It is difficult to calculate the energy levels and eigenstates of a large physical system on a classical computer because of the exponentially growing size of the Hilbert space. In this work, we experimentally demonstrate a quantum algorithm which could solve this problem via simulated resonant transitions. Using a four-qubit quantum simulator in which two qubits are used as ancillas for control and measurement, we obtain the energy spectrum of a 2-qubit low-energy effective Hamiltonian of the water molecule. The simulated transitions allow the state of the quantum simulator to transform and access large regions of the Hilbert space, including states that have no overlap with the initial state. Furthermore, we make use of this algorithm to efficiently prepare specific eigenstates on the simulator according to the measured eigenenergies.

With the development of deep learning, the use of convolutional neural networks (CNN) to improve the land cover classification accuracy of hyperspectral remote sensing images (HSRSI) has become a research hotspot. In HSRSI semantics segmentation, the traditional dataset partition method may cause information leakage, which poses challenges for a fair comparison between models. The performance of the model based on “convolutional-pooling-fully connected” structure is limited by small sample sizes and high dimensions of HSRSI. Moreover, most current studies did not involve how to choose the number of principal components with the application of the principal component analysis (PCA) to reduce dimensionality. To overcome the above challenges, firstly, the non-overlapping sliding window strategy combined with the judgment mechanism is introduced, used to split the hyperspectral dataset. Then, a PSE-UNet model for HSRSI semantic segmentation is designed by combining PCA, the attention mechanism, and UNet, and the factors affecting the performance of PSE-UNet are analyzed. Finally, the cumulative variance contribution rate (CVCR) is introduced as a dimensionality reduction metric of PCA to study the Hughes phenomenon. The experimental results with the Salinas dataset show that the PSE-UNet is superior to other semantic segmentation algorithms and the results can provide a reference for HSRSI semantic segmentation.

We propose a quantum algorithm for solving the following problem: given the Hamiltonian of a physical system and one of its eigenvalues, how do we obtain the corresponding eigenstate? The algorithm is based on the resonance phenomenon. For a probe qubit coupled to a quantum system, the system exhibits resonance dynamics when the frequency of the probe qubit matches a transition frequency in the system. Therefore the system can be guided to evolve to the eigenstate with a known eigenvalue by inducing the resonance between the probe qubit and a designed transition in the system. This algorithm can also be used to obtain the energy spectrum of a physical system and can achieve even quadratic speedup over the phase estimation algorithm.

Preparing the ground state of a system is an important task in physics. We propose a quantum algorithm for preparing the ground state of a physical system that can be simulated on a quantum computer. The system is coupled to an ancillary qubit, by introducing a resonance mechanism between the ancilla qubit and the system, and combined with measurements performed on the ancilla qubit, the system can be evolved to monotonically converge to its ground state through an iterative procedure. We have simulated the application of this algorithm for the Afflect-Kennedy-Lieb-Tasaki model, whose ground state can be used as resource state in one-way quantum computation.

We propose an efficient approach for deterministically generating scalable cluster states with photons. This approach involves unitary transformations performed on atoms coupled to optical cavities. Its operation cost scales linearly with the number of qubits in the cluster state, and photon qubits are encoded such that single-qubit operations can be easily implemented by using linear optics. Robust optical one-way quantum computation can be performed since cluster states can be stored in atoms and then transferred to photons that can be easily operated and measured. Therefore, this proposal could help in performing robust large-scale optical one-way quantum computation. DOI: http://dx.doi.org/10.1103/PhysRevA.81.052332 © 2010 The American Physical Society