Noisy amplitude estimation with low-depth algorithms

This sample demonstrates a low-depth algorithm to perform amplitude estimation using Maximum Likelihood Estimation under the assumption that depolarizing noise acts on the qubits. Specifically, this Azure Quantum notebook implements a noisy version of the Power Law Amplitude Estimation algorithm from [Tiron et al.] and uses both Python and Q# for this quantum-classical approach. Currently, it runs on the quantum simulator and not on hardware.

The sample can be run in two different ways:

• Azure Quantum service
• Python + Q# with Jupyter Notebook

Running the sample on the Azure Quantum service

Make sure that you have created and selected a quantum workspace. Then upload the notebook NoisyAmpEst.ipynb into the My Notebooks section and follow the instructions.

Running the sample locally with Jupyter Notebook

Make sure that you have followed the Q# + Python environment quickstart for the Quantum Development Kit, and then start a new Jupyter Notebook session from the folder containing this sample:

cd noisy-amp-est
jupyter notebook

Once Jupyter starts, open the NoisyAmpEst.ipynb notebook and follow the instructions there.

Manifest

• NoisyAmpEst.ipynb: Python + Q# notebook for this sample.

References

To learn more about hybrid approaches to amplitude estimation see:

• [Tiron et al.]: Tudor Giurgica-Tiron, Iordanis Kerenidis, Farrokh Labib, Anupam Prakash, and William Zeng (2022), "Low depth algorithms for quantum amplitude estimation", Quantum, Volume 6, pp. 745; arXiv:2012.03348