47,552 research outputs found

    The Augmented Synthetic Control Method

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    The synthetic control method (SCM) is a popular approach for estimating the impact of a treatment on a single unit in panel data settings. The "synthetic control" is a weighted average of control units that balances the treated unit's pre-treatment outcomes as closely as possible. A critical feature of the original proposal is to use SCM only when the fit on pre-treatment outcomes is excellent. We propose Augmented SCM as an extension of SCM to settings where such pre-treatment fit is infeasible. Analogous to bias correction for inexact matching, Augmented SCM uses an outcome model to estimate the bias due to imperfect pre-treatment fit and then de-biases the original SCM estimate. Our main proposal, which uses ridge regression as the outcome model, directly controls pre-treatment fit while minimizing extrapolation from the convex hull. This estimator can also be expressed as a solution to a modified synthetic controls problem that allows negative weights on some donor units. We bound the estimation error of this approach under different data generating processes, including a linear factor model, and show how regularization helps to avoid over-fitting to noise. We demonstrate gains from Augmented SCM with extensive simulation studies and apply this framework to estimate the impact of the 2012 Kansas tax cuts on economic growth. We implement the proposed method in the new augsynth R package

    Quantum superiority for verifying NP-complete problems with linear optics

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    Demonstrating quantum superiority for some computational task will be a milestone for quantum technologies and would show that computational advantages are possible not only with a universal quantum computer but with simpler physical devices. Linear optics is such a simpler but powerful platform where classically-hard information processing tasks, such as Boson Sampling, can be in principle implemented. In this work, we study a fundamentally different type of computational task to achieve quantum superiority using linear optics, namely the task of verifying NP-complete problems. We focus on a protocol by Aaronson et al. (2008) that uses quantum proofs for verification. We show that the proof states can be implemented in terms of a single photon in an equal superposition over many optical modes. Similarly, the tests can be performed using linear-optical transformations consisting of a few operations: a global permutation of all modes, simple interferometers acting on at most four modes, and measurement using single-photon detectors. We also show that the protocol can tolerate experimental imperfections.Comment: 10 pages, 6 figures, minor corrections, results unchange
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