long ago in an ancient land there lived the king who was bored and wanted a new challenging game a wise man invented chess on brought it to the king the King liked it so much he offered the man any reward he wanted the man asked for a grain of rice for the first square of the chessboard two grains for the next and so on for the 64 squares it’s a square doubling the number of grains of the square before the King thought this would be easy but the number of grains raised to an astronomical sum as usual by computers were designed to play chess even world chess champion Garry Kasparov was bitten by a machine in 1997 so how could a humble amateur even dream of beating a computer with this knowledge will become unbeatable and humanity will perish to the parallels computers [Music] [Music] quantum chess works in a similar way to classical chess but pcs are described by a wave function they are obviously confined to a square chess board this can be mobilized based where potential well with 8l l being the size of each box the wave function is characterized by the position of the piece for example this piece is in the fifth horizontal Square and sixth vertical square therefore we have chosen M and M to be 5 and 6 respectively the chess world has 64 squares will then consider a sixty four dimensional basis as we have the wave functions of a potential well we know that they are orthogonal ok let’s fast forward to the interesting part considering this game is quantum common quantum effects can be appreciated such as the infamous tunnel effect it is known that in classical chess the knight can jump over any piece in quantum chess however any piece may do this tunneling through another piece there’s a significant difference though the probability of jumping won’t be a hundred percent and the wavefunction of the piece will change subsequently the probability of champion will be given by the following transmission coefficient the throat again we eventually arrive to this position now we want to move the rook channeling through this pawn but how can we do this when I want to move the rook but there’s a pond in the middle that creates a potential barrier of let’s look at our table yep 10 electron volts looking at the energy of the tower and the length of the square we want to Taurus Pass will substitute these values in the previous formula and we get the following probabilities note the tail is 0.01 nanometers you’ll be thinking there’s no way the world is stopped small but to worry not we are just looking at things through a microscope so what happens if we take it away okay back to our problem when you move the rule once you decide the direction in which you are moving you can’t change its position in the other axis so we can consider a one-dimensional potential well the wave function we obtain is the following we have considered that the work can be in two places with different probabilities don’t forget to normalize now the Night Moves classically that’s a check the Black Knight is threatening the white king so we’ll want to capture it but should we do it with the rook over the Queen let’s see which mode gives us the highest probability for success we want the probability of London in the square where X is between l and 2l therefore the probability will be given by the following integral this probability is say independent so it will oscillate we want to maximize it and this will happen when the cosine is 1 using the data we have a numerical value for T however if you want to move the Queen we’ll need to take into account that for a given x position we can have several values for y this is a wave function we have to consider will make a similar integral with respect to two variables which is separable multiplying the probability of X being between l and 2l and the probability of Y being between 2l and 3 L we obtain this probability it is obvious that we have higher probability of success if we move the rook we now just have to wait for the probability to be maximum for this exercise we’ve been inspired by a real quantum chess game in this game there are two types of moves standard classical moves and quantum knows pawns can’t go quantum in a quantum move you can move up to two standard moves but you will have a 50% chance of not having moved at all to know what is actually going on one mistake in measurement this will happen when you try to capture a piece since only one piece can be at each square at the same time once you make a measurement the wavefunction of the piece collapses and the pieces that are found or not found at the square you are making the measurement in will apply these rules for the last part of the game consider the black work is divided in two with these probabilities we can checkmate by either making a standard move with this 25% work or a quantum move with the 75% one if blood chooses to make a standard move the Rope would keep its current probabilities but the 25% one would be the one threatening the kingdom with the quantum of however the rule could be in three different squares with twenty five thirty seven point five and 37.5% probabilities there for quantum move is a smarter you human fools I already knew about that now I will move this 75 percent rope to get higher chances of winning [Music] well that was CeCe [Applause] [Music]

infinitamente genial