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Purifying Deep Boltzmann Machines for Thermal Quantum States
Yusuke Nomura1, Nobuyuki Yoshioka2,3, Franco Nori3,4,5
1RIKEN Center for Emergent Matter Science, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan.
Physical Review Letters
|August 23, 2021
Summary
We present two novel deep neural network methods to model quantum many-body systems at finite temperatures. These approaches accurately represent quantum states, enabling the study of complex systems even with frustration.
Area of Science:
- Quantum physics
- Computational physics
- Machine learning
Background:
- Accurately representing finite-temperature quantum many-body states is computationally challenging.
- Neural network wave functions offer a promising, expressive ansatz for quantum states.
Purpose of the Study:
- To develop novel deep neural network (DNN) approaches for constructing purified finite-temperature states of quantum many-body systems.
- To demonstrate the efficacy of these DNN methods for investigating strongly correlated systems.
Main Methods:
- Developed a deterministic approach using deep Boltzmann machines to represent the purified Gibbs state exactly.
- Employed stochastic sampling to optimize network parameters for approximating imaginary time evolution.
Main Results:
- Both methods successfully represent the Gibbs state using neural-network wave functions.
- Numerical simulations on transverse-field Ising and Heisenberg models confirmed the methods' power.
- Investigated finite-temperature properties of strongly correlated systems, including those with frustration.
Conclusions:
- The developed DNN approaches are effective for studying finite-temperature properties of quantum many-body systems.
- These methods offer flexibility and can exploit quantum-to-classical mapping.
- The techniques are robust even in the presence of frustration, a common challenge in condensed matter physics.
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