arXiv subjects

Robert Carr

Publications and source records attributed to Robert Carr.

3 recordsLinked to original sources

arXiv2023

Verifying Quantum Phase Estimation (QPE) using Prove-It

The general-purpose interactive theorem-proving assistant called Prove-It was used to verify the Quantum Phase Estimation (QPE) algorithm, specifically claims about its outcome probabilities. Prove-It is unique in its ability to express sophisticated mathematical statements, including statements about quantum circuits, integrated firmly within its formal theorem-proving framework. We demonstrate our ability to follow a textbook proof to produce a formally certified proof, highlighting useful automation features to fill in obvious steps and make formal proving nearly as straightforward as informal theorem proving. Finally, we make comparisons with formal theorem-proving in other systems where similar claims about QPE have been proven.

quant-ph↗

arXiv2023

Instance-specific linear relaxations of semidefinite optimization problems

We introduce a generic technique to obtain linear relaxations of semidefinite programs with provable guarantees based on the commutativity of the constraint and the objective matrices. We study conditions under which the optimal value of the SDP and the proposed linear relaxation match, which we then relax to provide a flexible methodology to derive effective linear relaxations. We specialize these results to provide linear programs that approximate well-known semidefinite programs for the max cut problem proposed by Poljak and Rendl, and the Lovasz theta number; we prove that the linear program proposed for max cut certifies a known eigenvalue bound for the maximum cut value and is in fact stronger. Our ideas can be used to warm-start algorithms that solve semidefinite programs by iterative polyhedral approximation of the feasible region. We verify this capability through multiple experiments on the max cut semidefinite program, the Lovasz theta number and on three families of semidefinite programs obtained as convex relaxations of certain quadratically constrained quadratic problems.

math.OC↗

arXiv2022

Wayne State Universitys Dan Zowada Memorial Observatory: Characterization and Pipeline of a 0.5 Meter Robotic Telescope

Wayne State University's Dan Zowada Memorial Observatory is a fully robotic 0.5m telescope and imaging system located under the dark skies of New Mexico. The observatory is particularly suited to time domain astronomy: the observation of variable objects, such as tidal disruption events, supernovae, and active galactic nuclei. We have developed a software suite for image reduction, alignment and stacking, and calculation of absolute photometry in the Sloan filters used at the telescope. Our pipeline also performs image subtraction to enable photometry of objects embedded in bright backgrounds such as galaxies. The 5 sigma detection limit of the Zowada Observatory for integration of 16 x 90 second exposures is 19.0 magnitude in g-band, 18.1 magnitude in r-band, 17.9 magnitude in i-band, and 16.6 magnitude in z-band. For a 3 sigma detection limit, measurements may be performed with greater uncertainties as deep as 19.9, 19.1. 18.9 and 17.5 magnitude in griz bands, respectively.

astro-ph.IM↗