noisy-intermediate-scale quantum (NISQ) devices. When running such algorithms, effects due to quantum noise are inevitable. In our work, we consider a well-known hybrid algorithm, the quantum approximate optimization algorithm (QAOA). We study the effects on QAOA from typical quantum noise channels, and produce several numerical results. Our research indicates that the output state fidelity, i.e., the cost function obtained from QAOA, decreases exponentially with respect to the number of gates and noise strength. Moreover, we find that when noise is not serious, the optimized parameters will not deviate from their ideal values. Our result provides evidence for the effectiveness of hybrid algorithms running on NISQ devices.