Improving Variational Quantum Optimization using CVaR

Panagiotis Kl. Barkoutsos; Giacomo Nannicini; Anton Robert; Ivano Tavernelli; Stefan Woerner

doi:10.22331/q-2020-04-20-256

Improving Variational Quantum Optimization using CVaR

Panagiotis Kl. Barkoutsos¹, Giacomo Nannicini², Anton Robert^1,3, Ivano Tavernelli¹, and Stefan Woerner¹

¹IBM Research – Zurich
²IBM T.J. Watson Research Center
³École Normale Supérieure, PSL University, Paris

Published:	2020-04-20, volume 4, page 256
Eprint:	arXiv:1907.04769v3
Doi:	https://doi.org/10.22331/q-2020-04-20-256
Citation:	Quantum 4, 256 (2020).

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Abstract

Hybrid quantum/classical variational algorithms can be implemented on noisy intermediate-scale quantum computers and can be used to find solutions for combinatorial optimization problems. Approaches discussed in the literature minimize the expectation of the problem Hamiltonian for a parameterized trial quantum state. The expectation is estimated as the sample mean of a set of measurement outcomes, while the parameters of the trial state are optimized classically. This procedure is fully justified for quantum mechanical observables such as molecular energies. In the case of classical optimization problems, which yield diagonal Hamiltonians, we argue that aggregating the samples in a different way than the expected value is more natural. In this paper we propose the Conditional Value-at-Risk as an aggregation function. We empirically show -- using classical simulation as well as quantum hardware -- that this leads to faster convergence to better solutions for all combinatorial optimization problems tested in our study. We also provide analytical results to explain the observed difference in performance between different variational algorithms.

► BibTeX data

@article{Barkoutsos2020improving,
  doi = {10.22331/q-2020-04-20-256},
  url = {https://doi.org/10.22331/q-2020-04-20-256},
  title = {Improving {V}ariational {Q}uantum {O}ptimization using {CV}a{R}},
  author = {Barkoutsos, Panagiotis Kl. and Nannicini, Giacomo and Robert, Anton and Tavernelli, Ivano and Woerner, Stefan},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {4},
  pages = {256},
  month = apr,
  year = {2020}
}

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