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arXiv:quant-ph/0006122

Construction of a Scalable, Uniform and Universal Quantum Network and Its Applications

An Min Wang

Published Jun 27, 2000• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.quant-ph/0006122

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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.
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.
Quantum computing leverages quantum mechanical concepts, including superposition, entanglement, and interference, to solve problems that traditional computers cannot handle efficiently. This study presents a comprehensive overview of the field, covering both the theoretical foundations and the latest developments in quantum hardware and algorithms. This study covers fundamental elements, qubits, gates, and circuits while emphasizing quantum parallelism as a distinctive feature. To illustrate efficiency gains, we explore notable algorithms like Shor’s factorization procedure and Grover’s search algorithm. Furthermore, we analyze recent advancements in quantum hardware, focusing on superconducting qubits, trapped ions, and photonic quantum computers, with an emphasis on implementations by IBM, Google, and other industry leaders. The discussion also addresses major challenges such as decoherence, noise, and the need for quantum error correction to achieve fault tolerance. Finally, we explore emerging applications in cryptography, optimization, quantum machine learning, and material simulation, and identify critical open problems that must be addressed to realize scalable, universal quantum computing. Our review underscores the transformative potential of quantum technologies across science and industry.
The standard approach to universal fault-tolerant quantum computing is to develop a general purpose quantum error correction mechanism that can implement a universal set of logical gates fault-tolerantly. Given such a scheme, any quantum algorithm can be realized fault-tolerantly by composing the relevant logical gates from this set. However, we know that quantum computers provide a significant quantum advantage only for specific quantum algorithms. Hence, a universal quantum computer can likely gain from compiling such specific algorithms using tailored quantum error correction schemes. In this work, we take the first steps towards such algorithm-tailored quantum fault-tolerance. We consider Trotter circuits in quantum simulation, which is an important application of quantum computing. We develop a solve-and-stitch algorithm to systematically synthesize physical realizations of Clifford Trotter circuits on the well-known n,n-2,2error-detecting code family. Our analysis shows that this family implements Trotter circuits with optimal depth, thereby serving as an illuminating example of tailored quantum error correction. We achieve fault-tolerance for these circuits using flag gadgets, which add minimal overhead. The solve-and-stitch algorithm has the potential to scale beyond this specific example and hence provide a principled approach to tailored fault-tolerance in quantum computing.