. . . "Quanten-Fouriertransformation"@de . . . . . . . "Transform\u00E9e de Fourier quantique"@fr . . . . "\u91CF\u5B50\u5085\u7ACB\u8449\u8B8A\u63DB\uFF08quantum Fourier transform\uFF09\u662F\u4E00\u7A2E\u96E2\u6563\u5085\u7ACB\u8449\u8B8A\u63DB\uFF0C\u5C07\u539F\u5F0F\u5206\u89E3\u6210\u66F4\u70BA\u7C21\u55AE\u7684\u591A\u500B\u4E48\u6B63\u77E9\u9663\u7684\u7A4D\u3002\u5229\u7528\u9019\u822C\u7684\u5206\u89E3\u65B9\u5F0F\uFF0C\u96E2\u6563\u5085\u7ACB\u8449\u8B8A\u63DB\u53EF\u4EE5\u7528\u4F5C\u91CF\u5B50\u96FB\u8DEF\uFF0C\u5176\u5305\u542B\u4E86\u591A\u500B\u54C8\u9054\u746A\u9598\u8207\u53D7\u63A7\u79FB\u76F8\u9598\u3002 \u91CF\u5B50\u5085\u7ACB\u8449\u8B8A\u63DB\u5728\u91CF\u5B50\u6F14\u7B97\u6CD5\u4E2D\u6709\u591A\u8655\u61C9\u7528\uFF0C\u4EE5\u5176\u53EF\u63D0\u4F9B\u76F8\u4F4D\u4F30\u7B97\u6B65\u9A5F\u7684\u7406\u8AD6\u57FA\u790E\uFF0C\u5728\u4E00\u4E9B\u6F14\u7B97\u6CD5\u4E2D\u4F54\u6838\u5FC3\u5730\u4F4D\uFF0C\u4F8B\u5982\u7528\u5728\u505A\u8CEA\u56E0\u6578\u5206\u89E3\u7684\u79C0\u723E\u6F14\u7B97\u6CD5\uFF08Shor's algorithm\uFF09\u3001\u4EE5\u53CA\uFF08hidden subgroup problem\uFF09\u3002"@zh . . . . "En informatique quantique, la transform\u00E9e de Fourier quantique (TFQ) est une transformation lin\u00E9aire sur des bits quantiques, et est l'analogie quantique de la transform\u00E9e de Fourier discr\u00E8te . La transform\u00E9e de Fourier quantique est l'un des nombreux algorithmes quantiques, qui incluent notamment l'algorithme de Shor qui permet de factoriser et de calculer le logarithme discret, l' algorithme d'estimation de phase quantique qui estime les valeurs propres d'un op\u00E9rateur unitaire et les algorithmes traitant du probl\u00E8me de sous-groupe cach\u00E9 . La transform\u00E9e de Fourier quantique a \u00E9t\u00E9 d\u00E9couverte par Don Coppersmith ."@fr . . . . . . . . . "Die Quanten-Fouriertransformation ist ein Algorithmus aus dem Gebiet der Quanteninformatik. Sie ist eine Zerlegung der diskreten Fouriertransformation in ein Produkt unit\u00E4rer Matrizen. Dadurch kann sie als Quantenschaltkreis aus Hadamard-Gattern und implementiert werden. Die Quanten-Fouriertransformation ist ein wesentlicher Bestandteil eines der prominentesten Quantenalgorithmen, des Shor-Algorithmus."@de . "In computazione quantistica, la trasformata di Fourier quantistica (abbreviazione dall'inglese: QFT) \u00E8 una trasformazione lineare su qubit, ed \u00E8 l'analogo quantistico della trasformata discreta di Fourier inversa. La trasformata di Fourier quantistica fa parte di molti algoritmi quantistici, in particolare l'algoritmo di fattorizzazione di Shor per fattorizzare e calcolare il logaritmo discreto, l'algoritmo quantistico di stima della fase per stimare gli autovalori di un operatore unitario, e algoritimi per il problema del sottogruppo nascosto. La trasformata di Fourier quantistica fu inventata da Don Coppersmith. La trasformata di Fourier quantistica pu\u00F2 essere effettuata efficientemente su un computer quantistico, con una particolare scomposizione in un prodotto di matrici unitarie pi\u00F9 semplici. Usando una semplice scomposizione, la trasformata di Fourier discreta su ampiezze pu\u00F2 essere implementato come un che consiste solo di porte di Hadamard e porte di phase shift controllate, dove \u00E8 il numero dei qubit. Ci\u00F2 pu\u00F2 essere paragonato alla trasformata di Fourier discreta classica, che ha porte (dove \u00E8 il numero dei bit), che \u00E8 esponenzialmente pi\u00F9 di . I migliori algoritmi noti per la trasformata di Fourier quantistica (agli ultimi anni 2000) necessitano solo di porte per ottenere una buona approssimazione."