{"id":3093,"date":"2021-01-11T12:31:05","date_gmt":"2021-01-11T10:31:05","guid":{"rendered":"https:\/\/inlab.fib.upc.edu\/?p=3093"},"modified":"2021-01-11T12:31:05","modified_gmt":"2021-01-11T10:31:05","slug":"que-puede-aportar-la-fisica-cuantica-la-computacion","status":"publish","type":"post","link":"https:\/\/inlab.fib.upc.edu\/es\/uncategorized-ca-en\/que-puede-aportar-la-fisica-cuantica-la-computacion","title":{"rendered":"\u00bfQu\u00e9 puede aportar la f\u00edsica cu\u00e1ntica a la computaci\u00f3n?"},"content":{"rendered":"<p>\u00bfOs imagin\u00e1is un ordenador haciendo c\u00e1lculos extraordinariamente complejos, de los que s\u00f3lo de pensarlo ya causan v\u00e9rtigo, mientras tom\u00e1is tranquilamente una taza de caf\u00e9? Pues quiz\u00e1s no hay que imaginarlo mucho.<\/p>\n<p>Un grupo de centros de investigaci\u00f3n chinos, liderados por Jian-Wei Pan y Chao-Yang Lu, ha creado un sistema cu\u00e1ntico llamado Jiuzhang que ha sido capaz de resolver unos c\u00e1lculos extremadamente complicados en 200 segundos.<\/p>\n<p><!--more--><\/p>\n<p>\u00bfOs imagin\u00e1is un ordenador haciendo c\u00e1lculos extraordinariamente complejos, de los que s\u00f3lo de pensarlo ya causan v\u00e9rtigo, mientras tom\u00e1is tranquilamente una taza de caf\u00e9? Pues quiz\u00e1s no hay que imaginarlo mucho.<\/p>\n<p>Un grupo de centros de investigaci\u00f3n chinos, liderados por Jian-Wei Pan y Chao-Yang Lu, ha creado un sistema cu\u00e1ntico llamado Jiuzhang &#8211; en honor a un manual pr\u00e1ctico de matem\u00e1ticas escrito entre los siglos I y II AEC en China &#8211; que ha sido capaz de resolver unos c\u00e1lculos extremadamente complicados en 200 segundos; hito que public\u00f3 la revista <em>Science <\/em>el pasado 18 de diciembre. Para resolver el mismo problema, un superordenador convencional habr\u00eda tardado 2.500 millones de a\u00f1os! Tomar una taza de caf\u00e9 o esperar que la evoluci\u00f3n vaya desde las bacterias hasta nosotros. Esta escala de tiempo representa la mitad de la edad de la Tierra. As\u00ed pues, la eficiencia incrementa en un factor de 10<sup>14<\/sup>.<\/p>\n<p>Los c\u00e1lculos que aborda el proyecto chino para demostrar la potencia de su sistema cu\u00e1ntico se corresponden a un problema de f\u00edsica de part\u00edculas conocido como \u00abmuestreo de bosones\u00bb. Este sistema cu\u00e1ntico pionero que han desarrollado se caracteriza porque sus qubits son fotones y trabaja a temperatura ambiente. En contraposici\u00f3n, en el a\u00f1o 2019 Google present\u00f3 la computadora cu\u00e1ntica Sycamore de 53 qubits, la cual, a diferencia del sistema cu\u00e1ntico Jiuzhang, es programable pero tiene que trabajar a temperaturas cercanas al cero absoluto, -273.15 \u00b0 C. A pesar de que el sistema cu\u00e1ntico Jiuzhang no es programable y s\u00f3lo resuelve unos c\u00e1lculos en concreto, si el problema es bastante relevante, puede ser interesante construir una m\u00e1quina espec\u00edficamente para abordarlo. Este proyecto chino ha demostrado la utilidad de la fot\u00f3nica para construir ordenadores cu\u00e1nticos y ha arreciado esta l\u00ednea de investigaci\u00f3n.<\/p>\n<p>Para entender el enorme potencial que ofrece la tecnolog\u00eda cu\u00e1ntica es importante presentar el qubit.<\/p>\n<p>En primer lugar repasamos como se define el bit. El bit &#8211; del ingl\u00e9s,<strong> bi<\/strong>nary digi<strong>t<\/strong>, \u00abd\u00edgito binario\u00bb &#8211; es la unidad de informaci\u00f3n m\u00ednima utilizada en Inform\u00e1tica y en Teor\u00eda de la Informaci\u00f3n. Un bit puede tener solo dos estados mutuamente excluyentes que se representan habitualmente con 0 y 1.