Introduction: With the advent of the FinTech revolution, technology and innovation have taken centre stage throughout the globe. Every business alike, ranging from multi-national companies [...]
Reading Time: 3minutes Eunice Wong is on a mission to show other people, especially women, that they can become financially independent and has found she has a natural flaw for trading – something that surprised her as she never studied finance. “Actually I wanted to be a rock star when I was younger. […]
The humble and frankly unrecognisable origins of esports make today’s spectacle seem all the more impressive. It wasn’t always ratings busting viewerships and...
The $textit{stabilizer rank}$ of a quantum state $psi$ is the minimal $r$ such that $left| psi right rangle = sum_{j=1}^r c_j left|varphi_j rightrangle$ for $c_j in mathbb{C}$ and stabilizer states $varphi_j$. The running time of several classical simulation methods for quantum circuits is determined by the stabilizer rank of the $n$-th tensor power of single-qubit magic states. We prove a lower bound of $Omega(n)$ on the stabilizer rank of such states, improving a previous lower bound of $Omega(sqrt{n})$ of Bravyi, Smith and Smolin [7]. Further, we prove that for a sufficiently small constant $delta$, the stabilizer rank of any state which is $delta$-close to those states is $Omega(sqrt{n}/log n)$. This is the first non-trivial lower bound for approximate stabilizer rank. Our techniques rely on the representation of stabilizer states as quadratic functions over affine subspaces of $mathbb{F}_2^n$, and we use tools from analysis of boolean functions and complexity theory. The proof of the first result involves a careful analysis of directional derivatives of quadratic polynomials, whereas the proof of the second result uses Razborov-Smolensky low degree polynomial approximations and correlation bounds against the majority function.
Logistics costs in large part are determined by the underlying price of fuel. Over the past decade, fuel costs have dramatically increased, which has increased the cost of ocean, air and road freight. While 20Cube, a freight forwarder in Australia, goes above and beyond to streamline logistics processes and help customers save money, fuel prices are set by macroeconomic supply and demand forces beyond the control of any one industry actor. In this article, 20Cube shares three factors that influence shipping costs, giving you a better understanding of the market so you can anticipate changes early and be prepared. 1. […]
Whether you already are a real estate agent and you’re looking to relocate, or you’re in the process of getting your license, you’ve probably had your eyes set on selling homes in California.
