Exponential Scaling Barriers for Variational Quantum Eigensolvers

• URL: http://arxiv.org/abs/2603.13073v1
• Date: Fri, 13 Mar 2026 15:18:31 GMT
• Title: Exponential Scaling Barriers for Variational Quantum Eigensolvers
• Abstract summary: Variational Quantum Eigensolver (VQE) is widely regarded as a promising algorithm for calculating ground states of quantum systems.<n>We scrutinize how the computational cost of adaptive VQE scales with the size of the target system.
• Score: 2.602373867794406
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The Variational Quantum Eigensolver (VQE) is widely regarded as a promising algorithm for calculating ground states of quantum systems that are intractable for classical computers. This promise is typically motivated by the hope of mitigating the exponential growth of Hilbert space with system size. Here we scrutinize how the computational cost of adaptive VQE scales with the size of the target system. We demonstrate that the Rényi entropy derived from classical simulations predicts the required number of adaptive iterations of VQE with high accuracy ($R^2 \approx 0.99$). We validate this on a benchmarking set of more than 20 different molecules with active spaces ranging from four to ten orbitals. For these molecules, we find an exponential scaling of the number of adaptive iterations, and in turn, of the circuit depth with the system size. We therefore conclude that it is unlikely that VQE in its current form is able to simulate large molecular systems with high fidelity without exponential resource requirements.

Related papers

• Alleviating the Sparse Matrix Scaling Bottleneck in Adaptive VQE via High-Order Taylor State Evolution [0.0]
  Variational Quantum Eigensolver (VQE) is a leading algorithm for noisy intermediate-scale quantum devices.<n>Its adaptive variants (e.g., ADAPT-VQE) suffer from severe classical simulation bottlenecks during the ansatz growth phase.<n>We present a resource-efficient software-layer framework that completely bypasses dense matrix exponentiation.
  arXiv  Detail & Related papers  (2026-06-29T01:40:26Z)
• SpinGQE: A Generative Quantum Eigensolver for Spin Hamiltonians [42.007194397302825]
  Ground state search is central to quantum computing.<n>We present SpinGQE, an extension of the Generative Quantum Eigensolver framework to spin Hamiltonians.<n>We employ a transformer-based decoder to learn over quantum circuits that produce low-energy states.
  arXiv  Detail & Related papers  (2026-03-25T13:38:15Z)
• Guided sampling ansätzes for variational quantum computing [1.055551340663609]
  We introduce a class of guided sampling ansatzes that depend on the system interactions and measured state samples as well as a parameter space.<n>With only 200 circuit executions per structure on the IonQ Aria quantum computer, our calculations produced total energies around the relaxed structure with errors well below $1.59times10-3$ Ha.
  arXiv  Detail & Related papers  (2025-08-19T15:21:23Z)
• Efficient charge-preserving excited state preparation with variational quantum algorithms [33.03471460050495]
  We introduce a charge-preserving VQD (CPVQD) algorithm, designed to incorporate symmetry and the corresponding conserved charge into the VQD framework. Results show applications in high-energy physics, nuclear physics, and quantum chemistry.
  arXiv  Detail & Related papers  (2024-10-18T10:30:14Z)
• High-Entanglement Capabilities for Variational Quantum Algorithms: The Poisson Equation Case [0.07366405857677226]
  This research attempts to resolve problems by utilizing the IonQ Aria quantum computer capabilities. We propose a decomposition of the discretized equation matrix (DPEM) based on 2- or 3-qubit entanglement gates and is shown to have $O(1)$ terms with respect to system size. We also introduce the Globally-Entangling Ansatz which reduces the parameter space of the quantum ansatz while maintaining enough expressibility to find the solution.
  arXiv  Detail & Related papers  (2024-06-14T16:16:50Z)
• Nonlinear dynamics as a ground-state solution on quantum computers [39.58317527488534]
  We present variational quantum algorithms (VQAs) that encode both space and time in qubit registers. The spacetime encoding enables us to obtain the entire time evolution from a single ground-state computation.
  arXiv  Detail & Related papers  (2024-03-25T14:06:18Z)
• Classical Chaos in Quantum Computers [39.58317527488534]
  Current-day quantum processors, comprising 50-100 qubits, operate outside the range of quantum simulation on classical computers. We demonstrate that the simulation of classical limits can be a potent diagnostic tool potentially mitigating this problem. We find that classical and quantum simulations lead to similar stability metrics in systems with $mathcalO$ transmons.
  arXiv  Detail & Related papers  (2023-04-27T18:00:04Z)
• Towards Neural Variational Monte Carlo That Scales Linearly with System Size [67.09349921751341]
  Quantum many-body problems are central to demystifying some exotic quantum phenomena, e.g., high-temperature superconductors. The combination of neural networks (NN) for representing quantum states, and the Variational Monte Carlo (VMC) algorithm, has been shown to be a promising method for solving such problems. We propose a NN architecture called Vector-Quantized Neural Quantum States (VQ-NQS) that utilizes vector-quantization techniques to leverage redundancies in the local-energy calculations of the VMC algorithm.
  arXiv  Detail & Related papers  (2022-12-21T19:00:04Z)
• Improved variational quantum eigensolver via quasi-dynamical evolution [0.0]
  The variational quantum eigensolver (VQE) is a hybrid quantum-classical algorithm designed for current and near-term quantum devices. There are problems with VQE that forbid a favourable scaling towards quantum advantage. We propose and extensively test a quantum annealing inspired algorithm that supplements VQE. The improved VQE avoids barren plateaus, exits local minima, and works with low-depth circuits.
  arXiv  Detail & Related papers  (2022-02-21T11:21:44Z)
• Constructing Local Bases for a Deep Variational Quantum Eigensolver for Molecular Systems [0.6181093777643575]
  We discuss the performance of the deep VQE algorithm applied to quantum chemistry problems. Specifically, we examine different subspaceforming methods and compare their accuracy and complexity on a 10 H-atom treelike molecule. We find that the deep VQE can simulate the electron-correlation energy of the ground state to an error of below 1%.
  arXiv  Detail & Related papers  (2022-02-17T06:52:37Z)
• Simulating periodic systems on quantum computer [7.332046127518237]
  We present two schemes to improve the accuracy of quantum simulations for extended systems. One is a modified VQE algorithm, which introduces a unitary transformation of Hartree-Fock orbitals to avoid the complex Hamiltonian. The second is a Post-VQE approach combining VQE with the quantum subspace expansion approach (VQE/QSE)
  arXiv  Detail & Related papers  (2020-08-07T01:56:32Z)
• Quantum-optimal-control-inspired ansatz for variational quantum algorithms [105.54048699217668]
  A central component of variational quantum algorithms (VQA) is the state-preparation circuit, also known as ansatz or variational form. Here, we show that this approach is not always advantageous by introducing ans"atze that incorporate symmetry-breaking unitaries. This work constitutes a first step towards the development of a more general class of symmetry-breaking ans"atze with applications to physics and chemistry problems.
  arXiv  Detail & Related papers  (2020-08-03T18:00:05Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.