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Leveraging quantum properties to enhance complex learning tasks has been proven feasible, with excellent recent achievements in the field of unsupervised learning. However, current quantum schemes neglect adaptive adjustments for unsupervised task scenarios. This work proposes a novel quantum unsupervised similarity learning method, QUSL. Firstly, QUSL uses similarity triplets for unsupervised learning, generating positive samples by perturbing anchor images, achieving a learning process independent of classical algorithms. Subsequently, combining the feature interweaving of triplets, QUSL employs metaheuristic algorithms to systematically explore high-performance mapping processes, obtaining quantum circuit architectures more suitable for unsupervised image similarity tasks. Ultimately, QUSL realizes feature learning with lower quantum resource costs. Comprehensive numerical simulations and experiments on quantum computers demonstrate that QUSL outperforms state-of-the-art quantum methods. QUSL achieves over 50% reduction in critical quantum resource utilization. QUSL improves similarity detection correlation by up to 19.5% across multiple datasets, exhibiting robustness in NISQ environments. While using fewer quantum resources, QUSL shows potential for large-scale unsupervised tasks.

The Hidden Quantum Markov Model (HQMM) has significant potential for analyzing time-series data and studying stochastic processes in the quantum domain as an upgrading option with potential advantages over classical Markov models. In this paper, we introduced the split HQMM (SHQMM) for implementing the hidden quantum Markov process, utilizing the conditional master equation with a fine balance condition to demonstrate the interconnections among the internal states of the quantum system. The experimental results suggest that our model outperforms previous models in terms of scope of applications and robustness. Additionally, we establish a new learning algorithm to solve parameters in HQMM by relating the quantum conditional master equation to the HQMM. Finally, our study provides clear evidence that the quantum transport system can be considered a physical representation of HQMM. The SHQMM with accompanying algorithms present a novel method to analyze quantum systems and time series grounded in physical implementation.

In this paper, we propose a method to construct the decay amplitudes in the orbital ($L$) and spin ($S$) coupling scheme for particles with arbitrary spins. For the $1\to 2$ decay with only massive particles involved, the angular dependence is completely encoded in the angular momentum part, and the spins of daughter particles are coupled in the rest frame of the mother particle, which contributes only a constant factor. For the sequential decay, the total amplitude is constructed by the two $1\to2$ amplitudes evaluated in the rest frame of their own mother particles, and then they are transformed to the common frame, usually chosen as the laboratory frame, by certain Lorentz transformations. In this way, it is easy to add the amplitudes of possible different decay chains coherently. If massless particles show up in the final states, the polarizations are expressed in helicity basis and the amplitudes are modified correspondingly., Comment: 16 pages, 0 figures

As an important resource to realize quantum information, quantum correlation displays different behaviors, freezing phenomenon and non-localization, which are dissimilar to the entanglement and classical correlation, respectively. In our setup, the ordering of quantum correlation is represented for different quantization methods by considering an open quantum system scenario. The machine learning method (neural network method) is then adopted to train for the construction of a bridge between the R\`{e}nyi discord ($\alpha=2$) and the geometric discord (Bures distance) for $X$ form states. Our results clearly demonstrate that the machine learning method is useful for studying the differences and commonalities of different quantizing methods of quantum correlation.

As a universal quantum character of quantum correlation, the freezing phenomenon is researched by geometry and quantum discord methods, respectively. In this paper, the properties of R`enyi discord is studied for two independent Dimer System coupled to two correlated Fermi-spin environments under the non-Markovian condition. We further demonstrate that the freezing behaviors still exist for R`enyi discord and study the effects of different parameters on this behaviors., Comment: 6 pages, 5 figures