Todays Thought

You have to laugh at the things that hurt you just to keep yourself in balance, just to keep the world from running you plumb crazy. 

-Ken Kesey, novelist (17 Sep 1935-2001)

Why is ATSC 3.0 Taking So Long?

 Why is ATSC 3.0 Taking So Long?

Commentary: The NextGen TV broadcast standard is facing several threats, including some of its own making.

A Short Guide to Hard Problems

 A Short Guide to Hard Problems

What’s easy for a computer to do, and what’s almost impossible? Those questions form the core of computational complexity. We present a map of the landscape.

Why Are There 7 Days In a Week? EXPLAINED

Frisco 11-year-old sets off on secret mission to help the homeless

Frisco 11-year-old sets off on secret mission to help the homeless 

11-year-old Treyson Pierce started a fundraiser in May, but kept it hidden from his mom.

Occam's Razor - rational principles explained

Grover's algorithm

 Grover's algorithm

n quantum computing, Grover's algorithm, also known as the quantum search algorithm, refers to a quantum algorithm for unstructured search that finds with high probability the unique input to a black box function that produces a particular output value, using just ${\displaystyle �(\sqrt{�})}$ evaluations of the function, where ${\displaystyle �}$ is the size of the function's domain. It was devised by Lov Grover in 1996.^[1]

The analogous problem in classical computation cannot be solved in fewer than ${\displaystyle �(�)}$ evaluations (because, on average, one has to check half of the domain to get a 50% chance of finding the right input). Charles H. Bennett, Ethan Bernstein, Gilles Brassard, and Umesh Vazirani proved that any quantum solution to the problem needs to evaluate the function ${\displaystyle \mathrm{\Omega }(\sqrt{�})}$ times, so Grover's algorithm is asymptotically optimal.^[2] Since classical algorithms for NP-complete problems require exponentially many steps, and Grover's algorithm provides at most a quadratic speedup over the classical solution for unstructured search, this suggests that Grover's algorithm by itself will not provide polynomial-time solutions for NP-complete problems (as the square root of an exponential function is an exponential, not polynomial, function).^[3]

Unlike other quantum algorithms, which may provide exponential speedup over their classical counterparts, Grover's algorithm provides only a quadratic speedup. However, even quadratic speedup is considerable when ${\displaystyle �}$ is large, and Grover's algorithm can be applied to speed up broad classes of algorithms.^[3] Grover's algorithm could brute-force a 128-bit symmetric cryptographic key in roughly 2⁶⁴ iterations, or a 256-bit key in roughly 2¹²⁸ iterations. It may not be the case that Grover's algorithm poses a significantly increased risk to encryption over existing classical algorithms, however.^[4]