Efficient Learning of Pauli Channels

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Provides concrete, efficiently implementable routines to learn Pauli channels: general full-channel estimation requires n·2^n/ε^2 measurements to recover Pauli probabilities to relative precision using randomized compiling, long sequences of single-qubit Cliffords/Paulis, Walsh–Hadamard transforms and exponential fits; s-sparse channels recover with about s·n measurements and O(s n^2) classical time via hashing and peeling; bounded-degree Markov-factor channels learn in polynomial time with ~N^2 log N samples (exp(K) prefactor) giving global L1 guarantees that translate to diamond-distance for Pauli channels; demonstrated on 14-qubit IBM, 2^14 rates with ~2×10^5–10^6 shots, recovering probabilities down to ~10^−5.

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" chapters (15)

1. 0:00Introduction
2. 2:10Two classes of noise
3. 8:46General poly channels
4. 14:12Question
5. 26:08Sparse Channels
6. 29:08Subsampling
7. 34:38Factorization
8. 38:03Factor nodes
9. 38:51Estimating parameters
10. 40:46Rounding step
11. 49:03Experimental Data
12. 50:18Correlation Matrix
13. 51:51Sparse Error Reconstruction
14. 54:20Factorized Error Reconstruction
15. 56:48Conclusion