Entanglement-informed Construction of Variational Quantum Circuits

The Variational Quantum Eigensolver (VQE) is a promising tool for simulating ground states of quantum many-body systems on noisy quantum computers. Its effectiveness relies heavily on the ansatz, which must be both hardware-efficient for implementation on noisy hardware and problem-specific to avoid local minima and convergence problems. In this article, we explore entanglement-informed ansatz schemes that naturally emerge from specific models, aiming to balance accuracy with minimal use of two-qubit entangling gates, allowing for efficient use of techniques such as quantum circuit cutting. We focus on three models of quasi-1D Hamiltonians: (i) systems with impurities acting as entanglement barriers, (ii) systems with competing long-range and short-range interactions transitioning from a long-range singlet to a quantum critical state, and (iii) random quantum critical systems. For the first model, we observe a plateau in the ansatz accuracy, controlled by the number of entangling gates between subsystems. This behavior is explained by iterative capture of eigenvalues in the entanglement spectrum. In the second model, combining long-range and short-range entanglement schemes yields the best overall accuracy, leading to global convergence in the entanglement spectrum. For the third model, we use an renormalization group approach to build the short- and long-range entanglement structure of the ansatz. Our comprehensive analysis provides a new perspective on the design of ans\"atze based on the expected entanglement structure of the approximated state.