The Rug Rat Race

education, school, mothers, childcare, higher education

Cross-Country Evidence on the Link Between Volatility and Growth

This paper presents empirical evidence against the standard dichotomy in macroeconomics that separates growth from the volatility of economic fluctuations. In a sample of 92 countries as well as a sample of OECD countries, we find that countries with higher volatility have lower growth. The addition of standard control variables strengthens the negative relationship. We also find that government spending-induced volatility is negatively associated with growth even after controlling for both time- and country-fixed effects.

Quantum annealing with Jarzynski equality

We show a practical application of the Jarzynski equality in quantum computation. Its implementation may open a way to solve combinatorial optimization problems, minimization of a real single-valued function, cost function, with many arguments. We consider to incorpolate the Jarzynski equality into quantum annealing, which is one of the generic algorithms to solve the combinatorial optimization problem. The ordinary quantum annealing suffers from non-adiabatic transitions whose rate is characterized by the minimum energy gap $\Delta_{\rm min.}$ of the quantum system under consideration. The quantum sweep speed is therefore restricted to be extremely slow for the achievement to obtain a solution without relevant errors. However, in our strategy shown in the present study, we find that such a difficulty would not matter.Comment: 4 pages, to appear in Phys. Rev. Let

Scheduling Bidirectional Traffic on a Path

We study the fundamental problem of scheduling bidirectional traffic along a path composed of multiple segments. The main feature of the problem is that jobs traveling in the same direction can be scheduled in quick succession on a segment, while jobs in opposing directions cannot cross a segment at the same time. We show that this tradeoff makes the problem significantly harder than the related flow shop problem, by proving that it is NP-hard even for identical jobs. We complement this result with a PTAS for a single segment and non-identical jobs. If we allow some pairs of jobs traveling in different directions to cross a segment concurrently, the problem becomes APX-hard even on a single segment and with identical jobs. We give polynomial algorithms for the setting with restricted compatibilities between jobs on a single and any constant number of segments, respectively

Quantum annealing with antiferromagnetic fluctuations

We introduce antiferromagnetic quantum fluctuations into quantum annealing in addition to the conventional transverse-field term. We apply this method to the infinite-range ferromagnetic p-spin model, for which the conventional quantum annealing has been shown to have difficulties to find the ground state efficiently due to a first-order transition. We study the phase diagram of this system both analytically and numerically. Using the static approximation, we find that there exists a quantum path to reach the final ground state from the trivial initial state that avoids first-order transitions for intermediate values of p. We also study numerically the energy gap between the ground state and the first excited state and find evidence for intermediate values of p that the time complexity scales polynomially with the system size at a second-order transition point along the quantum path that avoids first-order transitions. These results suggest that quantum annealing would be able to solve this problem with intermediate values of p efficiently in contrast to the case with only simple transverse-field fluctuations.Comment: 19 pages, 11 figures; Added references; To be published in Physical Review

On the complexity of the multiple stack TSP, kSTSP

The multiple Stack Travelling Salesman Problem, STSP, deals with the collect and the deliverance of n commodities in two distinct cities. The two cities are represented by means of two edge-valued graphs (G1,d2) and (G2,d2). During the pick-up tour, the commodities are stored into a container whose rows are subject to LIFO constraints. As a generalisation of standard TSP, the problem obviously is NP-hard; nevertheless, one could wonder about what combinatorial structure of STSP does the most impact its complexity: the arrangement of the commodities into the container, or the tours themselves? The answer is not clear. First, given a pair (T1,T2) of pick-up and delivery tours, it is polynomial to decide whether these tours are or not compatible. Second, for a given arrangement of the commodities into the k rows of the container, the optimum pick-up and delivery tours w.r.t. this arrangement can be computed within a time that is polynomial in n, but exponential in k. Finally, we provide instances on which a tour that is optimum for one of three distances d1, d2 or d1+d2 lead to solutions of STSP that are arbitrarily far to the optimum STSP

On the Complexity of Local Search for Weighted Standard Set Problems

In this paper, we study the complexity of computing locally optimal solutions for weighted versions of standard set problems such as SetCover, SetPacking, and many more. For our investigation, we use the framework of PLS, as defined in Johnson et al., [JPY88]. We show that for most of these problems, computing a locally optimal solution is already PLS-complete for a simple neighborhood of size one. For the local search versions of weighted SetPacking and SetCover, we derive tight bounds for a simple neighborhood of size two. To the best of our knowledge, these are one of the very few PLS results about local search for weighted standard set problems

First order phase transition in the Quantum Adiabatic Algorithm

We simulate the quantum adiabatic algorithm (QAA) for the exact cover problem for sizes up to N=256 using quantum Monte Carlo simulations incorporating parallel tempering. At large N we find that some instances have a discontinuous (first order) quantum phase transition during the evolution of the QAA. This fraction increases with increasing N and may tend to 1 for N -> infinity.Comment: 5 pages, 3 figures. Replaced with published version; two figures slightly changed and some small changes to the tex

Geometries for universal quantum computation with matchgates

Matchgates are a group of two-qubit gates associated with free fermions. They are classically simulatable if restricted to act between nearest neighbors on a one-dimensional chain, but become universal for quantum computation with longer-range interactions. We describe various alternative geometries with nearest-neighbor interactions that result in universal quantum computation with matchgates only, including subtle departures from the chain. Our results pave the way for new quantum computer architectures that rely solely on the simple interactions associated with matchgates.Comment: 6 pages, 4 figures. Updated version includes an appendix extending one of the result

Flight Gate Assignment with a Quantum Annealer

Optimal flight gate assignment is a highly relevant optimization problem from airport management. Among others, an important goal is the minimization of the total transit time of the passengers. The corresponding objective function is quadratic in the binary decision variables encoding the flight-to-gate assignment. Hence, it is a quadratic assignment problem being hard to solve in general. In this work we investigate the solvability of this problem with a D-Wave quantum annealer. These machines are optimizers for quadratic unconstrained optimization problems (QUBO). Therefore the flight gate assignment problem seems to be well suited for these machines. We use real world data from a mid-sized German airport as well as simulation based data to extract typical instances small enough to be amenable to the D-Wave machine. In order to mitigate precision problems, we employ bin packing on the passenger numbers to reduce the precision requirements of the extracted instances. We find that, for the instances we investigated, the bin packing has little effect on the solution quality. Hence, we were able to solve small problem instances extracted from real data with the D-Wave 2000Q quantum annealer.Comment: Updated figure