The U.S., EU, and UK are coordinating a significant sanctions and export controls package to be implemented if Russia takes further action in Ukraine.
Restrictions are likely to target key Russian industries including finance, energy, and defense and would be far more severe and far-reaching than past sanctions.
New export controls could include restrictions on foreign-produced items made using U.S.-origin technology or software,…
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.
Tips to Banks for Optimizing Security Level in their Mobile Banking Apps The popularity of mobile banking services is on top of in-branch banking systems. Nearly 75% of bank account holders are installing banking apps...
We’ve all heard the rumors; a bear market is coming eventually. Whether it be in 2 months or six months is up for anyone to guess; however, we know it will be here, and you want to be prepared when it does. It’s nothing new in the crypto industry, and those that have been here […]
Investing in a ticketing system is a good start, but how do you get the most out of it? To keep your customer service team running like a well-oiled machine, you need to optimize your support ticketing workflows. This article gives you the recipe for reduced handling times and increased agent productivity and responsiveness when addressing customer queries and concerns.
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