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Behavior of the maximum likelihood in quantum state tomography

New Journal of Physics

Scholten, Travis L.; Blume-Kohout, Robin J.

Quantum state tomography on a d-dimensional system demands resources that grow rapidly with d. They may be reduced by using model selection to tailor the number of parameters in the model (i.e., the size of the density matrix). Most model selection methods typically rely on a test statistic and a null theory that describes its behavior when two models are equally good. Here, we consider the loglikelihood ratio. Because of the positivity constraint ρ ≥ 0, quantum state space does not generally satisfy local asymptotic normality (LAN), meaning the classical null theory for the loglikelihood ratio (the Wilks theorem) should not be used. Thus, understanding and quantifying how positivity affects the null behavior of this test statistic is necessary for its use in model selection for state tomography. We define a new generalization of LAN, metric-projected LAN, show that quantum state space satisfies it, and derive a replacement for the Wilks theorem. In addition to enabling reliable model selection, our results shed more light on the qualitative effects of the positivity constraint on state tomography.

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TYPE Journal Article YEAR 2018
DOIOSTIScopus

Concurrent multiscale modeling of microstructural effects on localization behavior in finite deformation solid mechanics

Computational Mechanics

Alleman, Coleman A.; Laros, James H.; Mota, Alejandro M.; Lim, Hojun L.; Littlewood, David J.

The heterogeneity in mechanical fields introduced by microstructure plays a critical role in the localization of deformation. To resolve this incipient stage of failure, it is therefore necessary to incorporate microstructure with sufficient resolution. On the other hand, computational limitations make it infeasible to represent the microstructure in the entire domain at the component scale. In this study, the authors demonstrate the use of concurrent multiscale modeling to incorporate explicit, finely resolved microstructure in a critical region while resolving the smoother mechanical fields outside this region with a coarser discretization to limit computational cost. The microstructural physics is modeled with a high-fidelity model that incorporates anisotropic crystal elasticity and rate-dependent crystal plasticity to simulate the behavior of a stainless steel alloy. The component-scale material behavior is treated with a lower fidelity model incorporating isotropic linear elasticity and rate-independent J2 plasticity. The microstructural and component scale subdomains are modeled concurrently, with coupling via the Schwarz alternating method, which solves boundary-value problems in each subdomain separately and transfers solution information between subdomains via Dirichlet boundary conditions. In this study, the framework is applied to model incipient localization in tensile specimens during necking.

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TYPE Journal Article YEAR 2018
DOIOSTIScopusDOIOSTIScopus

A Future with Quantum Machine Learning

Computer

DeBenedictis, Erik

Could combining quantum computing and machine learning with Moore's law produce a true 'rebooted computer'? This article posits that a three-technology hybrid-computing approach might yield sufficiently improved answers to a broad class of problems such that energy efficiency will no longer be the dominant concern.

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TYPE Journal Article YEAR 2018
DOIOSTIScopus

PIMS: Memristor-Based Processing-in-Memory-and-Storage

Cook, Jeanine C.

Continued progress in computing has augmented the quest for higher performance with a new quest for higher energy efficiency. This has led to the re-emergence of Processing-In-Memory (PIM) ar- chitectures that offer higher density and performance with some boost in energy efficiency. Past PIM work either integrated a standard CPU with a conventional DRAM to improve the CPU- memory link, or used a bit-level processor with Single Instruction Multiple Data (SIMD) control, but neither matched the energy consumption of the memory to the computation. We originally proposed to develop a new architecture derived from PIM that more effectively addressed energy efficiency for high performance scientific, data analytics, and neuromorphic applications. We also originally planned to implement a von Neumann architecture with arithmetic/logic units (ALUs) that matched the power consumption of an advanced storage array to maximize energy efficiency. Implementing this architecture in storage was our original idea, since by augmenting storage (in- stead of memory), the system could address both in-memory computation and applications that accessed larger data sets directly from storage, hence Processing-in-Memory-and-Storage (PIMS). However, as our research matured, we discovered several things that changed our original direc- tion, the most important being that a PIM that implements a standard von Neumann-type archi- tecture results in significant energy efficiency improvement, but only about a O(10) performance improvement. In addition to this, the emergence of new memory technologies moved us to propos- ing a non-von Neumann architecture, called Superstrider, implemented not in storage, but in a new DRAM technology called High Bandwidth Memory (HBM). HBM is a stacked DRAM tech- nology that includes a logic layer where an architecture such as Superstrider could potentially be implemented.

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TYPE SAND Report YEAR 2018
DOIDOIOSTIOSTI

Geometric Hitting Set for Segments of Few Orientations

Theory of Computing Systems

Fekete, Sandor P.; Huang, Kan; Mitchell, Joseph S.B.; Parekh, Ojas D.; Phillips, Cynthia A.

We study several natural instances of the geometric hitting set problem for input consisting of sets of line segments (and rays, lines) having a small number of distinct slopes. These problems model path monitoring (e.g., on road networks) using the fewest sensors (the “hitting points”). We give approximation algorithms for cases including (i) lines of 3 slopes in the plane, (ii) vertical lines and horizontal segments, (iii) pairs of horizontal/vertical segments. We give hardness and hardness of approximation results for these problems. We prove that the hitting set problem for vertical lines and horizontal rays is polynomially solvable.

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TYPE Journal Article YEAR 2018
DOIOSTIScopus
Results 3351–3400 of 9,998
Results 3351–3400 of 9,998