Neural Importance Resampling Enables Scalable and Unbiased Neural Quantum State Simulations

Simulating complex quantum systems remains a significant challenge in modern physics, and neural quantum states (NQS) offer a promising approach, though current sampling methods often limit their practical application. Eimantas Ledinauskas and Egidijus Anisimovas, both from the Institute of Theoretical Physics and Astronomy at Vilnius University, alongside their colleagues, present a new sampling algorithm called Neural Importance Resampling (NIR) that overcomes many of these limitations. NIR combines the strengths of importance resampling with a separately trained autoregressive network, allowing for efficient and unbiased sampling without imposing restrictive architectural constraints on the NQS. This innovative method not only supports stable and scalable training, including for systems with multiple interacting states, but also demonstrably outperforms traditional Markov chain Monte Carlo methods and achieves results comparable to the highly accurate, yet computationally demanding, density matrix renormalization group technique, establishing NIR as a robust and versatile tool for variational NQS algorithms.

Markov chain Monte Carlo (MCMC) methods frequently suffer from slow processing and require careful manual adjustments, while autoregressive neural networks impose restrictions on the design of the networks themselves, hindering flexibility.

Neural Networks Simulate Quantum Many-Body Systems

Researchers are tackling the problem of simulating quantum systems, a notoriously difficult task for classical computers as system size increases. They explore using neural networks to represent the quantum state of a system, aiming to overcome the limitations of traditional methods. The method employs a variational approach, defining a parameterized quantum state using a neural network and then optimizing the parameters to minimize the system’s energy. The core innovation lies in the use of Neural Importance Sampling (NIS) within the variational optimization process. NIS improves the efficiency of Monte Carlo integration, better sampling the configuration space of the quantum system and leading to more accurate energy estimates and faster optimization.

The authors address limitations of existing neural network quantum state methods, such as slow convergence and difficulty scaling to larger systems, by presenting NIS as a way to mitigate these problems. The method details how NIS is integrated into the neural network quantum state framework, defining a proposal distribution using the neural network and then reweighting samples to obtain a more accurate estimate of the expectation value. This advancement addresses limitations found in existing methods like Markov chain Monte Carlo (MCMC) and autoregressive neural networks, both commonly used to represent and explore the behavior of these systems. Traditional MCMC methods often struggle with slow processing and require careful manual adjustments, while autoregressive networks impose restrictions on the design of the neural networks themselves, hindering flexibility. NIR overcomes these challenges by combining importance resampling with a dedicated neural network trained to accurately predict the probability distribution of the quantum state.

This approach allows for efficient and unbiased sampling without the architectural constraints of autoregressive methods, and reduces the need for manual tuning required by MCMC. The method proves particularly effective when seeking multiple low-energy states simultaneously, a task made easier by its compatibility with complex, multi-state wave functions. In tests on a challenging two-dimensional quantum model, NIR demonstrably outperformed MCMC, achieving more reliable results in difficult scenarios. Furthermore, NIR’s performance was competitive with the highly regarded density matrix renormalization group (DMRG) method, a benchmark for accuracy in this field. This decoupling of the sampling process from the network architecture overcomes key drawbacks of existing methods, particularly in complex systems. Demonstrated on the two-dimensional transverse-field Ising model, NIR achieves stable training even in challenging regimes where MCMC methods struggle, and yields results comparable to the more established density matrix renormalization group (DMRG) methods. These findings establish NIR as a robust and scalable alternative for sampling within variational neural quantum state algorithms, especially when dealing with multi-state systems. The authors acknowledge that, like other methods, NIR’s performance is influenced by the specific parameters of the system being studied. Future work could explore the application of NIR to a wider range of physical models and investigate its potential for further optimization and scalability.