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 choice, which must be both hardware-efficient for implementation on noisy hardware

and problem-specific to avoid local minima and convergence problems. Here, 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 like

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

inform the short and long-range entanglement structure of the ansatz. Our comprehensive analysis

provides a new perspective on the design of ansatz schemes based on the expected entanglement

structure of the approximated state.