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arXiv:2307.06492

Universal Quantum Walk Control Plane for Quantum Networks

Matheus Guedes de Andrade, Nitish K. Panigrahy, Wenhan Dai, Saikat Guha, Don Towsley

Published Jul 12, 2023• 0 citations
arXivHTMLPDF

Abstract

Quantum networks are complex systems formed by the interaction among quantum processors through quantum channels. Analogous to classical computer networks, quantum networks allow for the distribution of quantum operations among quantum processors. In this work, we describe a Quantum Walk Control Protocol (QWCP) to perform distributed quantum operations in a quantum network. We consider a generalization of the discrete-time coined quantum walk model that accounts for the interaction between quantum walks in the network graph with quantum registers inside the network nodes. QWCP allows for the implementation of networked quantum services, such as distributed quantum computing and entanglement distribution, abstracting hardware implementation and the transmission of quantum information through channels. Multiple interacting quantum walks can be used to propagate entangled control signals across the network in parallel. We demonstrate how to use QWCP to perform distributed multi-qubit controlled gates, which shows the universality of the protocol for distributed quantum computing. Furthermore, we apply the QWCP to the task of entanglement distribution in a quantum network.

DOI
10.48550/arxiv.2307.06492

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Quantum networks are complex systems formed by the interaction among quantum processors through quantum channels. Analogous to classical computer networks, quantum networks allow for the distribution of quantum operations among quantum processors. In this work, we describe a Quantum Walk Control Protocol (QWCP) to perform distributed quantum operations in a quantum network. We consider a generalization of the discrete-time coined quantum walk model that accounts for the interaction between quantum walks in the network graph with quantum registers inside the network nodes. QWCP allows for the implementation of networked quantum services, such as distributed quantum computing and entanglement distribution, abstracting hardware implementation and the transmission of quantum information through channels. Multiple interacting quantum walks can be used to propagate entangled control signals across the network in parallel. We demonstrate how to use QWCP to perform distributed multi-qubit controlled gates, which shows the universality of the protocol for distributed quantum computing. Furthermore, we apply the QWCP to the task of entanglement distribution in a quantum network.
Quantum networks are complex systems formed by the interaction among quantum processors through quantum channels. Analogous to classical computer networks, quantum networks allow for the distribution of quantum computation among quantum computers. In this work, we describe a quantum walk protocol to perform distributed quantum computing in a quantum network. The protocol uses a quantum walk as a quantum control signal to perform distributed quantum operations. We consider a generalization of the discrete-time coined quantum walk model that accounts for the interaction between a quantum walker system in the network graph with quantum registers inside the network nodes. The protocol logically captures distributed quantum computing, abstracting hardware implementation and the transmission of quantum information through channels. Control signal transmission is mapped to the propagation of the walker system across the network, while interactions between the control layer and the quantum registers are embedded into the application of coin operators. We demonstrate how to use the quantum walker system to perform a distributed CNOT operation, which shows the universality of the protocol for distributed quantum computing. Furthermore, we apply the protocol to the task of entanglement distribution in a quantum network.
The Quantum Walk Control Protocol (QWCP) enables universal distributed quantum computing in quantum networks. In its debut, QWCP was specified in terms of logical quantum operations required by a quantum network to implement the protocol. In this paper, we propose two possible implementations of the QWCP based on different ways to encode quantum walks in physical qubits. The proposed encodings require different numbers of qubits and remote entangled states to perform control operations. Our approaches help to bridge the gap between the logical description of the QCWP and possible physical realizations of the protocol.
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Universal quantum computation can be realised using both continuous-time and discrete-time quantum walks. We present a version based on single particle discrete-time quantum walk to realize multi-qubit computation tasks. The scalability of the scheme is demonstrated by using a set of walk operations on a closed lattice form to implement the universal set of quantum gates on multi-qubit system. We also present a set of experimentally realizable walk operations that can implement Grover's algorithm, quantum Fourier transformation and quantum phase estimation algorithms. An elementary implementation of error detection and correction is also presented. Analysis of space and time complexity of the scheme highlights the advantages of quantum walk based model for quantum computation on systems where implementation of quantum walk evolution operations is an inherent feature of the system.
We propose a simple interaction protocol to be implemented on a scalable quantum network, in which the quantum nodes consist of qubit systems confined in cavities. The nodes are deterministically coupled by transmission and reflection of a single photon, which is disentangled from the qubits at the end of the coupling operation. This single photon can generate an entangling controlled-phase gate between any selected number of qubits in the network. Our multiqubit gate reaches a much higher fidelity compared to schemes concatenating one-qubit and two-qubit gates; thus it forms an efficient basis for universal quantum computing distributed over multiple processor units. In our analysis we consider atomic qubits coupled to optical photons, while the scheme can be readily generalized to other architectures, such as superconducting qubit nodes coupled by microwave photons.
Abstract In large-scale quantum networks, quantum repeaters provide an efficient method to distribute entangled states among selected nodes for realizing long-distance and complicated quantum communications. However, extending quantum repeater protocols to high-dimensional quantum states in existing experiments faces great challenges. Owing to the feasible physical implementations of quantum walks, we proposed various basic modules applicable to quantum repeaters for distributing high-dimensional entangled states via quantum walks, including d-dimensional Bell states and multi-particle d-dimensional GHZ states. Furthermore, based on the above schemes, we provided a high-dimensional entanglement distribution scheme for arbitrary quantum tree networks. By searching for a Steiner tree in a quantum network, we can achieve high-dimensional entanglement distributions over an arbitrary quantum network. We constructed a quantum fractal network based on d-dimensional GHZ states and analyzed the quantum transport properties of continuous quantum walks in the network. Compared with the continuous quantum walk on the Sierpinski gasket, the quantum walk on the new fractal network spreads more widely within the same time frame. Finally, we conducted five experiments to implement various basic modules of 2-party or 3-party entanglement distribution schemes in a superconducting quantum processor. Our study can serve as a building block for constructing large and complex quantum networks.