A Quantum Monte Carlo Method at Fixed Energy

In this paper we explore new ways to study the zero temperature limit of quantum statistical mechanics using Quantum Monte Carlo simulations. We develop a Quantum Monte Carlo method in which one fixes the ground state energy as a parameter. The Hamiltonians we consider are of the form $H=H_{0}+\lambda V$ with ground state energy E. For fixed $H_{0}$ and V, one can view E as a function of $\lambda$ whereas we view $\lambda$ as a function of E. We fix E and define a path integral Quantum Monte Carlo method in which a path makes no reference to the times (discrete or continuous) at which transitions occur between states. For fixed E we can determine $\lambda(E)$ and other ground state properties of H

Quantifying the power of multiple event interpretations

A number of methods have been proposed recently which exploit multiple highly-correlated interpretations of events, or of jets within an event. For example, Qjets reclusters a jet multiple times and telescoping jets uses multiple cone sizes. Previous work has employed these methods in pseudo-experimental analyses and found that, with a simplified statistical treatment, they give sizable improvements over traditional methods. In this paper, the improvement gain from multiple event interpretations is explored with methods much closer to those used in real experiments. To this end, we derive a generalized extended maximum likelihood procedure. We study the significance improvement in Higgs to bb with both this method and the simplified method from previous analysis. With either method, we find that using multiple jet radii can provide substantial benefit over a single radius. Another concern we address is that multiple event interpretations might be exploiting similar information to that already present in the standard kinematic variables. By examining correlations between kinematic variables commonly used in LHC analyses and invariant masses obtained with multiple jet reconstructions, we find that using multiple radii is still helpful even on top of standard kinematic variables when combined with boosted decision trees. These results suggest that including multiple event interpretations in a realistic search for Higgs to bb would give additional sensitivity over traditional approaches.Comment: 13 pages, 2 figure

Quantum money from knots

Quantum money is a cryptographic protocol in which a mint can produce a quantum state, no one else can copy the state, and anyone (with a quantum computer) can verify that the state came from the mint. We present a concrete quantum money scheme based on superpositions of diagrams that encode oriented links with the same Alexander polynomial. We expect our scheme to be secure against computationally bounded adversaries.Comment: 22 pages, 5 figure

Unstructured Randomness, Small Gaps and Localization

We study the Hamiltonian associated with the quantum adiabatic algorithm with a random cost function. Because the cost function lacks structure we can prove results about the ground state. We find the ground state energy as the number of bits goes to infinity, show that the minimum gap goes to zero exponentially quickly, and we see a localization transition. We prove that there are no levels approaching the ground state near the end of the evolution. We do not know which features of this model are shared by a quantum adiabatic algorithm applied to random instances of satisfiability since despite being random they do have bit structure

Productivity and misallocation in general equilibrium

We provide a general non-parametric formula for aggregating microeconomic shocks in general equilibrium economies with distortions such as taxes, markups, frictions to resource reallocation, and nominal rigidities. We show that the macroeconomic impact of a shock can be boiled down into two components: its “pure” technology effect; and its effect on allocative efficiency arising from the associated reallocation of resources, which can be measured via changes in factor income shares. We also derive a formula showing how these two components are determined by structural microeconomic parameters such as elasticities of substitution, returns to scale, factor mobility, and network linkages. Overall, our results generalize those of Solow (1957) and Hulten (1978) to economies with distortions. To demonstrate their empirical relevance, we pursue different applications, focusing on markup distortions. For example, we operationalize our non-parametric results and show that improvements in allocative efficiency account for about 50% of measured TFP growth over the period 1997-2015. We also implement our structural results and conclude that eliminating markups would raise TFP by about 40%, increasing the economywide cost of monopoly distortions by two orders of magnitude compared to the famous 0.1% estimates of Harberger (1954)

The macroeconomic impact of microeconomic shocks: beyond Hulten's Theorem

We provide a nonlinear characterization of the macroeconomic impact of microeconomic productivity shocks in terms of reduced-form non-parametric elasticities for efficient economies. We also show how structural parameters are mapped to these reduced-form elasticities. In this sense, we extend the foundational theorem of Hulten (1978) beyond first-order terms. Key features ignored by first-order approximations that play a crucial role are: structural elasticities of substitution, network linkages, structural returns to scale, and the extent of factor reallocation. Higher-order terms magnify negative shocks and attenuate positive shocks, resulting in an output distribution that is asymmetric, fat-tailed, and has a lower mean even when shocks are symmetric and thin-tailed. In our calibration, output losses due to business-cycle fluctuations are an order of magnitude larger than the cost calculated by Lucas (1987). Second-order terms also show how shocks to critical sectors can have large macroeconomic impacts, tripling the estimated impact of the 1970s oil price shocks