The Variational Quantum Eigensolver: a review of methods and best practices

• URL: http://arxiv.org/abs/2111.05176v3
• Date: Thu, 25 Aug 2022 10:49:41 GMT
• Title: The Variational Quantum Eigensolver: a review of methods and best practices
• Authors: Jules Tilly, Hongxiang Chen, Shuxiang Cao, Dario Picozzi, Kanav Setia, Ying Li, Edward Grant, Leonard Wossnig, Ivan Rungger, George H. Booth, Jonathan Tennyson
• Abstract summary: The variational quantum eigensolver (or VQE) uses the variational principle to compute the ground state energy of a Hamiltonian. This review aims to provide an overview of the progress that has been made on the different parts of the algorithm.
• Score: 3.628860803653535
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The variational quantum eigensolver (or VQE) uses the variational principle to compute the ground state energy of a Hamiltonian, a problem that is central to quantum chemistry and condensed matter physics. Conventional computing methods are constrained in their accuracy due to the computational limits. The VQE may be used to model complex wavefunctions in polynomial time, making it one of the most promising near-term applications for quantum computing. Finding a path to navigate the relevant literature has rapidly become an overwhelming task, with many methods promising to improve different parts of the algorithm. Despite strong theoretical underpinnings suggesting excellent scaling of individual VQE components, studies have pointed out that their various pre-factors could be too large to reach a quantum computing advantage over conventional methods. This review aims to provide an overview of the progress that has been made on the different parts of the algorithm. All the different components of the algorithm are reviewed in detail including representation of Hamiltonians and wavefunctions on a quantum computer, the optimization process, the post-processing mitigation of errors, and best practices are suggested. We identify four main areas of future research:(1) optimal measurement schemes for reduction of circuit repetitions; (2) large scale parallelization across many quantum computers;(3) ways to overcome the potential appearance of vanishing gradients in the optimization process, and how the number of iterations required for the optimization scales with system size; (4) the extent to which VQE suffers for quantum noise, and whether this noise can be mitigated. The answers to these open research questions will determine the routes for the VQE to achieve quantum advantage as the quantum computing hardware scales up and as the noise levels are reduced.

Related papers

• Scalable Quantum Algorithms for Noisy Quantum Computers [0.0]
  This thesis develops two main techniques to reduce the quantum computational resource requirements. The aim is to scale up application sizes on current quantum processors. While the main focus of application for our algorithms is the simulation of quantum systems, the developed subroutines can further be utilized in the fields of optimization or machine learning.
  arXiv  Detail & Related papers  (2024-03-01T19:36:35Z)
• 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)
• 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)
• QNEAT: Natural Evolution of Variational Quantum Circuit Architecture [95.29334926638462]
  We focus on variational quantum circuits (VQC), which emerged as the most promising candidates for the quantum counterpart of neural networks. Although showing promising results, VQCs can be hard to train because of different issues, e.g., barren plateau, periodicity of the weights, or choice of architecture. We propose a gradient-free algorithm inspired by natural evolution to optimize both the weights and the architecture of the VQC.
  arXiv  Detail & Related papers  (2023-04-14T08:03:20Z)
• Error Analysis of the Variational Quantum Eigensolver Algorithm [0.18188255328029254]
  We study variational quantum eigensolver (VQE) and its individual quantum subroutines. We show through explicit simulation that the VQE algorithm effectively collapses already when single errors occur during a quantum processing call.
  arXiv  Detail & Related papers  (2023-01-18T02:02:30Z)
• Reducing the cost of energy estimation in the variational quantum eigensolver algorithm with robust amplitude estimation [50.591267188664666]
  Quantum chemistry and materials is one of the most promising applications of quantum computing. Much work is still to be done in matching industry-relevant problems in these areas with quantum algorithms that can solve them.
  arXiv  Detail & Related papers  (2022-03-14T16:51:36Z)
• Efficient Classical Computation of Quantum Mean Values for Shallow QAOA Circuits [15.279642278652654]
  We present a novel graph decomposition based classical algorithm that scales linearly with the number of qubits for the shallow QAOA circuits. Our results are not only important for the exploration of quantum advantages with QAOA, but also useful for the benchmarking of NISQ processors.
  arXiv  Detail & Related papers  (2021-12-21T12:41:31Z)
• The Cost of Improving the Precision of the Variational Quantum Eigensolver for Quantum Chemistry [0.0]
  We study how various types of errors affect the variational quantum eigensolver (VQE) We find that the optimal way of running the hybrid classical-quantum optimization is to allow some noise in intermediate energy evaluations.
  arXiv  Detail & Related papers  (2021-11-09T06:24:52Z)
• Quantum algorithms for quantum dynamics: A performance study on the spin-boson model [68.8204255655161]
  Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. variational quantum algorithms have become an indispensable alternative, enabling small-scale simulations on present-day hardware. We show that, despite providing a clear reduction of quantum gate cost, the variational method in its current implementation is unlikely to lead to a quantum advantage.
  arXiv  Detail & Related papers  (2021-08-09T18:00:05Z)
• VQE Method: A Short Survey and Recent Developments [5.9640499950316945]
  The variational quantum eigensolver (VQE) is a method that uses a hybrid quantum-classical computational approach to find eigenvalues and eigenvalues of a Hamiltonian. VQE has been successfully applied to solve the electronic Schr"odinger equation for a variety of small molecules. Modern quantum computers are not capable of executing deep quantum circuits produced by using currently available ansatze.
  arXiv  Detail & Related papers  (2021-03-15T16:25:36Z)
• Quantum circuit architecture search for variational quantum algorithms [88.71725630554758]
  We propose a resource and runtime efficient scheme termed quantum architecture search (QAS) QAS automatically seeks a near-optimal ansatz to balance benefits and side-effects brought by adding more noisy quantum gates. We implement QAS on both the numerical simulator and real quantum hardware, via the IBM cloud, to accomplish data classification and quantum chemistry tasks.
  arXiv  Detail & Related papers  (2020-10-20T12:06:27Z)

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.