We analyze the quantum Hopfield model in which an extensive number of patterns are embedded in the presence of a uniform transverse field. This analysis employs the replica method under the replica symmetric ansatz on the Suzuki-Trotter representation of the model, while keeping the number of Trotter slices $M$ finite. The statistical properties of the quantum Hopfield model in imaginary time are reduced to an effective $M$-spin long-range classical Ising model, which can be extensively studied using a dedicated Monte Carlo algorithm. This approach contrasts with the commonly applied static approximation, which ignores the imaginary time dependency of the order parameters, but allows $M \to \infty$ to be taken analytically. During the analysis, we introduce an exact but fundamentally weaker static relation, referred to as the quasi-static relation. We present the phase diagram of the model with respect to the transverse field strength and the number of embedded patterns, indicating a small but quantitative difference from previous results obtained using the static approximation.
Analysis of the Hopfield Model Incorporating the Effects of Unlearning
The University of Tokyo（东京大学）；Department of Physics, The University of Tokyo（东京大学物理系）；Institute for Physics of Intelligence, The University of Tokyo（东京大学智能物理学研究所）；Trans-Scale Quantum Science Institute, The University of Tokyo（东京大学跨尺度量子科学研究所）
The infinite volume limit of the Hopfield neural networks in the replica-symmetric regime
Sapienza Università di Roma（罗马第一大学）；Istituto Nazionale di Fisica Nucleare, Sezione di Roma（意大利国家核物理研究所罗马分部）；CNR Nanotec, Salento Unit（意大利国家研究委员会纳米技术研究所莱切单元）；Università del Salento（萨伦托大学）；Istituto Nazionale di Fisica Nucleare, Sezione di Lecce（意大利国家核物理研究所莱切分部）
Storage and Learning phase transitions in the Random-Features Hopfield Model
University of Rome ‘La Sapienza’（罗马第一大学）；CNR-NANOTEC, Institute of Nanotechnology（意大利国家研究委员会纳米技术研究所）；Politecnico di Torino（都灵理工大学）；Bocconi University（博科尼大学）
Do Hopfield Networks Dream of Stored Patterns? A Statistical-Mechanical Theory of Dreaming in Multidirectional Associative Memories
Sapienza Università di Roma（罗马大学）；Istituto Nazionale di Fisica Nucleare（意大利国家核物理研究所）；Istituto Nazionale d’Alta Matematica, GNFM（意大利高等数学研究所）；Università del Salento（莱切萨伦托大学）
Università del Salento（萨兰托大学）；Istituto Nazionale di Fisica Nucleare（国家核物理研究所）；Sapienza Università di Roma（罗马第一大学）；Istituto Nazionale d’Alta Matematica（国家高等数学研究所）；Bar-Ilan University（巴伊兰大学）
Quantum effects in rotationally invariant spin glass models
The University of Tokyo（东京大学）；Institute for Physics of Intelligence, The University of Tokyo（东京大学物理智能研究所）；Trans-Scale Quantum Science Institute, The University of Tokyo（东京大学跨尺度量子科学研究所）
Partial annealing and pattern decorrelation in associative neural networks
Università del Salento（萨伦托大学）；Istituto Nazionale di Fisica Nucleare, Sezione di Lecce（意大利国家核物理研究所莱切分部）；Sapienza Università di Roma（罗马第一大学）；Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1（意大利国家核物理研究所罗马一分部）；CNR-Nanotec, unità di Lecce（国家研究委员会纳米技术研究所莱切单元）；Université Paris-Saclay（巴黎萨克雷大学）