@it . "15266"^^ . "\u91CF\u5B50\u5085\u7ACB\u8449\u8B8A\u63DB\uFF08quantum Fourier transform\uFF09\u662F\u4E00\u7A2E\u96E2\u6563\u5085\u7ACB\u8449\u8B8A\u63DB\uFF0C\u5C07\u539F\u5F0F\u5206\u89E3\u6210\u66F4\u70BA\u7C21\u55AE\u7684\u591A\u500B\u4E48\u6B63\u77E9\u9663\u7684\u7A4D\u3002\u5229\u7528\u9019\u822C\u7684\u5206\u89E3\u65B9\u5F0F\uFF0C\u96E2\u6563\u5085\u7ACB\u8449\u8B8A\u63DB\u53EF\u4EE5\u7528\u4F5C\u91CF\u5B50\u96FB\u8DEF\uFF0C\u5176\u5305\u542B\u4E86\u591A\u500B\u54C8\u9054\u746A\u9598\u8207\u53D7\u63A7\u79FB\u76F8\u9598\u3002 \u91CF\u5B50\u5085\u7ACB\u8449\u8B8A\u63DB\u5728\u91CF\u5B50\u6F14\u7B97\u6CD5\u4E2D\u6709\u591A\u8655\u61C9\u7528\uFF0C\u4EE5\u5176\u53EF\u63D0\u4F9B\u76F8\u4F4D\u4F30\u7B97\u6B65\u9A5F\u7684\u7406\u8AD6\u57FA\u790E\uFF0C\u5728\u4E00\u4E9B\u6F14\u7B97\u6CD5\u4E2D\u4F54\u6838\u5FC3\u5730\u4F4D\uFF0C\u4F8B\u5982\u7528\u5728\u505A\u8CEA\u56E0\u6578\u5206\u89E3\u7684\u79C0\u723E\u6F14\u7B97\u6CD5\uFF08Shor's algorithm\uFF09\u3001\u4EE5\u53CA\uFF08hidden subgroup problem\uFF09\u3002"@zh . . . . . . . "En computaci\u00F3n cu\u00E1ntica, la transformada cu\u00E1ntica de Fourier es una transformaci\u00F3n sobre bits cu\u00E1nticos, y es la analog\u00EDa cu\u00E1ntica de la transformada de Fourier discreta. La transformada de Fourier es una parte de muchos algoritmos cu\u00E1nticos, el algoritmo de factorizaci\u00F3n de Shor y el c\u00E1lculo del logaritmo discreto, el algoritmo de estimaci\u00F3n de fase para estimar los eigenvalores de un operador unitario, y logaritmos para HSP (hidden subgroup problem). La transformada de Fourier puede ser realizada eficientemente en un ordenador cu\u00E1ntico, con una particular descomposici\u00F3n en un producto de matrices unitarias simples. Usando una descomposici\u00F3n simple, la trasformaci\u00F3n discreta de Fourier puede ser implementada como un circuito cu\u00E1ntico que tiene solo puertas Hadamard y puertas de desplazamiento de fase controladas, donde es el n\u00FAmero de qubits.\u200B Esto puede ser comparado con la transformada de Fourier discreta, que utiliza puertas (donde es el n\u00FAmero de bits), lo cual es exponencialmente mayor que . Sin embargo, la transformada cu\u00E1ntica de Fourier act\u00FAa sobre un estado cu\u00E1ntico, mientras que la trasformada de Fourier cl\u00E1sica act\u00FAa sobre un vector, as\u00ED que no todas las tareas que usan la transformada de Fourier cl\u00E1sica pueden utilizar la ventaja de esta aceleraci\u00F3n exponencial. Los mejores algoritmos cu\u00E1nticos de transformada de Fourier conocidos actualmente requieren solo puertas para alcanzar una aproximaci\u00F3n eficiente.