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<p>In this paper, we study an important class of generative models, variational autoencoder (VAE) and conditional variational autoencoder (CVAE), to learn the abstract probability distribution of the training set to perform the task of quantum state reconstruction in quantum many-body systems. Specifically, the transverse-field Ising model (TFIM) is studied so that it generates the ground state solution in the form of the original quantum pure state, and the original quantum mixed state needed for the generative model are obtained by adding local depolarization noise with different probabilities <i>p</i> to each qubit of the ground state so that it loses part of the information. The information-complete positive operator-valued measure (POVM) is then used to generate the original probability distribution of quantum pure and mixed state, and the input training set of the generative model is obtained by sampling the original probability distribution, which can convert the quantum state reconstruction problem in quantum many-body systems into a mathematical statistical problem that can be solved by VAE. On this basis, the CVAE is used to reconstruct quantum pure states and mixed states under different values of magnetic filed <i>h</i> and <i>p</i> of 4 qubits and 32 qubits. The performance of quantum state reconstruction is tested by fidelity comparison. The numerical simulation experimental results show that the fidelity of probability distributions and density matrices reconstructed by the CVAE for 4-qubit pure states tend to decrease and then increase with increasing <i>h</i>, and it can reconstruct quantum pure states with high quality for larger <i>p</i>. As <i>p</i> increases, the fidelity of probability distributions and density matrices reconstructed from 4-qubit mixed states exhibit higher quality and fewer fluctuations in the reconstruction. Finally, the CVAE can perform high-quality reconstruction of local observables reconstructed by higher 32-qubit mixed states.</p>

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Reconstructing quantum states with VAE and CVAE

  • 期刊论文

  • 发表日期：

    2025年6月2日

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  • Shuang Cong,
  • Chenyu Su

摘要

In this paper, we study an important class of generative models, variational autoencoder (VAE) and conditional variational autoencoder (CVAE), to learn the abstract probability distribution of the training set to perform the task of quantum state reconstruction in quantum many-body systems. Specifically, the transverse-field Ising model (TFIM) is studied so that it generates the ground state solution in the form of the original quantum pure state, and the original quantum mixed state needed for the generative model are obtained by adding local depolarization noise with different probabilities p to each qubit of the ground state so that it loses part of the information. The information-complete positive operator-valued measure (POVM) is then used to generate the original probability distribution of quantum pure and mixed state, and the input training set of the generative model is obtained by sampling the original probability distribution, which can convert the quantum state reconstruction problem in quantum many-body systems into a mathematical statistical problem that can be solved by VAE. On this basis, the CVAE is used to reconstruct quantum pure states and mixed states under different values of magnetic filed h and p of 4 qubits and 32 qubits. The performance of quantum state reconstruction is tested by fidelity comparison. The numerical simulation experimental results show that the fidelity of probability distributions and density matrices reconstructed by the CVAE for 4-qubit pure states tend to decrease and then increase with increasing h, and it can reconstruct quantum pure states with high quality for larger p. As p increases, the fidelity of probability distributions and density matrices reconstructed from 4-qubit mixed states exhibit higher quality and fewer fluctuations in the reconstruction. Finally, the CVAE can perform high-quality reconstruction of local observables reconstructed by higher 32-qubit mixed states.