From c9b3b20bd2145e9b0ad88e07c8c47480f275fbf6 Mon Sep 17 00:00:00 2001 From: Mirko Amico Date: Tue, 25 Jun 2024 13:57:11 -0600 Subject: [PATCH] add reference --- docs/notebooks/cvar-cost-function.ipynb | 6 +++++- 1 file changed, 5 insertions(+), 1 deletion(-) diff --git a/docs/notebooks/cvar-cost-function.ipynb b/docs/notebooks/cvar-cost-function.ipynb index fb3c7ae..2cf77dc 100644 --- a/docs/notebooks/cvar-cost-function.ipynb +++ b/docs/notebooks/cvar-cost-function.ipynb @@ -16,10 +16,14 @@ "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", + "\n", "\n", "## 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)" ] }, {