[Paper Review] A quantum walk control plane for distributed quantum computing in quantum networks

Matheus Guedes de Andrade, Wenhan Dai+2 more|arXiv (Cornell University)|Jun 17, 2021

Quantum Computing Algorithms and Architecture25 references5 citations

TL;DR

This paper proposes a quantum walk-based control plane for distributed quantum computing in quantum networks, using a quantum walker as a control signal that propagates across network nodes to coordinate universal quantum operations. The protocol enables universal distributed quantum computation, demonstrated via a CNOT gate and entanglement distribution, by encoding control logic in the walker's evolution and interactions with data qubits via unitary coin and interaction operators.

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.

Motivation & Objective

• To design a universal, hardware-agnostic control protocol for distributed quantum computing in quantum networks.
• To abstract quantum network control from physical implementations while maintaining universality for quantum operations.
• To enable distributed quantum operations such as CNOT and entanglement distribution using quantum walk dynamics.
• To map control signal propagation to walker evolution across network nodes, with interactions encoded in unitary operators.
• To demonstrate the protocol's universality through implementation of a 2-qubit CNOT gate and GHZ state generation.

Proposed method

• The protocol uses a generalized discrete-time coined quantum walk model where the walker system interacts with data qubits at each node via unitary interaction operators.
• Control logic is encoded in the walker's state evolution, with coin operators determining the direction of propagation and interaction with data qubits.
• The interaction between walker and data qubits is modeled using a controlled-unitary interaction operator $ K_v $, which acts on qubits at node $ v $ based on the number of walkers passing through it.
• The protocol maps control signal transmission to the walker's hop-by-hop propagation across the network graph, with time evolution corresponding to discrete steps.
• For entanglement distribution, the protocol uses a spanning tree structure with $ k $ walkers entangled in a superposition over paths to leaves, enabling multi-path entanglement generation.
• The protocol is implemented using a network-wide spanning tree $ \mathcal{T} $, where each walker traverses a unique path from the root to a leaf, with time complexity $ \mathcal{O}(\max_{j}|p_j|) $.

Experimental results

Research questions

• RQ1 Can a quantum walk be used as a universal control signal for distributed quantum operations in arbitrary quantum network topologies?
• RQ2 How can the interaction between a quantum walker and data qubits be formalized to enable universal quantum computation?
• RQ3 What is the minimal set of unitary operations required to implement a distributed CNOT gate using a quantum walk control plane?
• RQ4 How can entanglement distribution be achieved using a multi-walker quantum walk protocol with path-dependent evolution?
• RQ5 What are the latency and fidelity constraints of the protocol in realistic quantum network scenarios?

Key findings

• The protocol achieves universal distributed quantum computing by enabling any quantum operation in the Hilbert space of all data qubits across network nodes.
• A 2-qubit CNOT operation between qubits in separate nodes is successfully implemented using the quantum walk control plane, demonstrating universality.
• Entanglement distribution for a GHZ state is achieved using $ k $ entangled walkers traversing a spanning tree, with the protocol completing in $ \mathcal{O}(\max_{j}|p_j|) $ time steps.
• For a 5×5 grid, the protocol completes in 7 time steps, corresponding to the longest path in the spanning tree, with $ k=7 $ walkers.
• The interaction operator $ K_v $ is defined as $ \bigotimes_{q_v} X_{qv}^{1/W_v} $, where $ W_v $ is the number of walkers passing through node $ v $, ensuring consistent operation across multiple walkers.
• The protocol abstracts physical implementation details, relying on perfect unitary operations under idealized error-corrected conditions, with fidelity bounded by coin and shift operator performance in practice.