Generalized Quantum Teleportation Protocol

Öz

Within the scope of this study, generalization of the single qubit (quantum bit) teleportation protocol to multi-qubit systems has been examined. Then, the possibilities of teleporting to more than one target were discussed and a protocol for this was proposed. Within the scope of the developed theoretical framework, the generalization of quantum logic gates that modify qubits is also discussed. General versions of these quantum logic gates have been created and they have been shown to work for special cases in the literature. It has been determined that the equations formed in the theoretical framework established as a result of the generalization of the teleportation to many qubits and many targets, contain a pattern, and a way to carry out the protocol without dealing with complex tensor products one by one is proposed through this pattern. Within the scope of the study, Python computer programs were created for multi-qubit - single target, multi-qubit - multi-target protocols. It has been observed that the created programs successfully produce the results predicted by the theoretical framework presented. Through these programs, it is possible to perform long and error-free mathematical operations in a short time. The generated program results also prove the existence of the above-mentioned pattern.

Anahtar Kelimeler

• Quantum Teleportation
• Qubit
• Quantum Logic Gate

Genelleştirilmiş Kuantum Işınlama Protokolü

Öz

Bu çalışma kapsamında literatürde var olan tek kubit(kuantum bit) ışınlanma/telenakil (quantum teleportation) protokolünün çok kubit sistemlere genellenmesi incelenmiştir. Ardından, birden fazla hedefe telenakil olanakları tartışılarak, buna dair bir protokol önerilmiştir. Geliştirilen teorik çerçeve kapsamında, kubitler üzerinde değişiklik yapan kuantum mantık kapılarının da genellenmesi tartışılmıştır. Söz konusu kuantum mantık kapılarının genel versiyonları oluşturulmuş olup, literatürdeki özel durumlar için çalıştıkları gösterilmiştir. Işınlanmanın çok kubit-çok hedefe genellenmesi sonucu kurulan teorik çerçevede oluşan denklemlerin bir örüntü içerdiği belirlenmiş olup, bu örüntü aracılığı ile karmaşık tensör çarpımları ile tek tek uğraşmaksızın da protokolün gerçekleştirilebileceği bir yol önerilmiştir. Çalışma kapsamında çok kubit - tek hedef, çok kubit – çok hedef protokollerine yönelik Python bilgisayar programları oluşturulmuştur. Oluşturulan programların, sunulan teorik çerçevenin ön gördüğü sonuçları başarılı bir şekilde ürettiği gözlenmiştir. Bu programlar aracılığı ile, uzun ve hata yapma olasılığı yüksek matematiksel işlemlerin kısa sürede ve hatasız yapılabilmesinin olanağı yaratılmıştır. Oluşturulan program sonuçları aynı zamanda, yukarıda bahsedilen örüntünün varlığını kanıtlamaktadır.

Anahtar Kelimeler

• Kuantum Işınlaması
• Kuantum Bit
• Kuantum Mantık Kapısı
• Quantum Teleportation
• Qubit
• Quantum Logic Gate

Kaynakça

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