Bilgi çağında olduğumuz artık su götürmez bir gerçektir. Üretilen, depolanan, aktarılan bilginin miktarı her geçen gün hızla büyümektedir. Bilginin üretilmesi, depolanması, iletilmesi ve işlenmesi gibi temel konular multidisipliner konular olup aynı anda birçok bilim dalını ilgilendirir. Günümüzde fizikçiler, matematikçiler, bilgisayar bilimcileri, psikologlar, sosyologlar ve nörologlar bilginin işlenmesi ortak paydasında çalışmaktadırlar. Bilim insanlarının çalışmaları insan beyninin bilgiyi nasıl algıladığı, nasıl ürettiği, nasıl depoladığı, bunu yaparken beyinde hangi fiziksel ve kimyasal süreçlerin nasıl işlediği üzerinde yoğunlaşmış olup ‘Nihayetinde insan beyni gibi bilgiyi işleyebilen insandan yola çıkarak ve yine insan eliyle oluşturulmuş bir makineye ulaşılabilinecek mi?’ sorusuna cevap aranmaktadır. Bu soruya cevap vermek şu an için zor olsa da devasa veri tabanlarını analiz ederek sonuçlar çıkaran, kararlar verebilen ve adına yapay zekâ denilen bir oluşuma sahibiz. Başta yazılım mühendisleri olmak üzere, yukarıda adı geçen bilim dallarında bulunan araştırmacılar yapay zekâ alanında her geçen gün ilerlemeler kaydetmektedirler. Bu çalışmaların uygulamaya dökülmüş hallerini bankacılık, tıp, eğitim, askeriye hatta hukuk alanın da dahi görmekteyiz.
Devasa büyüklükte veri tabanlarını oluşturup işleyebilecek nitelikte süper bilgisayarlar var olmasına rağmen veri tabanlarının hacmi büyüdükçe bilgisayarların işlem yapabilme hacminin bir noktada yetersiz kalacağı, bir bilgisayara sığdırabileceğimiz mikro işlemci sayısı sınırlı olduğundan aşikârdır.
Bir bilgisayara daha çok mikroişlemci sığdırabilmek için mikroişlemcilerin fiziksel boyutlarının küçülmesi gerekir. Öyle ki sabit hacimli bir odaya sığdırabileceğimiz ceviz sayısı karpuz sayısından daha fazladır. Aynı şekilde fındık sayısı da ceviz sayısından daha fazladır. Boyutları küçülterek devam ettiğimizde karşımıza kuantum fiziği ilkeleri ile açıklanabilen bir düzen çıkar. Böylece fikri temellerini Richard Feynman’ın attığı, yapılabilirliği üzerine ilk önerisini David Deutsch’un ortaya koyduğu, Grover ve Shor gibi isimlerin önerileri ile altını çizdiği kuantum bilgi işleme alanına gireriz.
Kuantum mekaniksel parçacıkların, süper pozisyon durumunda olabilme ve dolanık durumda bulunabilme özellikleri sayesinde, kuantum bilgisayarların bilginin işlenmesi noktasında klasik (geleneksel) bilgisayarlardan belirli konularda çok daha üstün olduğu bilinmektedir. Ayrıca bilginin işlenmesi sırasında seri işlem yapabilmenin karşısına paralel işlem yapabilme özelliğini de koyduğumuzda bu üstünlük derecesinin daha da arttığı söylenebilir.
