4.7 Review

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

期刊

出版社

ELSEVIER
DOI: 10.1016/j.physrep.2022.08.003

关键词

Quantum computing; Variational methods; Noisy intermediate scale quantum devices; Electronic structure; Quantum chemistry; Many-body physics

资金

  1. industrial CASE (iCASE) studentship - UK EPSRC [EP/T517793/1, EP/P510270/1, EP/R513143/1]
  2. University College London
  3. Odyssey Therapeutics
  4. UCL
  5. National Natural Science Foundation of China [11875050, 12088101]
  6. NSAF, China [U1930403]
  7. UK government department for Business, Energy and Industrial Strategy through the UK National Quantum Technologies Programme
  8. Royal Society via a University Research Fellowship, United Kingdom
  9. European Research Council (ERC) under the European Union [759063]
  10. European Research Council (ERC) [759063] Funding Source: European Research Council (ERC)

向作者/读者索取更多资源

The variational quantum eigensolver (VQE) is a method used to compute the ground state energy of a Hamiltonian, which is important in quantum chemistry and condensed matter physics. It has the advantage of being able to model complex wavefunctions in polynomial time, making it a promising application for quantum computing. However, there are still many open questions regarding optimization, quantum noise, and other challenges, which require further research and exploration.
The variational quantum eigensolver (or VQE), first developed by Peruzzo et al. (2014), has received significant attention from the research community in recent years. It 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 facing exact modeling of the exponentially growing electronic wavefunction for these many-electron systems. The VQE may be used to model these complex wavefunctions in polynomial time, making it one of the most promising near-term applications for quantum computing. One important advantage is that variational algorithms have been shown to present some degree of resilience to the noise in the quantum hardware. 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, but without clear descriptions of how the diverse parts fit together. The potential practical advantages of the algorithm are also widely discussed in the literature, but with varying conclusions. 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 at disentangling the relevant literature to provide a comprehensive overview of the progress that has been made on the different parts of the algorithm, and to discuss future areas of research that are fundamental for the VQE to deliver on its promises. All the different components of the algorithm are reviewed in detail. These include the representation of Hamiltonians and wavefunctions on a quantum computer, the optimization process to find ground state energies, the post processing mitigation of quantum errors, and suggested best practices. We identify four main areas of future research: (1) optimal measurement schemes for reduction of circuit repetitions required; (2) large scale parallelization across many quantum computers; (3) ways to overcome the potential appearance of vanishing gradients in the optimization process for large systems, 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 in a tractable manner. 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.

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