A graduate student solved the problem of confirming quantum computing

Urmila Mahadev spent eight years in the master's program in search of an answer to one of the most basic questions of quantum computing: how do we know that the quantum computer did at least something at the quantum level?


 
A graduate student solved the problem of confirming quantum computing  
 
In the spring of 201? Urmila Mahadev was in a good position, in terms of the majority of graduate students. She has just solved the most important problem of quantum computing - the field of computer studies, deriving its capabilities from the strange laws of quantum physics. Together with her earlier works, Mahadev’s new result describing the so-called “Blind computation,” ...[/h]
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The principle of least action. Part 2

 3r3755. 3r3-31. The principle of least action. Part 2 last time
We briefly reviewed one of the most remarkable physical principles - the principle of least action, and stopped on an example that seemed to contradict it. In this article we will deal with this principle in a little more detail and see what happens in this example. 3r33737.  3r3755. 3r311.
3r33737.  3r3755. This time we need a little more math. However, I will again try to explain the main part of the article at an elementary level. I will highlight a bit more strict and difficult points, they can be skipped without prejudice to the basic understanding of the article. 3r33737...
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Solving the problem of finding the center line of a vessel

 3r? 3522. 3r3-31. 3r38080. The essence of the task
 3r? 3522. In the process of medical diagnosis, it may be necessary to examine the vessels of the patient. Such a study is called angiography. With the advent of tomographs, in addition to classical angiography, MRI and CT angiography methods have appeared, which, in contrast to traditional angiography, which gives only a flat image in one projection, allow us to obtain a complete three-dimensional representation of the vessels. To carry out such studies, a contrast is injected into the patient’s blood — a special substance that makes the vessels ...
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Sub-Zero: antique mechanical calculator. How to use it (with greetings from the 18th century)

Sub-Zero: antique mechanical calculator. How to use it (with greetings from the 18th century)A surprisingly elegant machine that has come down to us from those ancient times when not that the Internet did not exist - there were not even computers yet. Several characteristics of Sub-Zero, which were once emphasized by the marketers who promoted it: (1) works with numbers ± 999999; (2) adds and subtracts in seconds; (3) never wrong; (4) amazingly easy to use; (5) works silently; (6) made of high quality materials that meet German standards; (7) does not wear out. Created to live long.
 
So what is this machine? How does she perform calculations? What is her filling? How to use it for addition ...
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The secrets of impossible computing on GPU

Our experience of using a computing cluster of 480 AMD RX 480 GPU in solving math problems. As a problem, we took the proof of the theorem from the article by Professor A. Chudnov. “ Cyclic decompositions of sets, separating digraphs and cyclic classes of games with guaranteed win “. The task is to find the minimum number of participants of one coalition in coalition games Nim-type, guaranteeing the winning of one of the parties.
 
 
The secrets of impossible computing on GPU  
...
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The principle of least action. Part 1

The principle of least action. Part 1  
 
When I first learned about this principle, I had a feeling of some kind of mysticism. It seems that nature mysteriously sorts through all possible paths of movement of the system and selects the best of them.
 
 
Today I want to talk a little bit about one of the most remarkable physical principles - the principle of least action.
 
 

Prehistory


 
Since the time of Galileo, it was known that bodies, on which no forces act, move along straight lines, that is, along the shortest path. Light lines propagate along straight lines.
 
 
When reflected, the light also moves in such a way as to get from ...[/h]
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Twenty tasks (for crazy, amazing geometry)

Twenty tasks (for crazy, amazing geometry) 3r33556. 3r3-31. 3r? 3539. Warning doctor. 3r33540. Beware of these puzzles. Side effects can include lost afternoons, crumpled hair and exclamations “Aaaaah, here’s how it's done” are so loud that they can crack window glass. 3r3544.  3r33556. 3r3544.  3r33556. A few months ago I stumbled upon a math puzzle on Twitter. Catriona Shearer . They immediately fascinated me: each puzzle is so tangible, handmade, as if asking for it to be solved. And for each you can easily spend an hour of time, or even more. 3r3544.  3r33556. 3r3544.  3r33556. Ekaterin allowed me 3r3r14. hang
you on these puzzles ...
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These are the right bees: mechanical adaptation to dynamic effects

 3r33357. 3r3-31. These are the right bees: mechanical adaptation to dynamic effects 3r33333. 3r33337.  3r33357. 3r33337.  3r33357. 3r33333. The basis of the study [/b] 3r33337.  3r33357. 3r33337.  3r33357. At first glance, such a study seems a bit silly, because in essence it is the answer to the question “what would happen if you poke a stick at the hive?”. Well, firstly, this is not worth doing, as the bees are very touchy creatures (and stinging). Secondly, any living being, like any device, works according to a certain algorithm. In the case of bees, this algorithm is common to the entire swarm. From the point of view of mathematics, programming, and even the mechanics ...
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We calculate "magic squares" with the help of GPU

Hello habr.
 
 
The theme of "magic squares" is quite interesting, because on the one hand, they are known since antiquity, on the other hand, the calculation of the "magic square" even today is a very difficult computational problem. Recall that in order to construct the "magic square" NxN, it is necessary to write the numbers 1N * N so that the sum of its contours, verticals and diagonals is equal to the same number. If you just sort through the number of all the options for placing the digits for a 4x4 square, you get 16! = ??? ??? options.
 
 
We will think about how this can be done more effectively.
 
We calculate "magic squares" with the help of GPU ...
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Output of the curve function for smoothly limiting parameters, signals and not only in Wolfram Mathematica

There are a number of problems in which the range of output values ​​should be limited, while the input data can not guarantee this. In addition to forced situations, limiting the signal can also be a goal-oriented task - for example, when compressing a signal or implementing the "overdrive" effect.
 
 
The simplest implementation of a constraint is to force a certain value when a certain level is exceeded. For example, for a sinusoid with an increasing amplitude, it will look like this:
 
 
Output of the curve function for smoothly limiting parameters, signals and not only in Wolfram Mathematica  
 
In the role of the limiter, the function Clip acts here, as the argument of which the input signal and the constraint ...
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