MPS-Enhanced Variational Quantum Gibbs State Preparation

The preparation of Gibbs states is essential in quantum statistical mechanics and quantum computing, enabling the simulation of thermal equilibrium properties of quantum systems. This work focuses on variational approaches for large-scale Gibbs state preparation, leveraging the matrix product state (MPS) approximations. We benchmark two distinct ansatzes for variational Gibbs state preparation --- one performs well at low temperatures while the other excels at high temperatures, which can be attributed to differences in entanglement generation between them. A key challenge in the variational approaches is the efficient computation of the von Neumann entropy, which is needed to determine the free energy. To address this, we employ the MPS approximation of the purified state, which allows us to scale the Gibbs state preparation to larger systems. We demonstrate the effectiveness of our methods on both classical and quantum spin chains, presenting results from simulator and IBM quantum hardware. Advanced compilation techniques are applied to reduce circuit depth in experiments on the quantum device.