A Copositive Framework for Analysis of Hybrid Ising-Classical Algorithms

Recent years have seen significant advances in quantum/quantum-inspired technologies capable of approximately searching for the ground state of Ising spin Hamiltonians. The promise of leveraging such technologies to accelerate the solution of difficult optimization problems has spurred an increased interest in exploring methods to integrate Ising problems as part of their solution process, with existing approaches ranging from direct transcription to hybrid quantum-classical approaches rooted in existing optimization algorithms. While it is widely acknowledged that quantum computers should augment classical computers, rather than replace them entirely, comparatively little attention has been directed toward deriving analytical characterizations of their interactions. In this paper, we present a formal analysis of hybrid algorithms in the context of solving mixed-binary quadratic programs (MBQP) via Ising solvers. We show the exactness of a convex copositive reformulation of MBQPs, allowing the resulting reformulation to inherit the straightforward analysis of convex optimization. We propose to solve this reformulation with a hybrid quantum-classical cutting-plane algorithm. Using existing complexity results for convex cutting-plane algorithms, we deduce that the classical portion of this hybrid framework is guaranteed to be polynomial time. This suggests that when applied to NP-hard problems, the complexity of the solution is shifted onto the subroutine handled by the Ising solver

The Spitzer Extragalactic Representative Volume Survey (SERVS): The Environments of High-z SDSS Quasi-Stellar-Objects

This paper presents a study of the environments of SDSS Quasi-Stellar-Objects (QSOs) in the Spitzer Extragalactic Representative Volume Survey (SERVS). We concentrate on the high-redshift QSOs as these have not been studied in large numbers with data of this depth before. We use the IRAC 3.6-4.5{\mu}m colour of objects and ancillary r-band data to filter out as much foreground contamination as possible. This technique allows us to find a significant (> 4-{\sigma}) over-density of galaxies around QSOs in a redshift bin centred on z ~ 2.0 and a (> 2-{\sigma}) over-density of galaxies around QSOs in a redshift bin centred on z ~ 3.3. We compare our findings to the predictions of a semi-analytic galaxy formation model, based on the {\Lambda}CDM millennium simulation, and find for both redshift bins that the model predictions match well the source-density we have measured from the SERVS data.Comment: 13 pages, 12 figures, Accepted by Ap

Volumetric center method for stochastic convex programs using sampling

We develop an algorithm for solving the stochastic convex program (SCP) by combining Vaidya's volumetric center interior point method (VCM) for solving non-smooth convex programming problems with the Monte-Carlo sampling technique to compute a subgradient. A near-central cut variant of VCM is developed, and for this method an approach to perform bulk cut translation, and adding multiple cuts is given. We show that by using near-central VCM the SCP can be solved to a desirable accuracy with any given probability. For the two-stage SCP the solution time is independent of the number of scenarios

Daily Modulation as a Smoking Gun of Dark Matter with Significant Stopping

We point out that for a range of parameters, the flux of DM may be stopped significantly by its interactions with the Earth. This can significantly degrade the sensitivity of direct detection experiments to DM candidates with large interactions with terrestrial nuclei. We find that a significant region of parameter space remains unconstrained for DM $\lesssim$ a few GeV. For DM candidates with moderate levels of stopping power, the flux of DM may be blocked from below but not above a detector thereby producing a novel daily modulation. This can be explored by low threshold detectors placed on the surface or in shallow sites in the south hemisphere.Comment: 11 pages, 3 figures; v3 minor correction

Metamaterial Optics for Precision Cosmic Microwave Background Observation

The Cosmic Microwave Background (CMB) is the oldest light in the Universe. As such it provides deep insight into both early and late Universe physics, including the sum of the neutrino masses and possible signatures of inflation. To better characterize the temperature and polarization anisotropies of the CMB, new instruments need to be designed. The Atacama Cosmology Telescope (ACT) is a six meter telescope built to observe the CMB. This thesis describes contributions to new broadband receivers called ACTPol and Advanced ACTPol. The receiver has three independent cameras with feedhorn coupled, polarization sensitive superconducting bolometer detectors. The first two detector arrays for ACTPol are sensitive to 150 GHz. The other detector arrays are dichroic, sensitive to two frequency bands: the low frequency (20/40 GHz), mid frequency (90/150 GHz), and high frequency (150/220 GHz). I have further developed the three layer metamaterial antireflection (AR) coating technology used to realize the necessary bandwidth for the current dichroic detectors for the ACTPol and Advanced ACTPol instruments. In this thesis I describe work to push the boundaries of that technology beyond the current needs, and develop broader bandwidth, five layer AR coatings which could effectively cover 50-350 GHz, and higher frequency coatings which could work up to 2 THz. I also applied the metamaterial design and fabrication techniques to a different optical element for CMB observation: half-wave plates (HWPs). I began with a simple single frequency HWP for the ACTPol instrument, then went to a broadband, three stack HWP for the ACTPol and Advanced ACTPol dichroic bands. These HWPs represent a novel use of metamaterial technology, with significant benefits over traditional found material HWPs. With these optical elements, the ACT collaboration has published a number of scientific papers. We have reported new measurements of the temperature and polarization power spectra of the CMB. We have used the Sunayev-Zeldovich effect to measure the masses of galaxy clusters. We have detected the effects of gravitational lensing on the CMB, and compared this lensing mass profile to optical lensing measurements. This thesis is organized as follows. Chapter 1 gives an overview of Cosmology, including its history and current goals. Chapter 2 is a detailed description of the Atacama Cosmology Telescope and its various instrumentation. In Chapter 3 I discuss my work on the antireflection coatings. Chapter 4 is about my work on half-wave plates. Chapter 5 concludes with a discussion of the science my work has enabled and the future of the work presented in this thesis and CMB observations in general.PHDPhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/146072/1/kpcoughl_1.pd