Quantum Natural Gradient for Variational Bayes

Variational Bayes (VB) is a critical method in machine learning and statistics, underpinning the recent success of Bayesian deep learning. The natural gradient is an essential component of efficient VB estimation, but it is prohibitively computationally expensive in high dimensions. We propose a hybrid quantum-classical algorithm to improve the scaling properties of natural gradient computation and make VB a truly computationally efficient method for Bayesian inference in highdimensional settings. The algorithm leverages matrix inversion from the linear systems algorithm by Harrow, Hassidim, and Lloyd [Phys. Rev. Lett. 103, 15 (2009)] (HHL). We demonstrate that the matrix to be inverted is sparse and the classical-quantum-classical handoffs are sufficiently economical to preserve computational efficiency, making the problem of natural gradient for VB an ideal application of HHL. We prove that, under standard conditions, the VB algorithm with quantum natural gradient is guaranteed to converge. Our regression-based natural gradient formulation is also highly useful for classical VB

Global Phase Diagram of nu = 2 Quantum Hall Bilayers in Tilted Magnetic Field

We consider a bilayer quantum Hall system at total filling fraction nu=2 in tilted magnetic field allowing for charge imbalance as well as tunneling between the two layers. Using an "unrestricted Hartree Fock," previously discussed by Burkov and MacDonald (Phys Rev B 66 115323 2002), we examine the zero temperature global phase diagrams that would be accessed experimentally by changing the in-plane field and the bias voltage between the layers while keeping the tunneling between the two layers fixed. In accordance with previous work, we find symmetric and ferromagnetic phases as well as a first order transition between two canted phases with spontaneously broken U(1) symmetry. We find that these two canted phases are topologically connected in the phase diagram and, reminiscent of a first order liquid-gas transition, the first order transition line between these two phases ends in a quantum critical point. We develop a physical picture of these two phases and describe in detail the physics of the transition

Global phase diagram of = 2 quantum Hall bilayers in tilted magnetic fields

We consider a bilayer quantum Hall system at total filling fraction n=2 in tilted magnetic field allowing for charge imbalance as well as tunneling between the two layers. Using an “unrestricted Hartree Fock,” previously discussed by Burkov and MacDonald [Phys. Rev. B 66, 115323 (2002)], we examine the zero temperature global phase diagrams that would be accessed experimentally by changing the in-plane field and the bias voltage between the layers while keeping the tunneling between the two layers fixed. In accordance with previous work, we find symmetric and ferromagnetic phases as well as a first-order transition between two canted phases with spontaneously broken U(1) symmetry. We find that these two canted phases are topologically connected in the phase diagram and, reminiscent of a first-order liquid-gas transition, the first-order transition line between these two phases ends in a quantum critical point. We develop a physical picture of these two phases and describe in detail the physics of the transition.Physic

Collective modes of = 2 quantum Hall bilayers in tilted magnetic fields

We use the time-dependent Hartree Fock approximation to study the collective-mode spectra of n=2 quantum Hall bilayers in tilted magnetic fields, allowing for charge imbalance as well as tunneling between the two layers. In a previous companion paper to this work, we studied the zero-temperature global phase diagram of this system, which was found to include symmetric and ferromagnetic phases as well as a first-order transition between two canted phases with spontaneously broken U(1) symmetry. We further found that this first-order transition line ends in a quantum critical point within the canted region. In the current work, we study the excitation spectra of all of these phases and pay particular attention to the behavior of the collective modes near the phase transitions. We find, most interestingly, that the first-order transition between the two canted phases is signaled by a near softening of a magnetoroton minimum. Many of the collective-mode features explored here should be accessible experimentally in light-scattering experiments.Physic

Gas Source Molecular Beam Epitaxy of Compound Semiconductors

Contains an introduction and reports on seven research projects.Defense Advanced Research Projects Agency Subcontract 284-25041Joint Services Electronics Program Contract DAAL04-95-1-0038National Center for Integrated Photonic Technology Contract 542-381U.S. Army Research Office/ AASERT Contract DAAH04-93-G-0175National Science Foundation Grant DMR 92-02957Joint Services Electronics Program Grant DAAL04-95-1-0038National Science Foundation Grant DMR 90-22933National Science Foundation Grant DMR 92-02957National Center for Integrated Photonic Technology Contract 542-381MIT Lincoln LaboratoryNational Center for Integrated Photonic Technology Subcontract 542-383National Science Foundation DMR 94-0033

The Value Premium and the Fixed Supply of Assets

The paper demonstrates that the mean-variance framework with fixed payoffs can explain a range of well-established empirical facts -- such as the value premium and its dependence on size and the dependence of the cross-section of stock returns on fundamental accounting variables. The proposed static partial-equilibrium model leads to an interpretation of the value premium as compensation required to induce investors to hold assets available in abundance relative to investor demand (in the absence of such compensation). Implications asset owners are significant: the value premium is not a ``free lunch,'' unless the asset owners' optimal allocation to the value asset is higher than that of the average investor. The paper reports the results of empirical tests, which confirm the dependence of CAPM beta on fundamental factors, uncover a strong dependence of a number of risk metrics on size, and lend support to the proposed model

Are Conditional Factors Priced? Characterizing Risk Premia of Conditional Systematic Risk Factors with Staggered Regressions

We introduce the staggered Fama-MacBeth regression method and use it to evaluate economic significance of popular conditional systematic risk factors. Prior literature demonstrated that exposure to these factors is rewarded in the cross-section of stock returns. Much of the evidence comes from contemporaneous regressions; however, in predictive regressions, the evidence tends to disappear. The proposed staggered regression method combines the benefits of contemporaneous and predictive regressions while eliminating critical shortcomings. Using the method, we con rm the economic significance of downside risk, , relative downside risk, +, and coskewness, but not of exceedance correlations and related measures of asymmetric dependence

Asymmetries of Stock Returns and Price Delay

Prior studies have demonstrated that stock returns exhibit non-linear dependence -- down-side beta different from upside beta -- and asymmetric correlations -- higher correlations during periods of negative market moves than positive market moves. We provide empirical evidence that these asymmetries are intertwined with delayed pricing of negative and positive news. We demonstrate that negative news are incorporated in stock prices faster than positive news, and that idiosyncratic news are more likely to be priced during periods when systematic news are positive. Our results add to the growing evidence that investors have finite attention budgets to process information. They also imply that investors prioritize negative over positive news -- an effect not yet fully explained by theory