<\/p>\n<p>El desarrollo de la mec\u00e1nica cu\u00e1ntica permite establecer una nueva unidad de informaci\u00f3n: el qubit &#8211; del ingl\u00e9s, <strong>qu<\/strong>antum <strong>bit &#8211;<\/strong>. Los posibles estados del qubit son el |0\u27e9 y |1\u27e9 siguiendo la notaci\u00f3n de Dirac, que es la notaci\u00f3n est\u00e1ndar para los estados en mec\u00e1nica cu\u00e1ntica, y son an\u00e1logos a los estados 0 y 1 del bit cl\u00e1sico. La diferencia del qubit respecto del bit es que el qubit es una combinaci\u00f3n lineal de ambos estados |0\u27e9 y |1\u27e9, hecho que recibe el nombre de superposici\u00f3n.<br \/>\n&nbsp;<\/p>\n<p align=\"center\">|\u03c8\u27e9 = \u03b1 |0\u27e9 + \u03b2 |1\u27e9<\/p>\n<p>&nbsp;<\/p>\n<p>Los coeficientes \u03b1 y \u03b2 son n\u00fameros complejos (\u03b1, \u03b2&nbsp;<b style=\"color: rgb(32, 33, 36); font-family: arial, sans-serif; font-size: 16px;\">\u2208&nbsp;<\/b>\u2102) y determinan con qu\u00e9 probabilidad se obtienen los estados |0\u27e9 y |1\u27e9 cuando se hace una medida. De este modo, cuando <strong>medimos <\/strong>un qubit obtenemos el valor 0 con una probabilidad |\u03b1|<sup>2<\/sup>&nbsp;<strong>o <\/strong>el valor 1 con una probabilidad |\u03b2|<sup>2<\/sup>. Dado que la suma de las probabilidades correspondientes a todos los estados posibles es siempre 1, obtenemos la siguiente relaci\u00f3n:&nbsp;|\u03b1|<sup>2&nbsp;<\/sup>+ |\u03b2|<sup>2<\/sup>&nbsp;= 1.<\/p>\n<p>&nbsp;<\/p>\n<p class=\"rtecenter\"><img decoding=\"async\" alt=\"\" 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\" \/><\/p>\n<p align=\"center\">Figura 1. Representaci\u00f3n gr\u00e1fica del bit cl\u00e1sioc vs. la Esfera de Bloch (representaci\u00f3n de un 1 qubit).<\/p>\n<p>&nbsp;<\/p>\n<p>\nLa superposici\u00f3n de estados que introduce el qubit se extiende cuando en lugar de tener 1 qubit tenemos m\u00e1s. As\u00ed pues observamos que:<\/p>\n<ul>\n<li>1 bit puede ser 0 <strong>o <\/strong>1 mientras que 1 qubit representa una superposici\u00f3n de 0 <strong>y <\/strong>1.<\/li>\n<li>2 bits pueden ser 00, 01, 10 <strong>o <\/strong>11 mientras que 2 qubits representan una superposici\u00f3n de 00, 01, 10 <strong>y <\/strong>11.<\/li>\n<li>3 bits pueden ser 000, 001, 010, 011, 100, 101, 110 <strong>o <\/strong>111 mientras que 3 qubits representan una superposici\u00f3n de 000, 001, 010, 011, 100, 101, 110 <strong>y <\/strong>111.<\/li>\n<\/ul>\n<p>Y as\u00ed sucesivamente, de modo que un sistema cu\u00e1ntico con N qubits representa 2<sup>N<\/sup> estados <strong>simult\u00e1neamente<\/strong>.<\/p>\n<p>&nbsp;<\/p>\n<p align=\"center\"><img decoding=\"async\" alt=\"\" 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\" \/><\/p>\n<p align=\"center\">Figura 2. Representaci\u00f3n del Bit cl\u00e1sico vs. Representaci\u00f3n del Qubit.<\/p>\n<p align=\"center\">&nbsp;<\/p>\n<p>\nPor lo tanto, por un lado un sistema <strong>cl\u00e1sico <\/strong>funciona siguiendo una l\u00f3gica booleana y opera <strong>secuencialmente <\/strong>sobre N bits y, por otro lado, un sistema <strong>cu\u00e1ntico <\/strong>sigue una l\u00f3gica cu\u00e1ntica que permite operar en <strong>paralelo <\/strong>sobre&nbsp;2<sup>N<\/sup> estados.<\/p>\n<p>Del mismo modo que los sistemas cl\u00e1sicos utilizan las conocidas puertas l\u00f3gicas &#8211; AND, OR, XOR, NOT -, los sistemas cu\u00e1nticos se rigen por puertas cu\u00e1nticas. La naturaleza de las puertas cu\u00e1nticas viene establecida por la mec\u00e1nica cu\u00e1ntica y una de las propiedades m\u00e1s interesante es que, a diferencia de las puertas l\u00f3gicas de los sistemas cl\u00e1sicos, son reversibles.