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Scholten, Travis L.

Publications and source records attributed to Scholten, Travis L..

17 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Behavior of the maximum likelihood in quantum state tomography

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.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Characterizing Quantum Devices Using Model Selection

Quantum information processors are a new kind of computing device with the potential to solve certain problems very quickly. The quantum bits, or "ʺqubits,"ʺ that enable such processors are being developed at Sandia and around the world. In support of this effort, Sandia’s Center for Computing Research is designing methods and algorithms to characterize and debug the behavior of experimental qubits, such as trapped ions and electron spins in silicon. This is a challenge, because qubits are hard to characterize for exactly the same reason that they are powerful. Their behavior (and misbehavior) is far richer and more complicated than that of classical bits! The most reliable models of quantum errors have infinitely many parameters, and we never have enough data to fit all of them. Until now, researchers simply threw out most of these parameters resulting in a crude approximation that makes the problem tractable, but isn’t reliable or accurate enough for Sandia’s experimental work. Our new techniques use statistical model selection to identify “significant” error parameters on the fly, applying a data-­‐‑driven information criterion to choose a Hilbert space that describes the data well without overfitting. To find a reliable criterion, we needed to evaluate many candidates on an enormous corpus of test cases–for which we relied on Red Sky’s ability to run parallel Monte Carlo simulations. Our computations demonstrate how classic model selection methods have to be modified for quantum devices. These results will enable new techniques that identify the effective dimension of as-­‐‑built qubits on the fly, and then use this information to reliably pin down error behaviors and produce successively better and more useful qubits. This project highlights the close and productive relationship between Sandia and the University of New Mexico, where Travis Scholten is working towards a Ph.D. in physics. Both the intellectual environment of UNM and the high-­‐‑powered supercomputing available at Sandia were critical ingredients in achieving our research goals.

97 MATHEMATICS AND COMPUTING↗