Transcript cuantica
Richard Feynman: "El carácter de la ley física. Computer technology is making devices smaller and smaller… …reaching a point where classical physics is no longer a suitable model for the laws of physics. Physics and Computation • Information is stored in a physical medium, and manipulated by physical processes. • The laws of physics dictate the capabilities of any information processing device. • Designs of “classical” computers are implicitly based in the classical framework for physics • Classical physics is known to be wrong or incomplete… and has been replaced by a more powerful framework: quantum mechanics. The nineteenth century was known as the machine age, the twentieth century will go down in history as the information age. I believe the twentyfirst century will be the quantum age. Paul Davies, Professor Natural Philosophy – Australian Centre for Astrobiology The design of devices on such a small scale will require engineers to control quantum mechanical effects. Allowing computers to take advantage of quantum mechanical behaviour allows us to do more than cram increasingly many microscopic components onto a silicon chip… … it gives us a whole new framework in which information can be processed in fundamentally new ways. Un experimento óptico sencillo: 1 Detectores de fotones 0 Fuente de fotones Espejo semiplateado Consideremos que pasa si disparamos un único fotón: 1 50% 0 50% Explicación simple: el espejo semiplateado actúa como una moneda clásica, de forma aleatoria manda cada fotón a un detector u otro. Consideremos una modificación del experimento: Desde el punto de vista clásico esperaríamos que a pesar de la modificación, siguiéramos obteniendo experimentalmente una distribución 50-50… 1 100% E1 0 E2 Espejo normal Pero eso no ocurre: siempre se detecta en el mismo detector. Probabilidades clásicas Calcularemos las probabilidades de que el fotón llegue a uno de los dos detectores 0 o 1 a través de un árbol de posibilidades (los cuatro caminos posibles). 1 2 E1 1 2 1 2 1 2 E2 1 2 0 1 0 1 1 1 1 2 2 4 1 1 1 2 2 4 1 1 1 2 2 4 1 1 1 P (0) 4 4 2 1 1 1 2 2 4 P (1) 1 1 1 4 4 2 …vs probabilidades cuánticas. In quantum physics, we have probability amplitudes, which can have complex phase factors associated with them. 1 2 1 2 1 2 |0 1 2 |1 1 2 |0 1 2 |1 The probability amplitude associated with a path in the computation tree is obtained by multiplying the probability amplitudes on that path. In the example, the red path has amplitude 1/2, and the green path has amplitude –1/2. The probability amplitude for getting the answer |0 is obtained by adding the probability amplitudes… notice that the phase factors can lead to cancellations! The probability of obtaining |0 is obtained by squaring the total probability amplitude. In the example the probability of getting |0 is 2 1 1 0 2 2 Consideremos que pasa si disparamos un único fotón: 1 50% 0 50% ( x) e i …vs probabilidades cuánticas. 1 2 1 2 1 2 |0 1 2 |1 1 2 |0 1 2 |1 2 1 1 0 2 2 Explanation of experiment … consider a modification of the experiment… 100% The simplest explanation for 1 1 the modified setup would still 0 0 1 0 predict a 50-50 distribution… 2 2 1 1 2 0 1 1 1 1 01 2 2 1 0 2 full mirror When do we use which probability rules? •If no path information is revealed, we must use the quantum probability rules. •If full path information is revealed, we must use the classical probability rules. •If partial path information is revealed, we must use a combination of the two; i.e. there is a more general set of rules that encapsulates both. Quantum mechanics and information Any physical medium capable of representing 0 and 1 is in principle capable of storing any linear combination 0 0 1 1 What does 0 0 1 1 really mean?? It’s a “mystery”. THE mystery. We don’t understand it, but we can tell you how it works. (Feynman) The world of the quantum may be bizarre, but it is our world and our future. Gerard Milburn, author of Schrödinger’s Machines. Quantum mechanics and information Any physical medium capable of representing 0 and 1 is in principle capable of storing any linear combination 0 0 1 1 How does this affect computational complexity? How does this affect information security? How does this affect communication complexity? Would you believe a quantum proof? How does quantum information help us better understand physics? How does this affect what is feasibly computable? Which “infeasible” computational tasks become “feasible”? How does this affect “computationally secure” cryptography? What new computationally secure cryptosystems become possible?