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arXiv:quant-ph/0207064 · IEEE Transactions on Nanotechnology

Digital switching in the quantum domain

I.-M. Tsai, Sy‐Yen Kuo

Published Sep 1, 2002• 35 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1109/tnano.2002.806824

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IEEE Transactions on Computers•Sep 17, 2008•7 citations
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 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.
This chapter reviews some of the most important techniques for carrying quantum bits through a quantum information network. In order to avoid a fully meshed architecture, switching units are required to build a realistic network. Traditionally, there are two paradigms in doing digital switching: circuit switching and packet switching. The classical telephone network is a circuit switching network, while the Internet is a packet switching network. Although significant differences exist between circuit switching and packet switching, the main function of each node is to move data from an input port to an output port. In the field of classical digital switching, various techniques have been designed to perform this function. Compared with classical digital switching technology, quantum information science is a relatively new field of study. Modern packet switching networks take packets that share the same transmission line as input and each packet is transferred to its destination individually.
In this paper, we present a quantum multicasting network, called a generalized quantum connector (n-GQC), which can be used to multicast quantum information from n inputs to n outputs. This network is recursively constructed using n/2-GQCs and consists of O(n log2n) quantum gates. The key component of the n-GQC is another network, called an n-quantum concentrator (n-QC). This concentrator is also an n × n quantum network, and can route arbitrary quantum states on any m of its inputs to its top m outputs, for any m, 1 ¿ m ¿ n. Its quantum gate complexity is O(n log n). The quantum gate-level depths of n-QC and n-GQC are O(log2n) and O(log3n), respectively. Both n-QC and n-GQC are based on the classical self-routing concentrators and generalized connection networks given by Lee and Oruc [1]. While these networks work for multicasting classical packets, they cannot be used to multicast quantum packets as they employ balancer switches with both forward and backward propagation of packets. We introduce a quantum balancer switch that works using a forward propagation of packets only, thereby facilitating the n-QC and n-GQC designs presented in the paper.
Quantum networks are a keystone of the quantum internet. However, existing implementations remain largely confined to static point-to-point links due to the absence of a switching paradigm capable of dynamically routing fragile quantum entanglement without introducing decoherence. Here, we propose the Universal Quantum Switch, a foundational building block allowing on-demand, non-blocking, and encoding-agnostic routing of quantum information, as well as seamless modality conversion between disparate quantum platforms. We develop a prototype in thin-film lithium niobate and experimentally demonstrate robust switching with ≤4%\le 4\%≤4% decoherence via thermo-optic modulation and high-speed electro-optic switching of arbitrary entangled states at 1 MHz. Moreover, we show that our platform can support reconfiguration speeds up to 1 GHz. To our knowledge, this work represents the first demonstration of multi-node dynamic entanglement distribution at these speeds. Complementing these experimental results, we project the architecture's scalability, showing dimension-independent decoherence, and provide a scalable, interoperable building block for heterogeneous quantum network fabrics.
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.
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.