We introduce multipartite entanglement distribution protocols that use a quantum switch to deliver stabilizer states to a number of remote end users. As in existing schemes, the first step in our protocols involves Bell pair generation between the switch and each end user. However, unlike existing schemes that wait for all Bell pairs to be established before distributing the desired state -- for example, via a projective measurement -- our approach stores only a minimal subset of Bell pairs while processing every subsequent Bell pair immediately. In doing so, our protocols reduce the average Bell pair storage time compared to existing schemes, resulting in less cumulative noise as a direct consequence. On the theoretical side, our protocol design is grounded in the structure of vertex covers in graph states up to local complementation. Through a comprehensive numerical evaluation, we compare the fidelities of delivered states with those of a baseline scheme, for state sizes up to n = 50 qubits. Simulations also show that our protocols can achieve the critical fidelity threshold of 1/2 for multipartite entanglement in a wider range of depolarization rates and success probabilities of Bell-pair generation. Overall, our protocols always achieve an equal or higher fidelity of the distributed state, and can reduce infidelity by up to 45%.
We introduce multipartite entanglement distribution protocols that use a quantum switch to deliver stabilizer states to a number of remote end users. As in existing schemes, the first step in our protocols involves Bell pair generation between the switch and each end user. However, unlike existing schemes that wait for all Bell pairs to be established before distributing the desired state -- for example, via a projective measurement -- our approach stores only a minimal subset of Bell pairs while processing every subsequent Bell pair immediately. In doing so, our protocols reduce the average Bell pair storage time compared to existing schemes, resulting in less cumulative noise as a direct consequence. On the theoretical side, our protocol design is grounded in the structure of vertex covers in graph states up to local complementation. Through a comprehensive numerical evaluation, we compare the fidelities of delivered states with those of a baseline scheme, for state sizes up to n = 50 qubits. Simulations also show that our protocols can achieve the critical fidelity threshold of 1/2 for multipartite entanglement in a wider range of depolarization rates and success probabilities of Bell-pair generation. Overall, our protocols always achieve an equal or higher fidelity of the distributed state, and can reduce infidelity by up to 45%.
We study the minimum persistent memory required to distribute a graph state through a quantum switch. Specifically, consider a central switch that assists n remote users in distributing a graph state, using independently generated user-switch Bell pairs. Since Bell-pair generation is probabilistic, different links generally succeed at different times. When a Bell-pair is generated, the qubits may need to be stored in memory while waiting for other links to succeed. Recently, new protocols have been proposed to reduce this storage overhead by processing and releasing some switch qubits before all Bell links are available. However, these protocols do not characterize the minimum persistent switch memory required at each stage. Moreover, the local-cover method in the state-of-the-art Piecemaker protocol is computationally expensive for general target graphs.
In this work, we characterize the minimum persistent switch memory required after any subset of users' Bell links are generated and processed. We then develop an online stabilizer-transition protocol that attains this limit, which can be implemented in polynomial time in the number of qubits n. Remarkably, this optimal protocol can provide substantial memory reductions over existing heuristic approaches. In particular, for the path graph Pn over n users, Piecemaker protocol requires at least ⌊n/2⌋ qubits of peak persistent memory for \textit{every Bell-links generation order}, whereas under the order (1,2,…,n), our protocol requires only one persistent switch qubit. Finally, the same stabilizer-transition framework also provides a direct forward construction for sequential graph-state generation using the minimum number of quantum emitters, equal to the maximum of the height function.
