Learning quantum graph states with product measurements
- Publisher:
- Institute of Electrical and Electronics Engineers (IEEE)
- Publication Type:
- Conference Proceeding
- Citation:
- IEEE International Symposium on Information Theory - Proceedings, 2022, 2022-June, pp. 2963-2968
- Issue Date:
- 2022-01-01
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| Filename | Description | Size | |||
|---|---|---|---|---|---|
| Learning_quantum_graph_states_with_product_measurements_MARCO_TOMAMICHEL.pdf | Published version | 990.15 kB |
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We consider the problem of learning N identical copies of an unknown n-qubit quantum graph state with product measurements. These graph states have corresponding graphs where every vertex has exactly d neighboring vertices. Here, we detail an explicit algorithm that uses product measurements on multiple identical copies of such graph states to learn them. When n ≫ d and N = O(d log(1/ϵ) + d2 log n), this algorithm correctly learns the graph state with probability at least 1 - ϵ. From channel coding theory, we find that for arbitrary joint measurements on graph states, any learning algorithm achieving this accuracy requires at least Ω(log(1/ϵ) + d log n) copies when d = o (√ n). We also supply bounds on N when every graph state encounters identical and independent depolarizing errors on each qubit.
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