An Introduction to Variational Quantum Eigensolver Applied to Chemistry

• URL: http://arxiv.org/abs/2505.04768v2
• Date: Tue, 10 Jun 2025 15:31:41 GMT
• Title: An Introduction to Variational Quantum Eigensolver Applied to Chemistry
• Authors: Matheus da S. Fonseca, Caio M. Porto, Nicolás A. C. Carpio, Guilherme S. T. Moraes, Nelson H. Morgon, René A. Nome, Celso J. Villas-Boas,
• Abstract summary: Variational Quantum Algorithms (VQAs) stand out as a feasible approach to demonstrating advantages over classical methods in the near term.<n>We present the application of quantum mechanics to the study of molecules, provide an introduction to the fundamentals of quantum computing, and explore the integration of these fields by employing the VQE in molecular simulations.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: Quantum mechanics has introduced a new theoretical framework for the study of molecules, enabling the prediction of properties and dynamics through the solution of the Schr\"odinger equation applied to these systems. However, solving this equation is computationally expensive, which has led to the development of various mathematical frameworks and computational methods designed to balance the available resources with the desired level of accuracy. In particular, quantum computers have emerged as a promising technology with the potential to address these problems more efficiently in the coming decades, whether through reductions in memory, time, and energy consumption, $\textit{i. e.}$, reductions in computational complexity or by enhancing precision. This research field is known as Quantum Simulation. Given the current technological limitations of quantum computers, Variational Quantum Algorithms (VQAs), especially the Variational Quantum Eigensolver (VQE), stand out as a feasible approach to demonstrating advantages over classical methods in the near term. This feasibility arises from their lower demand for quantum gates and the reduced depth of the circuits required for their implementation. In this work, we present the application of quantum mechanics to the study of molecules, provide an introduction to the fundamentals of quantum computing, and explore the integration of these fields by employing the VQE in molecular simulations. Finally, we discuss the spatial and temporal complexity associated with the algorithm, highlighting its implications and challenges.

