Researchers from Google Quantum AI, including Salvatore Mandrà, Nikita Astrakhantsev, Sergei Isakov, Benjamin Villalonga, Brayden Ware, Tom Westerhout, and Kostyantyn Kechedzhi, have developed a new heuristic approach to simulate the out-of-equilibrium dynamics of two-dimensional quantum systems. This research, published in the journal Physical Review Letters, focuses on the Transverse-Field Ising Model (TFIM), a well-known model in statistical mechanics and condensed matter physics.
The team’s work addresses a significant challenge in classical simulations of quantum systems: the exponential resources required to simulate highly entangled wave functions, which are characteristic of systems exhibiting thermalization or pre-thermalization. These phenomena occur when a system reaches a steady state with a fixed energy density. While previous methods could simulate such systems at high energy densities without storing the full wave function, simulating systems at intermediate energy densities has proven difficult.
The researchers propose a heuristic approach to accelerate the convergence of Matrix Product State (MPS) simulations of expectation values, applicable across a broad range of energy densities. Their method involves rescaling the MPS results at low bond dimensions with a factor that depends on the fidelity of the MPS wave function. This technique allows for more efficient estimation of desired observables, such as expectation values of local operators and correlation functions.
To demonstrate the effectiveness of their approach, the researchers simulated the dynamics of the two-dimensional TFIM on a 7×8 grid with periodic boundary conditions. They achieved this using a maximum bond dimension of χ=4096 on a single A100 GPU. The results were compared to similar TFIM simulations performed on a digital quantum processor, showcasing the potential of their method for practical applications in quantum simulation.
For the energy industry, this research could have implications for understanding and modeling complex quantum systems relevant to energy storage, conversion, and materials science. By providing a more efficient way to simulate quantum dynamics, this heuristic approach could accelerate research and development in these areas, ultimately contributing to the advancement of clean energy technologies.
This article is based on research available at arXiv.