Topics in Pauli channel learning: quantum advantages and quantum noise characterization
Learning quantum processes is an important topic in quantum information science. Pauli channel, defined as a probabilistic mixture of n-qubit Pauli operators, is an important class of quantum processes widely used for quantum noise modeling. In this talk, I will discuss some theoretical results and applications of Pauli channel learning. First, I will introduce a theoretical framework of entanglement-enabled advantages in learning quantum processes, where the protocols for learning are classified by whether they utilize entanglement with an ancillary quantum memory. In this setting, we show that entanglement offers an exponential advantage in sample complexity for Pauli channel learning. Concretely, we prove Θ(2^n/ϵ^2) rounds of measurement is necessary and sufficient to learn every eigenvalue of an n-qubit Pauli channel to ϵ additive precision using entanglement-free scheme, while O(1/ϵ^2) copies of channels suffice using entanglement-assisted schemes; Secondly, I will discuss learning gate-dependent Pauli channels in the existence of state-preparation-and-measurement (SPAM) noise, a practical task relevant for quantum noise characterization and error mitigation. Fundamental results on the noise learnability and learning algorithms will be discussed; Finally, I will talk about a recent experiment with IBM Quantum on Pauli channel learning, highlighting the entanglement-enabled advantages in learning practically interesting quantum processes.
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