Positive-definite parametrization of mixed quantum states with deep neural networks
This work addresses the challenge of efficiently representing mixed quantum states for quantum systems with environmental interactions, offering a novel method that could impact quantum simulation and variational optimization in physics and quantum computing.
The authors tackled the problem of representing mixed quantum states in quantum systems interacting with an environment by introducing the Gram-Hadamard Density Operator (GHDO), a deep neural-network architecture that encodes positive semi-definite density operators with polynomial resources and allows direct sampling. They demonstrated significant improvements in simulating the steady state of the dissipative transverse-field Ising model, outperforming previous state-of-the-art variational approaches in estimating local observables and Rényi entropy.
We introduce the Gram-Hadamard Density Operator (GHDO), a new deep neural-network architecture that can encode positive semi-definite density operators of exponential rank with polynomial resources. We then show how to embed an autoregressive structure in the GHDO to allow direct sampling of the probability distribution. These properties are especially important when representing and variationally optimizing the mixed quantum state of a system interacting with an environment. Finally, we benchmark this architecture by simulating the steady state of the dissipative transverse-field Ising model. Estimating local observables and the Rényi entropy, we show significant improvements over previous state-of-the-art variational approaches.