Efficient, direct compilation of SU(N) operations into SNAP & Displacement gates

We present a function which connects the parameter of a previously published short sequence of selective number-dependent arbitrary phase (SNAP) and displacement gates acting on a qudit encoded into the Fock states of a superconducting cavity, $V_k(\alpha)=D(\alpha)R_\pi(k)D(-2\alpha)R_\pi(k)D(\alpha)$ to the angle of the Givens rotation $G(\theta)$ on levels $|k\rangle,|k+1\rangle$ that sequence approximates, namely $\alpha=\Phi(\theta) = \frac{\theta}{4\sqrt{k+1}}$. Previous publications left the determination of an appropriate $\alpha$ to numerical optimization at compile time. The map $\Phi$ gives us the ability to compile directly any $d$-dimensional unitary into a sequence of SNAP and displacement gates in $O(d^3)$ complex floating point operations with low constant prefactor, avoiding the need for numerical optimization. Numerical studies demonstrate that the infidelity of the generated gate sequence $V_k$ per Givens rotation $G$ scales as approximately $O(\theta^6)$. We find numerically that the error on compiled circuits can be made arbitrarily small by breaking each rotation into $m$ $\theta/m$ rotations, with the full $d\times d$ unitary infidelity scaling as approximately $O(m^{-4})$. This represents a significant reduction in the computational effort to compile qudit unitaries either to SNAP and displacement gates or to generate them via direct low-level pulse optimization via optimal control.Comment: 6 pages, 2 figure

Quantum adiabatic machine learning by zooming into a region of the energy surface

Recent work has shown that quantum annealing for machine learning, referred to as QAML, can perform comparably to state-of-the-art machine learning methods with a specific application to Higgs boson classification. We propose QAML-Z, an algorithm that iteratively zooms in on a region of the energy surface by mapping the problem to a continuous space and sequentially applying quantum annealing to an augmented set of weak classifiers. Results on a programmable quantum annealer show that QAML-Z matches classical deep neural network performance at small training set sizes and reduces the performance margin between QAML and classical deep neural networks by almost 50% at large training set sizes, as measured by area under the receiver operating characteristic curve. The significant improvement of quantum annealing algorithms for machine learning and the use of a discrete quantum algorithm on a continuous optimization problem both opens a class of problems that can be solved by quantum annealers and suggests the approach in performance of near-term quantum machine learning towards classical benchmarks

Causality Relationship between Agricultural Exports and Economic Growth in Ethiopia: A Case of Coffee,Oilseed and Pulses

This article investigated the causal relationships between agricultural exports and economic growth (GDP) in Ethiopia usin time series data for forty one years from 1973 to 2013. The study used Augmented Dickey Fuller (Dickey and Fuller, 1979) and Phillips-Perron(PP) (Phillips and Perron, 1988) to test for unit root and Granger  model to test causality. The result of stationarity test reveals that the null hypothesis that the variables have a unit root is not rejected in the case of all the variables at level form I (0). However, the null hypothesis that the first-differences of these variables have a unit root is rejected. This showed that, the series data is stationary at first difference and hence the variables are considered as integrated of order one or I (1) process. On the other hand the causality relationship found that there is bidirectional relationship between coffee export, oilseed export and economic growth whereas unidirectional relationship was found between pulses export and economic growth which is running from pulse export to economic growth (GDP). Based on the findings, it is recommended that policies aimed at increasing the productivity and quality of these cash crops should be implemented. Also additional value should be added to them before exporting. Correspondingly, there is also a need to devote resources on the production of non-export goods in order to increase exports since they have bi directional relationship. When this is done, it will lead to a higher rate of economic growth in Ethiopia Keywords: Agriculture, Agricultural exports, Economic growth, causality