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Summary: Entanglement-informed construction of variational quantum circuits

Alina Joch, Götz Silvester Uhrig, Benedikt Fauseweh

Published Jan 1, 2026• 0 citations
Publisher

Abstract

The variational quantum eigensolver 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 and problem-specific. In the publication [JUF25], we explore ideas about entanglement-informed ansatz choices that naturally emerge from specific entanglement structures. We investigate three models focusing on entanglement barriers and long-range interactions. We find that including the entanglement structure in the parameterized quantum circuit reduces the resources necessary to achieve a given accuracy.

DOI
10.18420/se2026-ws_23

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Abstract The variational quantum eigensolver 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. We investigate three models of quasi-1D Hamiltonians focusing on entanglement barriers and long-range interactions. We find that including the entanglement structure in the parameterized quantum circuit reduces the resources necessary to achieve a given accuracy. A better assessment is obtained by analyzing how the ansatz captures the entanglement spectrum. Our comprehensive analysis provides a new perspective on the design of ansätze based on the expected entanglement structure of the approximated state.
Variational quantum eigensolvers (VQEs) are one of the most important and effective applications of quantum computing, especially in the current noisy intermediate-scale quantum (NISQ) era. There are two main approaches for VQEs: problem-agnostic and problem-specific. For problem-agnostic methods, they often suffer from trainability issues. For problem-specific methods, their performance usually relies upon the choice of initial reference states, which are often hard to determine. In this paper, we propose an entanglement-variational hardware-efficient ansatz (EHA), and numerically compare it with some widely used ansatzes by solving benchmark problems in quantum many-body systems and quantum chemistry. Our EHA is problem-agnostic and hardware-efficient, is especially suitable for NISQ devices, and has potential for wide applications. Our EHA can achieve a higher level of accuracy in finding ground states and their energies in most cases, even compared with problem-specific methods. The performance of the EHA is robust to the choice of initial states and to parameter initialization, and it has the ability to quickly adjust the entanglement to the required amount, which is also the fundamental reason for its superiority.
Variational quantum algorithms (VQAs) have emerged in recent years as a promise to obtain quantum advantage. These task-oriented algorithms work in a hybrid loop combining a quantum processor and classical optimization. Using a specific class of VQA named variational quantum eigensolvers (VQEs), we choose some parameterized quantum circuits to benchmark them at entanglement witnessing and entangled ground state detection for many-body systems described by Heisenberg Hamiltonian, varying the number of qubits and shots. Quantum circuits whose structure is inspired by the Hamiltonian interactions presented better results on cost function estimation than problem-agnostic circuits.
Variational quantum algorithms (VQAs) have emerged in recent years as a promise to obtain quantum advantage. These task-oriented algorithms work in a hybrid loop combining a quantum processor and classical optimization. Using a specific class of VQA named variational quantum eigensolvers, we choose some parameterized quantum circuits to benchmark them at entanglement witnessing and entangled ground state detection for many-body systems described by Heisenberg Hamiltonian, varying the number of qubits and shots. Quantum circuits whose structure is inspired by the Hamiltonian interactions presented better results on cost function estimation than problem-agnostic circuits.
Abstract Variational quantum algorithms (VQAs) have emerged in recent years as a promise to obtain quantum advantage. These task-oriented algorithms work in a hybrid loop combining a quantum processor and classical optimization. Using a specific class of VQA named variational quantum eigensolvers (VQEs), we choose some parameterized quantum circuits to benchmark them at entanglement witnessing and entangled ground state detection for many-body systems described by Heisenberg Hamiltonian, varying the number of qubits and shots. Quantum circuits whose structure is inspired by the Hamiltonian interactions presented better results on cost function estimation than problem-agnostic circuits.
Abstract Adaptive construction of ansatz circuits offers a promising route towards applicable variational quantum eigensolvers on near-term quantum hardware. Those algorithms aim to build up optimal circuits for a certain problem and ansatz circuits are adaptively constructed by selecting and adding entanglers from a predefined pool. In this work, we propose a way to construct entangler pools with reduced size by leveraging classical algorithms. Our method uses mutual information between the qubits in classically approximated ground state to rank and screen the entanglers. The density matrix renormalization group method is employed for classical precomputation in this work. We corroborate our method numerically on small molecules. Our numerical experiments show that a reduced entangler pool with a small portion of the original entangler pool can achieve same numerical accuracy. We believe that our method paves a new way for adaptive construction of ansatz circuits for variational quantum algorithms.