Related papers

• VQC-MLPNet: An Unconventional Hybrid Quantum-Classical Architecture for Scalable and Robust Quantum Machine Learning [60.996803677584424]
  Variational Quantum Circuits (VQCs) offer a novel pathway for quantum machine learning.<n>Their practical application is hindered by inherent limitations such as constrained linear expressivity, optimization challenges, and acute sensitivity to quantum hardware noise.<n>This work introduces VQC-MLPNet, a scalable and robust hybrid quantum-classical architecture designed to overcome these obstacles.
  arXiv  Detail & Related papers  (2025-06-12T01:38:15Z)
• Limitations of Quantum Hardware for Molecular Energy Estimation Using VQE [0.0]
  Variational quantum eigensolvers (VQEs) are among the most promising quantum algorithms for solving electronic structure problems in quantum chemistry.<n>In this study, we investigate the capabilities and limitations of VQE algorithms implemented on current quantum hardware.
  arXiv  Detail & Related papers  (2025-06-04T14:19:18Z)
• Quantum Simulation for Dynamical Transition Rates in Open Quantum Systems [0.0]
  We introduce a novel and efficient quantum simulation method to compute dynamical transition rates in Markovian open quantum systems.<n>Our new approach holds the potential to surpass the bottlenecks of current quantum chemical research.
  arXiv  Detail & Related papers  (2024-12-23T02:53:05Z)
• Quantum Subroutine for Variance Estimation: Algorithmic Design and Applications [80.04533958880862]
  Quantum computing sets the foundation for new ways of designing algorithms. New challenges arise concerning which field quantum speedup can be achieved. Looking for the design of quantum subroutines that are more efficient than their classical counterpart poses solid pillars to new powerful quantum algorithms.
  arXiv  Detail & Related papers  (2024-02-26T09:32:07Z)
• Hamiltonian Encoding for Quantum Approximate Time Evolution of Kinetic Energy Operator [2.184775414778289]
  The time evolution operator plays a crucial role in the precise computation of chemical experiments on quantum computers. We have proposed a new encoding method, namely quantum approximate time evolution (QATE) for the quantum implementation of the kinetic energy operator.
  arXiv  Detail & Related papers  (2023-10-05T05:25:38Z)
• Quantum algorithms: A survey of applications and end-to-end complexities [90.05272647148196]
  The anticipated applications of quantum computers span across science and industry. We present a survey of several potential application areas of quantum algorithms. We outline the challenges and opportunities in each area in an "end-to-end" fashion.
  arXiv  Detail & Related papers  (2023-10-04T17:53:55Z)
• Use VQE to calculate the ground energy of hydrogen molecules on IBM Quantum [2.3889084213601346]
  We implement the Variational Quantum Eigensolver (VQE) algorithm using Qiskit on the IBM Quantum platform to calculate the ground state energy of a hydrogen molecule. Our fi ndings demonstrate that VQE can effi ciently calculate molecular properties with high accuracy.
  arXiv  Detail & Related papers  (2023-05-11T02:53:26Z)
• Quantum Annealing for Single Image Super-Resolution [86.69338893753886]
  We propose a quantum computing-based algorithm to solve the single image super-resolution (SISR) problem. The proposed AQC-based algorithm is demonstrated to achieve improved speed-up over a classical analog while maintaining comparable SISR accuracy.
  arXiv  Detail & Related papers  (2023-04-18T11:57:15Z)
• Quantum Machine Learning: from physics to software engineering [58.720142291102135]
  We show how classical machine learning approach can help improve the facilities of quantum computers. We discuss how quantum algorithms and quantum computers may be useful for solving classical machine learning tasks.
  arXiv  Detail & Related papers  (2023-01-04T23:37:45Z)
• Synergy Between Quantum Circuits and Tensor Networks: Short-cutting the Race to Practical Quantum Advantage [43.3054117987806]
  We introduce a scalable procedure for harnessing classical computing resources to provide pre-optimized initializations for quantum circuits. We show this method significantly improves the trainability and performance of PQCs on a variety of problems. By demonstrating a means of boosting limited quantum resources using classical computers, our approach illustrates the promise of this synergy between quantum and quantum-inspired models in quantum computing.
  arXiv  Detail & Related papers  (2022-08-29T15:24:03Z)
• Quantum Computation of Finite-Temperature Static and Dynamical Properties of Spin Systems Using Quantum Imaginary Time Evolution [0.0]
  We develop scalable quantum algorithms to study finite-temperature physics of quantum many-body systems. Our work demonstrates that the ansatz-independent QITE algorithm is capable of computing diverse finite-temperature observables on near-term quantum devices.
  arXiv  Detail & Related papers  (2020-09-08T06:49:08Z)
• Electronic structure with direct diagonalization on a D-Wave quantum annealer [62.997667081978825]
  This work implements the general Quantum Annealer Eigensolver (QAE) algorithm to solve the molecular electronic Hamiltonian eigenvalue-eigenvector problem on a D-Wave 2000Q quantum annealer. We demonstrate the use of D-Wave hardware for obtaining ground and electronically excited states across a variety of small molecular systems.
  arXiv  Detail & Related papers  (2020-09-02T22:46:47Z)
• An Application of Quantum Annealing Computing to Seismic Inversion [55.41644538483948]
  We apply a quantum algorithm to a D-Wave quantum annealer to solve a small scale seismic inversions problem. The accuracy achieved by the quantum computer is at least as good as that of the classical computer.
  arXiv  Detail & Related papers  (2020-05-06T14:18:44Z)
• Quantum Solver of Contracted Eigenvalue Equations for Scalable Molecular Simulations on Quantum Computing Devices [0.0]
  We introduce a quantum solver of contracted eigenvalue equations, the quantum analogue of classical methods for the energies. We demonstrate the algorithm though computations on both a quantum simulator and two IBM quantum processing units.
  arXiv  Detail & Related papers  (2020-04-23T18:35:26Z)
• Simulating quantum chemistry in the seniority-zero space on qubit-based quantum computers [0.0]
  We combine the so-called seniority-zero, or paired-electron, approximation of computational quantum chemistry with techniques for simulating molecular chemistry on gate-based quantum computers. We show that using the freed-up quantum resources for increasing the basis set can lead to more accurate results and reductions in the necessary number of quantum computing runs.
  arXiv  Detail & Related papers  (2020-01-31T19:44:37Z)

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.