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Distributed Quantum Walk Control Plane Implementation

André Ribeiro, Matheus Guedes de Andrade, Fábio Kon, Don Towsley

Published May 20, 2024• 0 citations
Publisher

Abstract

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.

DOI
10.5753/wqunets.2024.3392

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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.
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.
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.
In order to enable two parties to exchange their secret information equally, we propose a controlled quantum dialogue protocol based on quantum walks, which implements the equal exchange of secret information between the two parties with the help of the controller TP. The secret information is transmitted via quantum walks, by using this method, the previously required entangled particles do not need to be prepared in the initial phase, and the entangled particles can be produced spontaneously via quantum walks. Furthermore, to resist TP’s dishonest behavior, we use a hash function to verify the correctness of the secret information. The protocol analysis shows that it is safe and reliable facing some attacks, including intercept-measure-resend attack, entanglement attack, dishonest controller’s attack and participant attack. And has a slightly increasing efficiency comparing with the previous protocols. Note that the proposed protocol may be feasible because quantum walks prove to be implemented in different physical systems and experiments.
Discrete-time quantum walks (DTQWs) have broad applications in quantum computation and simulation, particularly in universal quantum computing. Prior research in circuit quantum electrodynamics (QED) has focused on implementing DTQWs in one-dimensional chains. However, to achieve practical quantum tasks, it is crucial to extend DTQWs to multidimensional networks with diverse structures. Here, we propose a protocol for realizing DTQWs in multidimensional networks, which accommodate nodes with different numbers of neighbors. Using this protocol, we numerically simulate a Grover walk search algorithm in a cubic network with circuit QED. Our simulations, which consider decoherence, align well with theoretical predictions. Our universal protocol can be adapted for various quantum systems and paves the way for DTQWs in multidimensional networks, which has potential applications in quantum computing and simulation.
We introduce some new perfect state transfer and teleportation schemes by quantum walks with two coins. Encoding the transferred information in coin 1 state and alternatively using two coin operators, we can perfectly recover the information on coin 1 state at target position only by at most two times of flipping operation. Based on quantum walks with two coins either on the line or on the NNN-circle, we can perfectly transfer any qubit state. In addition, using quantum walks with two coins either on complete graphs or regular graphs, we can first implement perfect qudit state transfer by quantum walks. Compared with existing schemes driven by one coin, more general graph structures can be used to perfectly transfer more general state. Moreover, the external control of coin operator during the transmitting process can be decreased greatly. Selecting coin 1 as the sender and coin 2 as the receiver, we also study how to realize generalized teleportation over long steps of walks by the above quantum walk models. Because quantum walks is an universal quantum computation model, our schemes may provide an universal platform for the design of quantum network and quantum computer.