\u200B"@es . . . . . . . . . . "Transformada Qu\u00E2ntica de Fourier"@pt . . "1123746557"^^ . . . . . "30872292"^^ . . . "In computazione quantistica, la trasformata di Fourier quantistica (abbreviazione dall'inglese: QFT) \u00E8 una trasformazione lineare su qubit, ed \u00E8 l'analogo quantistico della trasformata discreta di Fourier inversa. La trasformata di Fourier quantistica fa parte di molti algoritmi quantistici, in particolare l'algoritmo di fattorizzazione di Shor per fattorizzare e calcolare il logaritmo discreto, l'algoritmo quantistico di stima della fase per stimare gli autovalori di un operatore unitario, e algoritimi per il problema del sottogruppo nascosto. La trasformata di Fourier quantistica fu inventata da Don Coppersmith."@it . . "En computaci\u00F3n cu\u00E1ntica, la transformada cu\u00E1ntica de Fourier es una transformaci\u00F3n sobre bits cu\u00E1nticos, y es la analog\u00EDa cu\u00E1ntica de la transformada de Fourier discreta. La transformada de Fourier es una parte de muchos algoritmos cu\u00E1nticos, el algoritmo de factorizaci\u00F3n de Shor y el c\u00E1lculo del logaritmo discreto, el algoritmo de estimaci\u00F3n de fase para estimar los eigenvalores de un operador unitario, y logaritmos para HSP (hidden subgroup problem)."@es . . . . . . . . . . "Na computa\u00E7\u00E3o qu\u00E2ntica, a transformada de Fourier qu\u00E2ntica (abreviadamente: QFT) \u00E9 uma transforma\u00E7\u00E3o linear em bits qu\u00E2nticos e \u00E9 o an\u00E1logo qu\u00E2ntico da transformada discreta inversa de Fourier . A transformada de Fourier qu\u00E2ntica \u00E9 uma parte de muitos algoritmos qu\u00E2nticos, notavelmente o algoritmo de Shor para fatorar e calcular o logaritmo discreto, o algoritmo de estimativa de fase qu\u00E2ntica para estimar os valores pr\u00F3prios de um operador unit\u00E1rio e algoritmos para o problema do subgrupo oculto . A transformada qu\u00E2ntica de Fourier foi inventada por Don Coppersmith ."@pt . "\u91CF\u5B50\u5085\u7ACB\u8449\u8B8A\u63DB"@zh . . . . "Na computa\u00E7\u00E3o qu\u00E2ntica, a transformada de Fourier qu\u00E2ntica (abreviadamente: QFT) \u00E9 uma transforma\u00E7\u00E3o linear em bits qu\u00E2nticos e \u00E9 o an\u00E1logo qu\u00E2ntico da transformada discreta inversa de Fourier . A transformada de Fourier qu\u00E2ntica \u00E9 uma parte de muitos algoritmos qu\u00E2nticos, notavelmente o algoritmo de Shor para fatorar e calcular o logaritmo discreto, o algoritmo de estimativa de fase qu\u00E2ntica para estimar os valores pr\u00F3prios de um operador unit\u00E1rio e algoritmos para o problema do subgrupo oculto . A transformada qu\u00E2ntica de Fourier foi inventada por Don Coppersmith . A transformada qu\u00E2ntica de Fourier pode ser realizada de forma eficiente em um computador qu\u00E2ntico, com uma decomposi\u00E7\u00E3o particular em um produto de matrizes unit\u00E1rias mais simples. Usando uma decomposi\u00E7\u00E3o simples, a transformada discreta de Fourier em amplitudes podem ser implementadas como um circuito qu\u00E2ntico consistindo apenas em Port\u00F5es Hadamard e port\u00F5es de mudan\u00E7a de fase controlada, onde \u00E9 o n\u00FAmero de qubits. Isso pode ser comparado com a transformada discreta de Fourier cl\u00E1ssica, que leva port\u00F5es (onde \u00E9 o n\u00FAmero de bits), que \u00E9 exponencialmente maior que . No entanto, a transformada de Fourier qu\u00E2ntica atua em um estado qu\u00E2ntico, enquanto a transformada de Fourier cl\u00E1ssica atua em um vetor, portanto, nem toda tarefa que usa a transformada de Fourier cl\u00E1ssica pode tirar vantagem dessa acelera\u00E7\u00E3o exponencial. Os melhores algoritmos de transformada qu\u00E2ntica de Fourier conhecidos (no final de 2000) exigem apenas portas para conseguir uma aproxima\u00E7\u00E3o eficiente."