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IEEE Transactions on Computers

An Enhanced Universal N x N Fully Nonblocking Quantum Switch

Chuan-Ching Sue

Published Sep 17, 2008• 7 citations
Publisher

Abstract

This study develops a quantum switching device with fully nonblocking properties. Although previous studies have also presented quantum-based solutions for the blocking problem, the proposed schemes are characterized by an increased packet loss, a large number of quantum SWAP gates and an increased propagation delay time complexity. The current study overcomes these drawbacks by designing an N x N fully nonblocking quantum switch, in which the packet payload is passed through quantum SWAP gates while the packet header is passed through quantum control gates designed by applying a modified quantum Karnaugh mapping method. The allocation of quantum SWAP gates to the different layers within the switch is solved using a Perfect Matching in Complete Graph (PMiCG) algorithm with a time complexity of O(N!/(2N/2(N/2)!)). A symmetry-based heuristic method is proposed to reduce the time complexity of the search process for all the perfect matching pairs to a time complexity of O(N2). The performance of the proposed quantum switch is compared with that of a quantum self-routing packet switch and a quantum switching/quantum merge sorting scheme, respectively, in terms of the hardware complexity, the propagation delay time complexity, the auxiliary qubit complexity, and the packet loss probability.

DOI
10.1109/tc.2008.161

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This study develops a quantum switching device with fully nonblocking properties. Although previous studies have also presented quantum-based solutions for the blocking problem, the proposed schemes are characterized by an increased packet loss, a large number of quantum SWAP gates and an increased propagation delay time complexity. The current study overcomes these drawbacks by designing an N x N fully nonblocking quantum switch, in which the packet payload is passed through quantum SWAP gates while the packet header is passed through quantum control gates designed by applying a modified quantum Karnaugh mapping method. The allocation of quantum SWAP gates to the different layers within the switch is solved using a Perfect Matching in Complete Graph (PMiCG) algorithm with a time complexity of O(N!/(2N/2(N/2)!)). A symmetry-based heuristic method is proposed to reduce the time complexity of the search process for all the perfect matching pairs to a time complexity of O(N2). The performance of the proposed quantum switch is compared with that of a quantum self-routing packet switch and a quantum switching/quantum merge sorting scheme, respectively, in terms of the hardware complexity, the propagation delay time complexity, the auxiliary qubit complexity, and the packet loss probability.
A switching device is required to build a realistic network which can handle the explosive growth of network traffic. However, the drawback of the switching device is mainly focused on the blocking problem. Previous studies have presented the solutions in the quantum context to avoid blocking at the expense of increasing packet loss and the exponential size of quantum gates. In this paper, we design a fully non-blocking quantum switch using the linear number O(N2) of quantum SWAP gates. Comparisons with a previously proposed quantum self-routing packet switch is also presented in terms of the hardware complexity, the propagation delay and packet loss probability
Flexible distribution of data in the form of quantum bits (qubits) amongst spatially separated entities is an essential component of envisioned scalable quantum computing architectures. Since qubits cannot be copied, this operation of moving qubits can be relatively costly in terms of resources. Moreover, implementation of quantum gates requires precise and extensive classical control and computation too. Accordingly, we consider the problem of dynamically permuting groups of qubits, i.e., qubit packets using reconfigurable quantum switches in which routing information is calculated classically as a possible way to reduce this cost. We design a 2 x 2 switch based on the controlled-swap quantum gate and show that if switch settings are determined using efficient classical algorithms, then quantum switches can be mapped onto classical non-blocking interconnection switch topologies with low cost by using this switch. Specific quantum switch designs for the optimal Benes network and the planar Spanke-Bcnes network are given.
We present the design of a self-routing quantum packet switch which improves on a previous design given by the authors [1]. Like the earlier design, this switch too routes packets represented by quantum bits (qubits) but it reduces the routing overhead per packet from O(log N) qubits to O(1) qubits by eliminating the need for an extra "dummy" inputoutput pair and their associated "dummy" packets at each 2 2 internal switch. The quantum self-routing switch creates a superposition of all the maximum size non-blocking subsets of input packets at its outputs, which cannot be achieved by any classical self-routing switching network that is internally blocking. In addition to the network design, we give a method to characterize the output quantum state of the switch using the concepts of frames and balanced matrices.
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.
Quantum switching networks are analogs of classical switching networks in which classical switches are replaced by quantum switches. These networks are used to switch quantum data among a set of quantum sources and receivers. They can also be used to efficiently switch classical data, and help overcome some limitations of classical switching networks by utilizing the unique properties of quantum information systems, such as superposition and parallelism. In this thesis, we design several such networks which can be broadly put in the following three categories: 1. Quantum unicast networks: We give the design of quantum Baseline network (QBN) which is a self-routing and unicast quantum packet switch that uses the Baseline topology. The classical version of the network blocks packets internally even when there are no output contentions and each input packet is addressed to a different output. The QBN uses the principles of quantum superposition and parallelism to overcome such blocking. Also, for assignments that have multiple input packets addressed to an output, this network creates a quantum superposition of all these packets on that output, ensuring that all packets have non-zero probabilities of being observed on that output. 2. Quantum concentrators: We introduce a new network called quantum concentrator, which is a key component of our quantum multicasting network design. This concentrator is also an n × n quantum switching network, to be denoted by n-QC, and which, for any m, 1 ≤ m ≤ n, routes arbitrary quantum states on any m of its inputs to its top m outputs. This network uses O(n log n) quantum gates, and has a gate level depth of O(log 2 n). We also give several variations of this network, the main ones being order-preserving and priority quantum concentrators. 3. Quantum multicast networks: We first design a quantum multicasting network, called a generalized quantum connector (GQC) which can be used to multicast quantum information from n input sources to n outputs. Since general quantum states cannot be copied due to the no-cloning theorem, this network actually multicasts superposed classical information packets, contained in a finite number of qubits at each input. Copying needed for such multicasting is obtained by Wootters and Zurek's quantum copying machines or controlled-not gates. This n-input and n-output (n × n) network, to be denoted by n-GQC, is recursively constructed using n/2-GQCs and uses O(n log 2 n) quantum gates. The time complexity of this network in terms of gate level depth is O(log 3 n). We also give two variations of this network which improve its behavior when routing multicast assignments that have multiple input packets contending for same outputs.