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The learnability of Pauli noise

Senrui ChenYunchao LiuMatthew OttenAlireza SeifBill FeffermanLiang Jiang
Jun 2022
摘要
Recently, several noise benchmarking algorithms have been developed tocharacterize noisy quantum gates on today's quantum devices. A well-known issuein benchmarking is that not everything about quantum noise is learnable due tothe existence of gauge freedom, leaving open the question of what informationabout noise is learnable and what is not, which has been unclear even for asingle CNOT gate. Here we give a precise characterization of the learnabilityof Pauli noise channels attached to Clifford gates, showing that learnableinformation corresponds to the cycle space of the pattern transfer graph of thegate set, while unlearnable information corresponds to the cut space. Thisimplies the optimality of cycle benchmarking, in the sense that it can learnall learnable information about Pauli noise. We experimentally demonstratenoise characterization of IBM's CNOT gate up to 2 unlearnable degrees offreedom, for which we obtain bounds using physical constraints. In addition, wegive an attempt to characterize the unlearnable information by assuming perfectinitial state preparation. However, based on the experimental data, we concludethat this assumption is inaccurate as it yields unphysical estimates, and weobtain a lower bound on state preparation noise.
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