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Quantum Boltzmann machine extends the classical Boltzmann machine learning to the quantum regime, which makes its power to simulate the quantum states beyond the classical probability distributions. We develop the BFGS algorithm to study the corresponding optimization problem in quantum Boltzmann machine, especially focus on the target states being a family of states with parameters. As an typical example, we study the target states being the real symmetric two-qubit pure states, and we find two obvious features shown in the numerical results on the minimal quantum relative entropy: First, the minimal quantum relative entropy in the first and the third quadrants is zero; Second, the minimal quantum relative entropy is symmetric with the axes y = x and y = −x even with one qubit hidden layer. Then we theoretically prove these two features from the geometric viewpoint and the symmetry analysis. Our studies show that the traditional physical tools can be used to help us to understand some interesting results from quantum Boltzmann machine learning. * zhoudl72@iphy.ac.cn 1 arXiv:1808.04567v1 [quant-ph]

Coherent manipulation of a quantum system is one of the main themes in current physics researches. In this work, we design a circuit QED system with a tunable coupling between an artificial atom and a superconducting resonator while keeping the cavity frequency and the atomic frequency invariant. By controlling the time dependence of the external magnetic flux, we show that it is possible to tune the interaction from the extremely weak coupling regime to the ultrastrong coupling one. Using the quantum perturbation theory, we obtain the coupling strength as a function of the external magnetic flux. In order to show its reliability in the fields of quantum simulation and quantum computing, we study its sensitivity to noises.