**College**Essay

## Dissertation on animation of quantum algorithm

### Formal Methods in Quantum Circuit Design

Distributed algorithms are by nature difﬁcult to understand due to the existence of asynchronous threads of control that interacts and due to the lack of global state and time. Even if an algorithm starts from the same initial system conﬁguration, it may not result in the same output. The animation of an algorithm shows graphically its. QUANTUM ALGORITHMS FOR: QUANTUM PHASE ESTIMATION, APPROXIMATION OF THE TUTTE POLYNOMIAL AND BLACK-BOX STRUCTURES. by. HAMED AHMADI. B.S. Mathematics, Shahid Beheshti University, M.S. Mathematics, University of Tehran, A dissertation submitted in partial fulﬁllment of the requirements for the degree of Doctor of Philosophy. In this dissertation, we investigate three different problems in the field of Quantum computation. First, we discuss the quantum complexity of evaluating the Tutte polynomial of a planar graph. Furthermore, we devise a new quantum algorithm for approximating the phase of a unitary matrix. Finally, we provide quantum tools that can be utilized to extract the structure of black-box modules and.

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QUANTUM ALGORITHMS FOR: QUANTUM PHASE ESTIMATION, APPROXIMATION OF THE TUTTE POLYNOMIAL AND BLACK-BOX STRUCTURES. by. HAMED AHMADI. B.S. Mathematics, Shahid Beheshti University, M.S. Mathematics, University of Tehran, A dissertation submitted in partial fulﬁllment of the requirements for the degree of Doctor of Philosophy. Quantum Algorithms and Learning Theory Academisch Proefschrift ter verkrijging van de graad van doctor aan de Universiteit van Amsterdam op gezag van de Rector Magni cus prof. dr. ir. K.I.J. Maex This thesis is based on the following papers. For the rst ve papers, the. We describe quantum interrogation schemes for passive atomic clocks. During any given interrogation period, the optimal interrogation algorithm depends on the state of the clock -- specifically on the frequency deviation of the flywheel (classical oscillator) from the atomic standard. As a clock runs, it is possible to estimate this deviation.

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In this dissertation, we investigate three different problems in the field of Quantum computation. First, we discuss the quantum complexity of evaluating the Tutte polynomial of a planar graph. Furthermore, we devise a new quantum algorithm for approximating the phase of a unitary matrix. Finally, we provide quantum tools that can be utilized to extract the structure of black-box modules and. Thus, reducing the complexity time for classical algorithms used to solve problems such as the prime factorization problem and the period finding problem. The Quantum Fourier Transform is a principle component in Shor's algorithm. We will explicitly define the Quantum Fourier Transform and show that it is a unitary transformation. Traditional quantum algorithms with guaranteed performance generally require fully coherent quantum computers to operate, making error-correction a necessity. In contrast, variational quantum algorithms seek to remove this requirement by formulating the computation as the .

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Quantum mechanical computers can solve certain problems asymptotically faster than any classical computing device. Several fast quantum algorithms are known, but the nature of quantum speedup is not well understood, and inventing new quantum algorithms seems to be diﬃcult. In this thesis, we explore two approaches to designing quantum algorithms. projective quantum Monte Carlo algorithms Thesis submitted for the degree of Doctor Philosophiae Candidate: Inack Estelle Ma eva Supervisors: Sebastiano Pilati and Giuseppe E. Santoro. Acquista verit`a e non la vendere, acquista sapienza, istruzione e intelligenza. — Proverbi We describe quantum interrogation schemes for passive atomic clocks. During any given interrogation period, the optimal interrogation algorithm depends on the state of the clock -- specifically on the frequency deviation of the flywheel (classical oscillator) from the atomic standard. As a clock runs, it is possible to estimate this deviation.

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3) One generic technique used to compute the minimum of a given function is "gradient descent". We present a quantum gradient-calculation algorithm and a gradient-optimization algorithm that is quadratically faster than classical algorithms. In the second part of this thesis we look at quantum . Quantum mechanical computers can solve certain problems asymptotically faster than any classical computing device. Several fast quantum algorithms are known, but the nature of quantum speedup is not well understood, and inventing new quantum algorithms seems to be diﬃcult. In this thesis, we explore two approaches to designing quantum algorithms. Quantum Algorithms for Linear Algebra and Machine Learning by Anupam Prakash blogger.com, from the processed quantum state. In this dissertation we make progress on all three aspects of the quantum machine learning problem and present quantum algorithms for low rank approximation.