Kuantum bilgi işlemede kuantum mekaniksel parçacıkların kuantum durumlarına bilgi kodlanarak işlenir. Bu kuantum durumları bir fotonun yatay veya düşey polarizasyon durumları olabildiği gibi, spin özelliğine sahip elektron ve çekirdeklerin olası spin durumları da olabilir. Gelinen nokta itibariyle bir fotonun yatay veya düşey polarizasyonlarının lineer bir birleşimi veya spini ½ olan elektron veya çekirdeklerin olası iki durumunun (up ve down) lineer birleşimi kübit olarak tanımlanır. Bilgi de kübitlere kodlanarak işlenir. Burada lineer birleşim ifadesi aslında büyük önem taşır. Geleneksel bilgisayarlarda bilgi ya 0 ya da 1 durumlarına kodlanabilirken kuantum bilgi işleme de (kuantum bilgisayarlarda) bilgi her iki durumda aynı anda bulunabilen kübitlere kodlanır. Örneğin paranın bir yüzü 0 diğer yüzü 1 olarak alınırsa, klasik bilgisayarlarda sadece bir yüze bilgi kodlanır. Kodlamak istediğiniz başka bir bilgi için başka bir madeni paraya ihtiyaç duyarsınız. Geleneksel bilgisayarlarda bilginin kodlanmasındaki maliyeti bu benzetmeyle açıklayabiliriz. Ancak kuantum bilgi işlemede paranın her iki yüzüne de bilgi kodlayabilir ve işleyebilirsiniz. Ama burada tuhaf bir durum karşımıza çıkar. Yazı tura atarken paranın elden çıkıp tekrar elimize gelene kadar havada yaptığı dönme hareketini düşünün. Kuantum bilgi işlemede bilgi ancak madeni para dönme halindeyken işlenir. Bu dönme hareketi sırasında hangi yüzdeki bilginin olduğunu bilmediğimiz için her iki durumda vardır diyebiliriz. İşte bu kuantum fiziğinde süperpozisyon durumu, matematikte de lineer birleşim olarak adlandırılır. Diyelim ki para daha elimize düşmeden havada ikinci bir kişi tarafından yakalandı. Bu durumda baktığı yüzde (ölçüm yaptığında) ya sıfır ya da 1 durumunu görecektir. Gördüğünün dışındaki durum yok olacaktır. Bu benzetme kuantum bilgi işlemenin nasıl çalıştığına dair bir fikir vermekle beraber bilgi güvenliği açısından üstünlüğü de ortaya koymaktadır.
Bugün itibariyle kübitler kullanılarak yapılan çalışmalar oldukça artmıştır. Kübitler için kullanılacak kuantum kapıları, önerilen kuantum algoritmalardaki görevleri yerine getirirler. Ancak buna paralel olarak kuantum bilgi işlemenin kendi içinde hız, performans ve işlem hacmi açısından daha üstün hale gelmesini sağlayacak çalışmalar da mevcut olup her gün literatüre yeni çalışmalar eklenmektedir.
Yukarıda iki durumlu kuantum sistemlerine kübit denildiğini söylemiştik. Üç ve daha fazla durumlu kuantum sistemleri söz konusu olduğunda bu bilgi işleme birimleri küdit olarak tanımlanır. Daha özel olarak söylersek 3 durumlu sistemler kutrit, 4 durumlu sistemler ise kukuart olarak isimlendirilir. Peki, bu bilgi birimi küditlerin kübitlere göre nasıl bir avantajı var? Tam bu noktada karşımıza çığ gibi büyüyen bilgi işleme ve depolama hacmi çıkıyor. Örneğin n tane kübit ile aynı anda 2n bilgi kodlanıp işlenebilirken, n kutrit ile 3n, n kukuart ile 4n tane bilgi aynı anda kodlanıp işlenebiliyor. Bunu sayısal bir değerle şöyle ifade edebiliriz. Bilgi işlemek için 10 tane kübit kullanacaksak 1024 adet bilgi, 10 tane kütrit kullanacaksak 59049 adet bilgi ve 10 tane kukuart kullanacaksak 1048576 adet bilgi aynı anda kodlanıp işlenebilecek. Bu üstel artışın avantajları ile birlikte dezavantajlarının olup olmadığının çalışmaları yapılmaktadır. Ancak şu aşamada kübit yerine küdit kullanımının avantajları teorik olarak sevindirici sonuçlar vermektedir.
Küditler üzerine etki eden kuantum mantık kapıları olduğu gibi küditler üzerine etki edecek kuantum mantık kapıları çalışmaları da mevcut olup önerilen kapılar matematiksel olarak beklenen sonuçları sağlamaktadır. Eğer avantajları üstün gelirse, yapay zekâ ve veri işleme gibi alanlarda şaşırtıcı bir üstünlük insanlığı beklemektedir. Bunun daha nelere yol açabileceğini de hep birlikte bekleyip göreceğiz.
Bu yazıda kullandığım başlığı destekleyen bir isimlendirme mevcut değildir. Kübit ve küdit birleştirmek adına şahsımın yaptığı bir yakıştırmadır.
Yazar: Murat Kurt
Redaktör: Muammer Ceylan
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