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Quantum circuit design methods and applications

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  1. Tez No: 401285
  2. Yazar: ANMER DAŞKIN
  3. Danışmanlar: PROF. ANANTH GRAMA, PROF. SABRE KAIS
  4. Tez Türü: Doktora
  5. Konular: Bilgisayar Mühendisliği Bilimleri-Bilgisayar ve Kontrol, Computer Engineering and Computer Science and Control
  6. Anahtar Kelimeler: Belirtilmemiş.
  7. Yıl: 2014
  8. Dil: İngilizce
  9. Üniversite: Purdue University
  10. Enstitü: Yurtdışı Enstitü
  11. Ana Bilim Dalı: Belirtilmemiş.
  12. Bilim Dalı: Belirtilmemiş.
  13. Sayfa Sayısı: 142

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Özet (Çeviri)

Simulating quantum mechanical evolutions in general is difficult on classical com- puters because the size of the Hilbert space grows exponentially with the number of particles involved in the simulations. However, a quantum computer, which obeys the laws of quantum mechanics, is believed to perform such simulations more effi- ciently. The time evolution operator, a unitary matrix, of a quantum system acts as a quantum gate changing the state of the system in time. Therefore, any computation on quantum computers can be interpreted as a unitary transformation on quantum state vectors. Generally, quantum gates are sufficiently simple operations so as to avoid difficulty in the physical implementation. The implementation of a general given computation represented by a unitary matrix on quantum computers requires nding an array of elementary quantum gates describing the desired computation. This describes a matrix decomposition problem known as the quantum circuit design problem. In this dissertation, we address the following questions concerning quantum circuit designs: How hard is it to nd suitable quantum circuits for a given computation? What are the possible circuit design methods? How do we apply these to simula- tions of quantum problems, in particular quantum chemistry problems? To answer these questions, we categorize methods for designing quantum circuits as evolutionary algorithms and deterministic methods. We apply our developed group leaders opti- mization algorithm, an evolutionary algorithm, to nd quantum circuits for known quantum algorithms and the simulation of molecular Hamiltonians. Then, we present a deterministic circuit design approach to produce universal circuits, which can be programmable. Moreover, we show how to use these programmable circuit designs within the quantum phase estimation algorithm to nd eigenvalues of nonunitary matrices and study resonances in quantum systems. Finally, the quantum phase es- timation algorithm is employed to efficiently solve ranking problems: in particular, multiple network alignment is considered to nd the similarities between protein- protein interaction networks and molecular networks.

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