Regularization of Riemannian optimization: Application to process tomography and quantum machine learning
Researchers have extended Riemannian gradient descent methods for optimizing quantum channels by adding rank-penalizing regularization terms to the cost function, similar to Lasso. The goal is to bias the optimization toward channels that can be expressed with as few Kraus operators as possible. The abstract points to applications in quantum process tomography and quantum machine learning.
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What this could mean
- 0–2 yearsPlausible
This could enable quantum process tomography on current noisy devices to scale to more qubits by automatically discovering sparse Kraus representations, reducing the number of parameters and measurements needed.
If the rank penalty reliably drives optimization to low Kraus rank without sacrificing channel fidelity, then fewer parameters must be estimated, which in turn lowers the number of experimental settings required for process tomography. Existing Riemannian optimization libraries and Lasso-style regularization provide a credible basis, though their combination for quantum channels has not yet been demonstrated at scale.
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