47,552 research outputs found
The Augmented Synthetic Control Method
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
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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