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New Construction of an Universal Quantum Network and Its Applications

An Min Wang

Published Jun 27, 2000• 0 citations
OpenAlex

Abstract

We proposed a new candidate for the construction of an universal quantum network, which are built from the elementary quantum gates to the elements of quantum circuit, again to quantum subnetworks and finally to a whole quantum network. The main advantages of our scheme are its simplicity and standardization in construction, facility and directness in assembly and scale, reusage and update in engineering, realizability and procedurization in an effective construction. Moreover our universal quantum networks are potentially programmable. It is proved that all the elementary quantum gates can be written as our quantum subnetwork. This implies that our scheme is compatible with the known quantum gate-assembly schemes, and so the known results from a quantum computation to a set of the elementary quantum gates can be directly inherited and used in our scheme. As the applications of our construction scheme, we obtain the whole quantum networks for Shor's algorithm, Grover's algorithm and simulating Schr\\"odinger equation in general. This means that our universal quantum network can generally describe the known main results in quantum computation.

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We proposed a new candidate for the construction of an universal quantum network, which are built from the elementary quantum gates to the elements of quantum circuit, again to quantum subnetworks and finally to a whole quantum network. The main advantages of our scheme are its simplicity and standardization in construction, facility and directness in assembly and scale, reusage and update in engineering, realizability and procedurization in an effective construction. Moreover our universal quantum networks are potentially programmable. It is proved that all the elementary quantum gates can be written as our quantum subnetwork. This implies that our scheme is compatible with the known quantum gate-assembly schemes, and so the known results from a quantum computation to a set of the elementary quantum gates can be directly inherited and used in our scheme. As the applications of our construction scheme, we obtain the whole quantum networks for Shor's algorithm, Grover's algorithm and simulating Schr\"odinger equation in general. This means that our universal quantum network can generally describe the known main results in quantum computation.
We present a possible candidate of construction of a scalable, uniform and universal quantum network, which is built from quantum gates to elements of quantum circuit, again to quantum subnetworks and finally to an entire quantum network. Our scheme can overcome some difficulties of the existing schemes and makes improvements to different extent in the scale of quantum network, ability of computation, implementation of engineering, efficiency of quantum network, universality, compatibility, design principle, programmability, fault tolerance, error control, industrialization and commercialization {\it et. al} aspects. As the applications of this construction scheme, we obtain the entire quantum networks for Shor's algorithm, Grover's algorithm and solving Schrödinger equation in general. This implies that the scalable, uniform and universal quantum networks are able to generally describe the known main results and can be further applied to more interesting examples in quantum computations.
This thesis covers two main topics in quantum computing: universal quantum computation and quantum search. We first demonstrate how a quantum harmonic oscillator can be used to implement the universal set of quantum gates and thereby serve as one possible building block for a universal quantum computer. We then address the core and primary focus of this thesis, the theoretical construction of a machine that can compute every computable function, that is, a universal (i.e.programmable) quantum computer. We thereby settle the questions that have been raised over the years regarding the validity of the UQTM proposed by Deutsch in 1985. We then demonstrate how to interface the universal quantum computer to external quantum devices by developing programs that implement well-known oracle based algorithms, including the well-known Grover search algorithm, using networked quantum oracle devices. Finally, we develop a partial search oracle and explore symmetry based partial search algorithms utilizing this oracle.
The implementation of a quantum computer requires the realization of a large number of N-qubit unitary operations which represent the possible oracles or which are part of the quantum algorithm. Until now there have been no standard ways to uniformly generate whole classes of N-qubit gates. We develop a method to generate arbitrary controlled phase-shift operations with a single network of one-qubit and two-qubit operations. This kind of network can be adapted to various physical implementations of quantum computing and is suitable to realize the Deutsch-Jozsa algorithm as well as Grover's search algorithm.