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arXiv:2106.09839 · IEEE International Conference on Quantum Computing and Engineering (QCE)

A quantum walk control plane for distributed quantum computing in quantum networks

Matheus Guedes de Andrade, Wenhan Dai, Saikat Guha, Don Towsley

Published Oct 1, 2021• 21 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 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.

DOI
10.1109/qce52317.2021.00048

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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 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.
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.
Distributed quantum computing is a promising application of quantum networks as it leverages the power of interconnected small quantum computers to perform generic quantum operations that cannot be tackled by single computers alone. The key question in distributed quantum computing using quantum networks is applying a quantum gate on qubits that are geographically separated. In this work, we propose an optimization framework to describe distributed control policies that implement a quantum circuit with gates acting on qubits located in distinct nodes. The distributed control operations throughout the quantum network can be described by a logical control plane quantum walk protocol. We then investigate the problem of assigning logical qubits in a circuit description to physical qubits in the network, with the objective of minimizing the amount of quantum control information exchanged between nodes. We present an integer programming formulation for the problem that determines both qubit assignment and network paths for the transmission of quantum control information. Our formulation restricts to circuits with 2-qubit controlled gates and highlights the difficulty of the problem in terms of complexity. Our formulation can be used to analyze the demand for network resources in terms of the number of channel uses with respect to node capacity and circuit width.
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.
We explore a discrete-time, coined quantum walk on a quantum network where the coherent superposition of walker moves originates from the unitary interaction of the walker coin with the qubit degrees of freedom in the quantum network. The walk dynamics leads to a growth of entanglement between the walker and the network on one hand and, on the other, between the network qubits among themselves. The initial entanglement among the network qubits plays a crucial role in determining the asymptotic values of these entanglement measures and the quantum walk statistics. Specifically, the entanglement entropy of the walker-network state and the negativity of the quantum network-qubit state saturate to values increasing with the initial network entanglement. The asymptotic time-averaged walker-position probability distribution shows increasing localization around the initial walker position with higher initial network entanglement. A potential application of these results as a characterization tool for quantum network properties is suggested.
Abstract The utilization of quantum entanglement as a cryptographic resource has superseded conventional approaches to secure communication. Security and fidelity of intranetwork communication between quantum devices is the backbone of a quantum network. This work presents an protocol that generates entanglement between any two directly connected nodes of a quantum network to be used as a resource to enable quantum communication across that pair in the network. The protocol is based on a directed discrete-time quantum walk and paves the way for private inter-node quantum communication channels in the network. We also present the simulation results of this protocol on random networks generated from various models. We show that after implementation, the probability of the walker being at all nodes other than the source and target is negligible and this holds independent of the random graph generation model. This constitutes a viable method for the practical realisation of secure communication over any random network topology.
Computing Power of Quantum Mechanics There is much interest in developing quantum computers in order to perform certain tasks much faster than, or that are intractable for, a classical computer. A general quantum computer, however, requires the fabrication and operation a number of quantum logic devices (see the Perspective by Franson ). Broome et al. (p. 794 , published online 20 December) and Spring et al. (p. 798 , published online 20 December) describe experiments in which single photons and quantum interference were used to perform a calculation (the permanent of a matrix) that is very difficult on a classical computer. Similar to random walks, quantum walks on a graph describe the movement of a walker on a set of predetermined paths; instead of flipping a coin to decide which way to go at each point, a quantum walker can take several paths at once. Childs et al. (p. 791 ) propose an architecture for a quantum computer, based on quantum walks of multiple interacting walkers. The system is capable of performing any quantum operation using a subset of its nodes, with the size of the subset scaling favorably with the complexity of the operation.