@pt . . . . "\u041A\u0432\u0430\u043D\u0442\u043E\u0432\u043E\u0435 \u043F\u0440\u0435\u043E\u0431\u0440\u0430\u0437\u043E\u0432\u0430\u043D\u0438\u0435 \u0424\u0443\u0440\u044C\u0435"@ru . . "Transformada cu\u00E1ntica de Fourier"@es . "Kwantowa transformata Fouriera (ang. quantum Fourier transform, QFT) \u2013 kwantowa analogia dyskretnej transformaty Fouriera. Na dowolny -kubitowy stan bazowy dzia\u0142a ona jak nast\u0119puje: gdzie Nale\u017Cy zwr\u00F3ci\u0107 uwag\u0119, \u017Ce wielko\u015B\u0107 jest \u201Ezespolonym pierwiastkiem -tego rz\u0119du\u201D z liczby 1 (zob. wz\u00F3r de Moivre\u2019a). Spostrze\u017Cenie to pomaga wyobrazi\u0107 sobie, jak dzia\u0142a QFT, obrazuj\u0105c j\u0105 sobie w uk\u0142adzie wsp\u00F3\u0142rz\u0119dnych przestrzeni zespolonej."@pl . "Quantum Fourier transform"@en . . . . . . . . "\u041A\u0432\u0430\u043D\u0442\u043E\u0432\u043E\u0435 \u043F\u0440\u0435\u043E\u0431\u0440\u0430\u0437\u043E\u0432\u0430\u043D\u0438\u0435 \u0424\u0443\u0440\u044C\u0435 (\u0441\u043E\u043A\u0440. \u041A\u041F\u0424) \u2014 \u043B\u0438\u043D\u0435\u0439\u043D\u043E\u0435 \u043F\u0440\u0435\u043E\u0431\u0440\u0430\u0437\u043E\u0432\u0430\u043D\u0438\u0435 \u043A\u0432\u0430\u043D\u0442\u043E\u0432\u044B\u0445 \u0431\u0438\u0442\u043E\u0432 (\u043A\u0443\u0431\u0438\u0442\u043E\u0432), \u044F\u0432\u043B\u044F\u044E\u0449\u0435\u0435\u0441\u044F \u043A\u0432\u0430\u043D\u0442\u043E\u0432\u044B\u043C \u0430\u043D\u0430\u043B\u043E\u0433\u043E\u043C \u0434\u0438\u0441\u043A\u0440\u0435\u0442\u043D\u043E\u0433\u043E \u043F\u0440\u0435\u043E\u0431\u0440\u0430\u0437\u043E\u0432\u0430\u043D\u0438\u044F \u0424\u0443\u0440\u044C\u0435 (\u0414\u041F\u0424). \u041A\u041F\u0424 \u0432\u0445\u043E\u0434\u0438\u0442 \u0432\u043E \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u043E \u043A\u0432\u0430\u043D\u0442\u043E\u0432\u044B\u0445 \u0430\u043B\u0433\u043E\u0440\u0438\u0442\u043C\u043E\u0432, \u0432 \u043E\u0441\u043E\u0431\u0435\u043D\u043D\u043E\u0441\u0442\u0438 \u0432 \u0430\u043B\u0433\u043E\u0440\u0438\u0442\u043C \u0428\u043E\u0440\u0430 \u0440\u0430\u0437\u043B\u043E\u0436\u0435\u043D\u0438\u044F \u0447\u0438\u0441\u043B\u0430 \u043D\u0430 \u043C\u043D\u043E\u0436\u0438\u0442\u0435\u043B\u0438 \u0438 \u0432\u044B\u0447\u0438\u0441\u043B\u0435\u043D\u0438\u044F \u0434\u0438\u0441\u043A\u0440\u0435\u0442\u043D\u043E\u0433\u043E \u043B\u043E\u0433\u0430\u0440\u0438\u0444\u043C\u0430, \u0432 \u043A\u0432\u0430\u043D\u0442\u043E\u0432\u044B\u0439 \u0430\u043B\u0433\u043E\u0440\u0438\u0442\u043C \u043E\u0446\u0435\u043D\u043A\u0438 \u0444\u0430\u0437\u044B \u0434\u043B\u044F \u043D\u0430\u0445\u043E\u0436\u0434\u0435\u043D\u0438\u044F \u0441\u043E\u0431\u0441\u0442\u0432\u0435\u043D\u043D\u044B\u0445 \u0447\u0438\u0441\u0435\u043B \u0443\u043D\u0438\u0442\u0430\u0440\u043D\u043E\u0433\u043E \u043E\u043F\u0435\u0440\u0430\u0442\u043E\u0440\u0430 \u0438 \u0430\u043B\u0433\u043E\u0440\u0438\u0442\u043C\u044B \u0434\u043B\u044F \u043D\u0430\u0445\u043E\u0436\u0434\u0435\u043D\u0438\u044F \u0441\u043A\u0440\u044B\u0442\u043E\u0439 \u043F\u043E\u0434\u0433\u0440\u0443\u043F\u043F\u044B. \u041A\u0432\u0430\u043D\u0442\u043E\u0432\u043E\u0435 \u043F\u0440\u0435\u043E\u0431\u0440\u0430\u0437\u043E\u0432\u0430\u043D\u0438\u0435 \u0424\u0443\u0440\u044C\u0435 \u044D\u0444\u0444\u0435\u043A\u0442\u0438\u0432\u043D\u043E \u0438\u0441\u043F\u043E\u043B\u043D\u044F\u0435\u0442\u0441\u044F \u043D\u0430 \u043A\u0432\u0430\u043D\u0442\u043E\u0432\u044B\u0445 \u043A\u043E\u043C\u043F\u044C\u044E\u0442\u0435\u0440\u0430\u0445 \u043F\u0443\u0442\u0451\u043C \u0441\u043F\u0435\u0446\u0438\u0430\u043B\u044C\u043D\u043E\u0433\u043E \u0440\u0430\u0437\u043B\u043E\u0436\u0435\u043D\u0438\u044F \u043C\u0430\u0442\u0440\u0438\u0446\u044B \u0432 \u043F\u0440\u043E\u0438\u0437\u0432\u0435\u0434\u0435\u043D\u0438\u0435 \u0431\u043E\u043B\u0435\u0435 \u043F\u0440\u043E\u0441\u0442\u044B\u0445 \u0443\u043D\u0438\u0442\u0430\u0440\u043D\u044B\u0445 \u043C\u0430\u0442\u0440\u0438\u0446. \u0421 \u043F\u043E\u043C\u043E\u0449\u044C\u044E \u0442\u0430\u043A\u043E\u0433\u043E \u0440\u0430\u0437\u043B\u043E\u0436\u0435\u043D\u0438\u044F, \u0434\u0438\u0441\u043A\u0440\u0435\u0442\u043D\u043E\u0435 \u043F\u0440\u0435\u043E\u0431\u0440\u0430\u0437\u043E\u0432\u0430\u043D\u0438\u0435 \u0424\u0443\u0440\u044C\u0435 \u043D\u0430 \u0432\u0445\u043E\u0434\u043D\u044B\u0445 \u0430\u043C\u043F\u043B\u0438\u0442\u0443\u0434\u0430\u0445 \u043C\u043E\u0436\u0435\u0442 \u0431\u044B\u0442\u044C \u043E\u0441\u0443\u0449\u0435\u0441\u0442\u0432\u043B\u0435\u043D\u043E \u043A\u0432\u0430\u043D\u0442\u043E\u0432\u043E\u0439 \u0441\u0435\u0442\u044C\u044E, \u0441\u043E\u0441\u0442\u043E\u044F\u0449\u0435\u0439 \u0438\u0437 \u0432\u0435\u043D\u0442\u0438\u043B\u0435\u0439 \u0410\u0434\u0430\u043C\u0430\u0440\u0430 \u0438 \u043A\u043E\u043D\u0442\u0440\u043E\u043B\u0438\u0440\u0443\u0435\u043C\u044B\u0445 \u043A\u0432\u0430\u043D\u0442\u043E\u0432\u044B\u0445 \u0432\u0435\u043D\u0442\u0438\u043B\u0435\u0439, \u0433\u0434\u0435 \u2014 \u0447\u0438\u0441\u043B\u043E \u043A\u0443\u0431\u0438\u0442\u043E\u0432. \u041F\u043E \u0441\u0440\u0430\u0432\u043D\u0435\u043D\u0438\u044E \u0441 \u043A\u043B\u0430\u0441\u0441\u0438\u0447\u0435\u0441\u043A\u0438\u043C \u0414\u041F\u0424, \u0438\u0441\u043F\u043E\u043B\u044C\u0437\u0443\u044E\u0449\u0438\u043C \u044D\u043B\u0435\u043C\u0435\u043D\u0442\u043E\u0432 \u043F\u0430\u043C\u044F\u0442\u0438 ( \u2014 \u043A\u043E\u043B\u0438\u0447\u0435\u0441\u0442\u0432\u043E \u0431\u0438\u0442), \u0447\u0442\u043E \u044D\u043A\u0441\u043F\u043E\u043D\u0435\u043D\u0446\u0438\u0430\u043B\u044C\u043D\u043E \u0431\u043E\u043B\u044C\u0448\u0435, \u0447\u0435\u043C \u043A\u0432\u0430\u043D\u0442\u043E\u0432\u044B\u0445 \u0432\u0435\u043D\u0442\u0438\u043B\u0435\u0439 \u041A\u041F\u0424. \u041D\u0430\u0438\u043B\u0443\u0447\u0448\u0438\u0435 \u0438\u0437 \u0438\u0437\u0432\u0435\u0441\u0442\u043D\u044B\u0445 \u0430\u043B\u0433\u043E\u0440\u0438\u0442\u043C\u043E\u0432 \u043A\u0432\u0430\u043D\u0442\u043E\u0432\u043E\u0433\u043E \u043F\u0440\u0435\u043E\u0431\u0440\u0430\u0437\u043E\u0432\u0430\u043D\u0438\u044F \u0424\u0443\u0440\u044C\u0435 (\u043F\u043E \u0441\u043E\u0441\u0442\u043E\u044F\u043D\u0438\u044E \u043D\u0430 \u043A\u043E\u043D\u0435\u0446 2000) \u0437\u0430\u0434\u0435\u0439\u0441\u0442\u0432\u0443\u044E\u0442 \u0442\u043E\u043B\u044C\u043A\u043E \u0432\u0435\u043D\u0442\u0438\u043B\u0435\u0439 \u0434\u043B\u044F \u0434\u043E\u0441\u0442\u0438\u0436\u0435\u043D\u0438\u044F \u0436\u0435\u043B\u0430\u0435\u043C\u043E\u0433\u043E \u043F\u0440\u0438\u0431\u043B\u0438\u0436\u0435\u043D\u0438\u044F \u0440\u0435\u0437\u0443\u043B\u044C\u0442\u0430\u0442\u0430."@ru . "Kwantowa transformata Fouriera (ang. quantum Fourier transform, QFT) \u2013 kwantowa analogia dyskretnej transformaty Fouriera. Na dowolny -kubitowy stan bazowy dzia\u0142a ona jak nast\u0119puje: gdzie Nale\u017Cy zwr\u00F3ci\u0107 uwag\u0119, \u017Ce wielko\u015B\u0107 jest \u201Ezespolonym pierwiastkiem -tego rz\u0119du\u201D z liczby 1 (zob. wz\u00F3r de Moivre\u2019a). Spostrze\u017Cenie to pomaga wyobrazi\u0107 sobie, jak dzia\u0142a QFT, obrazuj\u0105c j\u0105 sobie w uk\u0142adzie wsp\u00F3\u0142rz\u0119dnych przestrzeni zespolonej."@pl . "In quantum computing, the quantum Fourier transform (QFT) is a linear transformation on quantum bits, and is the quantum analogue of the discrete Fourier transform. The quantum Fourier transform is a part of many quantum algorithms, notably Shor's algorithm for factoring and computing the discrete logarithm, the quantum phase estimation algorithm for estimating the eigenvalues of a unitary operator, and algorithms for the hidden subgroup problem. The quantum Fourier transform was discovered by Don Coppersmith. The quantum Fourier transform can be performed efficiently on a quantum computer with a decomposition into the product of simpler unitary matrices. The discrete Fourier transform on amplitudes can be implemented as a quantum circuit consisting of only Hadamard gates and controlled phase shift gates, where is the number of qubits. This can be compared with the classical discrete Fourier transform, which takes gates (where is the number of bits), which is exponentially more than . The quantum Fourier transform acts on a quantum state vector (a quantum register), and the classical Fourier transform acts on a vector. Both types of vectors can be written as lists of complex numbers. In the quantum case it is a sequence of probability amplitudes for all the possible outcomes upon measurement (called basis states, or eigenstates). Because measurement collapses the quantum state to a single basis state, not every task that uses the classical Fourier transform can take advantage of the quantum Fourier transform's exponential speedup. The best quantum Fourier transform algorithms known (as of late 2000) require only gates to achieve an efficient approximation."@en . . . . . "Trasformata di Fourier quantistica"@it . "En informatique quantique, la transform\u00E9e de Fourier quantique (TFQ) est une transformation lin\u00E9aire sur des bits quantiques, et est l'analogie quantique de la transform\u00E9e de Fourier discr\u00E8te . La transform\u00E9e de Fourier quantique est l'un des nombreux algorithmes quantiques, qui incluent notamment l'algorithme de Shor qui permet de factoriser et de calculer le logarithme discret, l' algorithme d'estimation de phase quantique