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miamico committed Jun 25, 2024
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"This notebook shows how to use the Conditional Value at Risk (CVaR) objective function introduced in [1] within the variational quantum optimization algorithms. For a given set of shots with corresponding objective values of the considered optimization problem, the CVaR with confidence level $\\alpha \\in [0, 1]$ is defined as the average of the $\\alpha$ best shots.\n",
"Thus, $\\alpha = 1$ corresponds to the standard expected value, while $\\alpha=0$ corresponds to the minimum of the given shots, and $\\alpha \\in (0, 1)$ is a tradeoff between focusing on better shots, but still applying some averaging to smoothen the optimization landscape.\n",
"\n",
"The notebook also shows how twirling and CVaR can be used in conjunction to obtain error mitigated probability distributions as show in [2].\n",
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"## References\n",
"\n",
"[1] [P. Barkoutsos et al., *Improving Variational Quantum Optimization using CVaR,* Quantum 4, 256 (2020).](https://quantum-journal.org/papers/q-2020-04-20-256/)"
"[1] [P. Barkoutsos et al., *Improving Variational Quantum Optimization using CVaR,* Quantum 4, 256 (2020).](https://quantum-journal.org/papers/q-2020-04-20-256/)\n",
"\n",
"[2] [S. Barron et al., *Provable bounds for noise-free expectation values computed from noisy samples,* arXiv:231200733](https://arxiv.org/abs/2312.00733)"
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