<\/p>\n<p>Esta breve explicaci\u00f3n plasma algunos de los aspectos fundamentales de la computaci\u00f3n cu\u00e1ntica que justifican el gran potencial de la revoluci\u00f3n cu\u00e1ntica que estamos viviendo. Actualmente, hay varias iniciativas dedicadas a investigar y desarrollar la emergente tecnolog\u00eda cu\u00e1ntica. En la Uni\u00f3n Europea est\u00e1 en marcha el proyecto Quantum Flagship, que cuenta con una financiaci\u00f3n de 1.000 millones de euros; en Estados Unidos hay una iniciativa cu\u00e1ntica nacional, que cuenta con 1.200 millones de d\u00f3lares, y China esta construyendo un laboratorio inmenso de tecnolog\u00eda cu\u00e1ntica y el programa nacional est\u00e1 dotado con 15.000 millones de d\u00f3lares.<\/p>\n<p>En un futuro, con la ayuda de la tecnolog\u00eda cu\u00e1ntica se espera que haya grandes avances en campos como la inteligencia artificial, la ciberseguridad o el desarrollo de redes neuronales cu\u00e1nticas, entre otras aplicaciones que ahora mismo no hemos ni imaginado debido al estado embrionario en el que a\u00fan se encuentra.<\/p>\n<p>Por \u00faltimo, es conveniente recordar la efem\u00e9ride del 9 de enero de 1954, cuando la empresa IBM present\u00f3 en Nueva York la primera calculadora de circuitos integrales o cerebro electr\u00f3nico ya que es posible que nosotros, ahora mismo, estemos viviendo un momento hist\u00f3rico an\u00e1logo con los avances en tecnolog\u00eda cu\u00e1ntica que pronostican un futuro esperanzador y lleno de nuevas posibilidades.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>BIBLIOGRAF\u00cdA \/ REFERENCIAS<\/strong>&nbsp;<\/p>\n<p>Nielsen, M. A. &amp; Chuang, I. L. (2012). Quantum Computation and Quantum Information. Cambridge: Cambridge University Press.<\/p>\n<p>Zhong HS, Wang H, Deng YH, Chen MC, Peng LC, Luo YH, Qin J, Wu D, Ding X, Hu Y, Hu P, Yang XY, Zhang WJ, Li H, Li Y, Jiang X, Gan L, Yang G, You L, Wang Z, Li L, Liu NL, Lu CY, Pan JW (2020). Quantum computational advantage using photons. Science 370(6523):1460-1463.<\/p>\n<p>Arute F, Arya K, Babbush R, Bacon D, et al. (2019). Quantum supremacy using a programmable superconducting processor. Nature. 574(7779):505-510.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u00bfOs imagin\u00e1is un ordenador haciendo c\u00e1lculos extraordinariamente complejos, de los que s\u00f3lo de pensarlo ya causan v\u00e9rtigo, mientras tom\u00e1is tranquilamente una taza de caf\u00e9? Pues quiz\u00e1s no hay que imaginarlo mucho. Un grupo de centros de investigaci\u00f3n chinos, liderados por Jian-Wei Pan y Chao-Yang Lu, ha creado un sistema cu\u00e1ntico llamado Jiuzhang que ha sido [&hellip;]<\/p>\n","protected":false},"author":594,"featured_media":3089,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[590],"tags":[],"experteses":[],"class_list":["post-3093","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-uncategorized-ca-en"],"acf":[],"_links":{"self":[{"href":"https:\/\/inlab.fib.upc.edu\/es\/wp-json\/wp\/v2\/posts\/3093","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/inlab.fib.upc.edu\/es\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/inlab.fib.upc.edu\/es\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/inlab.fib.upc.edu\/es\/wp-json\/wp\/v2\/users\/594"}],"replies":[{"embeddable":true,"href":"https:\/\/inlab.fib.upc.edu\/es\/wp-json\/wp\/v2\/comments?post=3093"}],"version-history":[{"count":0,"href":"https:\/\/inlab.fib.upc.edu\/es\/wp-json\/wp\/v2\/posts\/3093\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/inlab.fib.upc.edu\/es\/wp-json\/wp\/v2\/media\/3089"}],"wp:attachment":[{"href":"https:\/\/inlab.fib.upc.edu\/es\/wp-json\/wp\/v2\/media?parent=3093"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/inlab.fib.upc.edu\/es\/wp-json\/wp\/v2\/categories?post=3093"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/inlab.fib.upc.edu\/es\/wp-json\/wp\/v2\/tags?post=3093"},{"taxonomy":"experteses","embeddable":true,"href":"https:\/\/inlab.fib.upc.edu\/es\/wp-json\/wp\/v2\/experteses?post=3093"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}