qui estime les valeurs propres d'un op\u00E9rateur unitaire et les algorithmes traitant du probl\u00E8me de sous-groupe cach\u00E9 . La transform\u00E9e de Fourier quantique a \u00E9t\u00E9 d\u00E9couverte par Don Coppersmith . La transform\u00E9e de Fourier quantique peut \u00EAtre calcul\u00E9e efficacement \u00E0 l'aide d'un ordinateur quantique,en utilisant une d\u00E9composition en un produit de matrices unitaires plus simples. A l'aide de cette d\u00E9composition, la transform\u00E9e de Fourier discr\u00E8te sur amplitudes peut \u00EAtre mises en \u0153uvre sous la forme d'un circuit quantique avec un nombre de Portes d' Hadamard et de portes \u00E0 d\u00E9phasage command\u00E9 \u00E9voluant en , o\u00F9 est le nombre de qubits (le nombre de porte \u00E9volue selon une fonction en n^2). En comparaison, la transform\u00E9e de Fourier discr\u00E8te classique requiert un nombre de porte \u00E9voluant en , soit exponentiellement sup\u00E9rieur \u00E0 . La transform\u00E9e de Fourier quantique agit sur un vecteur d'\u00E9tat quantique, tandis que la transform\u00E9e de Fourier classique agit sur un vecteur(classique). Dans les deux cas ces vecteurs peuvent \u00EAtre \u00E9crits sous la forme de listes de nombres complexes. En ce qui concerne le cas quantique, ces nombres complexes repr\u00E9sentent les amplitudes de probabilit\u00E9 des diff\u00E9rents r\u00E9sultats obtenables par la mesure . \u00C9tant donn\u00E9 que la mesure r\u00E9duit l'\u00E9tat quantique \u00E0 une seule valeur (appel\u00E9e \u00E9tat de base ou \u00E9tat propre ), il n'est pas possible de profiter de l'acc\u00E9l\u00E9ration exponentielle apport\u00E9e par la transform\u00E9e de Fourier quantique pour chacune des t\u00E2ches impliquant la transform\u00E9e de Fourrier classique(la mesure d'un \u00E9tat quantique \u00E9tant irr\u00E9versible, on ne peut utiliser la transform\u00E9e quantique comme raccourci que si cela n'implique qu'une seule mesure) Les meilleurs algorithmes de transform\u00E9e de Fourier quantique connus \u00E0 ce jour (\u00E0 la fin des ann\u00E9es 2000) ne n\u00E9cessitent qu'un nombre en de portes pour obtenir une approximation efficace."@fr . . "Transformada qu\u00E0ntica de Fourier"@ca . . . . 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"In quantum computing, the quantum Fourier transform (QFT) is a linear transformation on quantum bits, and is the quantum analogue of the discrete Fourier transform. The quantum Fourier transform is a part of many quantum algorithms, notably Shor's algorithm for factoring and computing the discrete logarithm, the quantum phase estimation algorithm for estimating the eigenvalues of a unitary operator, and algorithms for the hidden subgroup problem. The quantum Fourier transform was discovered by Don Coppersmith."@en . . . "Die Quanten-Fouriertransformation ist ein Algorithmus aus dem Gebiet der Quanteninformatik. Sie ist eine Zerlegung der diskreten Fouriertransformation in ein Produkt unit\u00E4rer Matrizen. Dadurch kann sie als Quantenschaltkreis aus Hadamard-Gattern und implementiert werden. Die Quanten-Fouriertransformation ist ein wesentlicher Bestandteil eines der prominentesten Quantenalgorithmen, des Shor-Algorithmus."@de . . "Kwantowa transformata Fouriera"@pl . .