Two machine learning models reconstruct continuous Wigner functions from sparse phase-space measurements: a provably efficient regression model for sparse states (O(s⁴ log d) samples) and a self-supervised neural network for general states including experimental GKP code data.
Linear Regression with Limited Observation
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abstract
We consider the most common variants of linear regression, including Ridge, Lasso and Support-vector regression, in a setting where the learner is allowed to observe only a fixed number of attributes of each example at training time. We present simple and efficient algorithms for these problems: for Lasso and Ridge regression they need the same total number of attributes (up to constants) as do full-information algorithms, for reaching a certain accuracy. For Support-vector regression, we require exponentially less attributes compared to the state of the art. By that, we resolve an open problem recently posed by Cesa-Bianchi et al. (2010). Experiments show the theoretical bounds to be justified by superior performance compared to the state of the art.
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Learning to Reconstruct Wigner Functions in Phase Space
Two machine learning models reconstruct continuous Wigner functions from sparse phase-space measurements: a provably efficient regression model for sparse states (O(s⁴ log d) samples) and a self-supervised neural network for general states including experimental GKP code data.