Unsupervised detection of quantum phases and their order parameters from projective measurements

          @misc{ pirsa_PIRSA:23060038,
            doi = {10.48660/23060038},
            url = {https://pirsa.org/23060038},
            author = {},
            keywords = {Condensed Matter},
            language = {en},
            title = {Unsupervised detection of quantum phases and their order parameters from projective measurements},
            publisher = {Perimeter Institute},
            year = {2023},
            month = {jun},
            note = {PIRSA:23060038 see, \url{https://pirsa.org}}
          }
          

Abstract

Recently, machine learning has become a powerful tool for detecting quantum phases. While the sole information about the presence of transition is valuable, the lack of interpretability and knowledge on the detected order parameter prevents this tool from becoming a customary element of a physicist's toolbox. Here, we report designing a special convolutional neural network with adaptive kernels, which allows for fully interpretable and unsupervised detection of local order parameters out of spin configurations measured in arbitrary bases. With the proposed architecture, we detect relevant and simplest order parameters for the one-dimensional transverse-field Ising model from any combination of projective measurements in the x, y, or z basis. Moreover, we successfully tackle the bilinear-biquadratic spin-1 model with a nontrivial nematic order. We also consider extending the proposed approach to detecting topological order parameters. This work can lead to integrating machine learning methods with quantum simulators studying new exotic phases of matter.