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IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications

Quantum switching and quantum merge sorting

Sheng-Tzong Cheng, Chun-Yen Wang

Published Feb 1, 2006• 57 citations
Publisher

Abstract

This paper proposes a quantum switching architecture that can dynamically permute each input quantum data to its destination port to avoid using the fully connected networks. In addition, in order to reduce the execution time of the quantum switching, an efficient quantum merge sorting (QMS) algorithm that provides a parallel quantum computation is also developed. The quantum switching utilizes the QMS algorithm as a subroutine so that the total running time can be reduced to polylogarithmic time. Furthermore, to evaluate the feasibility of the quantum switching, we also define three different kinds of performance factors that can be used to estimate the complexity in implementation and the time delay in execution for quantum instruments. From the evaluation results, it can be seen that the proposed quantum switching is feasible in practice.

DOI
10.1109/tcsi.2005.856669

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This paper proposes a quantum switching architecture that can dynamically permute each input quantum data to its destination port to avoid using the fully connected networks. In addition, in order to reduce the execution time of the quantum switching, an efficient quantum merge sorting (QMS) algorithm that provides a parallel quantum computation is also developed. The quantum switching utilizes the QMS algorithm as a subroutine so that the total running time can be reduced to polylogarithmic time. Furthermore, to evaluate the feasibility of the quantum switching, we also define three different kinds of performance factors that can be used to estimate the complexity in implementation and the time delay in execution for quantum instruments. From the evaluation results, it can be seen that the proposed quantum switching is feasible in practice.
The emergence of quantum computers in the last decade has generated research interest in applications such as quantum sorting. Quantum sorting plays a critical role in creating ordered sets of data that can be better utilized, e.g., quantum ordered search or quantum network switching. In this paper, we propose a quantum sorting algorithm that combines highly parallelizable bitonic merge networks with perfect shuffle permutations (PSP), for sorting data represented in the quantum domain. The combination of bitonic networks with PSP improves the temporal complexity of bitonic merge sorting which is critical for reducing decoherence effects for quantum processing. We present space-efficient quantum circuits that can be used for quantum bit comparison and permutation. We also present a reconfigurable hardware quantum emulator for prototyping the proposed quantum algorithm. The emulator has a fully-pipelined architecture and supports double-precision floating-point computations, resulting in high throughput and accuracy. The proposed hardware architectures are implemented on a high-performance reconfigurable computer (HPRC). In our experiments, we emulated quantum sorting circuits of up to 31 fully-entangled quantum bits on a single FPGA node of the HPRC platform. To the best of our knowledge, our effort is the first to investigate a reconfigurable hardware emulation of quantum sorting using bitonic networks and perfect shuffle.
This paper proposes a novel parallel computing architecture fundamentally based on the principle of quantum state superposition. Traditional parallel computing relies on classical methods, often limited by the sequential nature of operations and the constraints of multiple processors. This architecture leverages the inherent ability of quantum systems to exist in multiple states simultaneously, offering a potential paradigm shift in computational efficiency. The core concept involves designing a system where multiple quantum computations can be executed concurrently, drastically reducing processing time for suitable algorithms. This paper details the architecture, outlines the key mathematical foundations, and explores the theoretical advantages of this approach. We present a framework for utilizing superposition to achieve parallelism, focusing on the manipulation of quantum states to represent and process multiple inputs or operations simultaneously. The potential impact of this architecture on various computational domains is discussed, highlighting areas where superposition-based parallelism could offer significant performance gains. The theoretical analysis demonstrates the potential for exponential speedups under certain conditions, contingent on the algorithm's suitability for superposition-based execution. Further research and development are needed to translate this architectural concept into a practical and scalable implementation.
Presents a switching architecture such that digital data can be switched in the quantum domain. The proposed mechanism supports unicasting as well as multicasting, and is strict-sense nonblocking. In addition, with appropriate interface conversion, this architecture can also be used to switch classical information. This results in a quantum switch that can be used to build classical and quantum information networks. To present this idea, we define the connection digraph which can be used to describe the behavior of a switch at a given time, then we show how a connection digraph can be implemented using elementary quantum gates. Compared with a traditional space or time domain switch, the proposed switching mechanism is much more scalable. Assuming an n/spl times/n quantum switch, the space consumption grows linearly, i.e., O(n), while the time complexity is O(1) for unicasting, and O(log/sub 2/n) for multicasting. Based on these advantages, a high-throughput switching device can be built simply by increasing the number of I/O ports.
Quantum computing, utilizing the unique properties of quantum mechanics, has the potential to revolutionize various fields. However, current quantum processors face challenges in scaling the number of qubits, limiting their practical applications. In response, Distributed Quantum Computing (DQC) has emerged as a promising paradigm where multiple interconnected Quantum Processing Units (QPUs) collaborate to execute quantum circuits. In this paper, we focus on designing networks to interconnect QPUs for the implementation of DQC. We find that in real-world experiments and systems, the photon collection and coupling efficiency is low, leading to significant performance degradation in direct connection networks. To address this limitation, we propose a novel multistage switching network tailored for DQC, which has low system complexity and high entanglement generation rates. The proposed switching network compriseslog⁡2(N)\log _{2}(N)log2​(N)stages andN/2N/2N/2binary switches at each stage, where N represents the number of QPUs. We prove that the proposed network is nonblocking and develop an efficient routing algorithm with a time complexity ofO(Nlog⁡(N))\mathcal {O}(N\log (N))O(Nlog(N)). Additionally, we show the success probability of entanglement generation in the proposed switching network. Extensive simulations demonstrate that our network significantly outperforms the highly efficient circuit-switching Beneš network and three direct connection networks.