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]

The Selectric Typewriter

 The Selectric Typewriter

The IBM ® Selectric typewriter was a radical innovation that completely disrupted the business typewriter market. It transformed the speed, accuracy and flexibility with which people could generate the written word, and helped pave the way for the use of typewriter keyboards as the primary method for humans to interact with computers...

Todays Thought

In hatred as in love, we grow like the thing we brood upon. What we loathe, we graft into our very soul. 

-Mary Renault, novelist (4 Sep 1905-1983)

Todays Thought

 Form follows function. 

-Louis Sullivan, architect (3 Sep 1856-1924)

Todays Thought

When wealth is passed off as merit, bad luck is seen as bad character. This is how ideologues justify punishing the sick and the poor. But poverty is neither a crime nor a character flaw. Stigmatize those who let people die, not those who struggle to live. 

-Sarah Kendzior, journalist and author (b. 1 Sep 1978)

Todays Thought

The decent moderation of today will be the least of human things tomorrow. At the time of the Spanish Inquisition, the opinion of good sense and of the good medium was certainly that people ought not to burn too large a number of heretics; extreme and unreasonable opinion obviously demanded that they should burn none at all. 

-Maurice Maeterlinck, poet, dramatist, and Nobel laureate (29 Aug 1862-1949)