Variational quantum amplitude estimation
Cambridge Quantum Computing Limited, SW1P 1BX London, United Kingdom
Published: | 2022-03-17, volume 6, page 670 |
Eprint: | arXiv:2109.03687v2 |
Doi: | https://doi.org/10.22331/q-2022-03-17-670 |
Citation: | Quantum 6, 670 (2022). |
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Abstract
We propose to perform amplitude estimation with the help of constant-depth quantum circuits that variationally approximate states during amplitude amplification. In the context of Monte Carlo (MC) integration, we numerically show that shallow circuits can accurately approximate many amplitude amplification steps. We combine the variational approach with maximum likelihood amplitude estimation [Y. Suzuki et al., Quantum Inf. Process. 19, 75 (2020)] in variational quantum amplitude estimation (VQAE). VQAE typically has larger computational requirements than classical MC sampling. To reduce the variational cost, we propose adaptive VQAE and numerically show in 6 to 12 qubit simulations that it can outperform classical MC sampling.
![](https://quantum-journal.org/wp-content/uploads/2022/03/figure1-1.png)
Featured image: Amplitude estimation error $\delta \theta$ as a function of the number of queries $N_{\mathrm{q}}$. We compare adaptive variational quantum amplitude estimation (symbols) to maximum likelihood amplitude estimation (MLAE) and classical Mont Carlo sampling.
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