Abstract Multipartite entangled states, such as Greenberger–Horne–Zeilinger (GHZ) states, are important resources in multiparty quantum networking tasks. We consider protocols for generating such states from networks of Bell pairs and local operations and classical communication. We present a computationally-efficient protocol for generating GHZ states that is also efficient with respect to the number of consumed Bell pairs, (local) gates, and Bell-pair sources. Our protocol: (1) requires O ( N ) gates in a network with N nodes, independent of the network topology; (2) has time complexity O ( N 2 ), avoiding the Steiner tree and any other computationally-hard problem; (3) maintains a near-optimal number of consumed Bell pairs. Numerically, our protocol outperforms those based on (approximate) Steiner trees with respect to the number of gates and Bell-pair sources. We prove that the minimal Bell-pair source cost is given by solving the graph-theoretic dominating set problem, and we demonstrate numerically that our protocol is nearly optimal for this quantity. Finally, we analytically characterize the impact of noisy Bell pairs and gates on the fidelity of the distributed GHZ states.
We study the performance (rate and fidelity) of distributing multipartite entangled states in a quantum network through the use of a central node. Specifically, we consider the scenario where the multipartite entangled state is first prepared locally at a central node and then transmitted to the end nodes of the network through quantum teleportation. As our first result, we present leading-order analytical expressions and lower bounds for both the rate and fidelity at which a specific class of multipartite entangled states, namely, Greenberger-Horne-Zeilinger (GHZ) states, are distributed. Our analytical expressions for the fidelity accurately account for time-dependent depolarizing noise encountered by individual quantum bits while stored in quantum memory, as verified using Monte Carlo simulations. As our second result, we compare the performance to the case where the central node is an entanglement switch and the GHZ state is created by the end nodes in a distributed fashion. Apart from these two results, we outline how the teleportation-based scheme could be physically implemented using trapped ions or nitrogen-vacancy centers in diamond.
The quantum internet will extend today's networks with a capability no classical infrastructure can offer: the distribution of entanglement between distant nodes. That single resource underlies services provably beyond classical reach, such as secure communication against computationally unbounded adversaries, blind delegated computation on remote quantum servers, and entangled networks of atomic clocks. Most of these services require a single multipartite state shared among several nodes at once — for the most part a graph state: one qubit per vertex of a graph, one entangling interaction per edge. This Thesis addresses the distribution of one such state: given an arbitrary network of entanglement switches, deliver the m-qubit path graph state, in the order the application requests, to m single-qubit end nodes — the weakest client model in the literature. Prior protocols support arbitrary topologies or such minimal end nodes, never both. The strongest of them are also centralized: the construction and the memory demand concentrate at a single node. The Thesis takes the opposite approach: a distributed protocol. The Path Graph State Distribution (PathGSD) protocol grows the target state one end node at a time behind a single reference qubit that walks a classically planned route, the shortest ordered Steiner walk. The work is partitioned among the switches, which coordinate only through entanglement and classical messages; no single node ever builds or stores the whole state. The design is deliberately simple, guided by engineering principles, and the simplicity pays at scale: planning is polynomial and completes in seconds on a network of 22,500 switches, where the closest optimization-based alternatives face exponential blow-up. Correctness is proved in the graph-state measurement calculus; a memory-reuse discipline and a parallel multi-domain execution mode complete the protocol. The protocol is implemented as communicating discrete-event processes on the QuantumSavory simulator, validated against exact theoretical expectations, and evaluated against the strongest available baselines: the star-specific Piecemaker and Factory protocols, simulated under noise, and the Graph State Transfer (GST) algorithm's proved cost expressions, evaluated exactly on arbitrary topologies. PathGSD consumes fewer Einstein-Podolsky-Rosen (EPR) pairs than the exact GST baseline on every single-domain family tested, keeps switch memory constant in the network size where the centralized baseline's grows, matches the star-specific protocols on their home topology, and reaches measured speed-ups of up to 1.9× when two administrative domains execute in parallel.
Building large-scale quantum computers, essential to demonstrating quantum advantage, is a key challenge. Quantum networks can help address this challenge by enabling the construction of large, robust, and more capable quantum computing platforms by connecting smaller quantum computers. Moreover, unlike classical systems, quantum networks can enable fully secured long-distance communication. Thus, quantum networks lie at the heart of the success of future quantum information technologies. In quantum networks, multipartite entangled states distributed over the network help implement and support many quantum network applications for communications, sensing, and computing. Our work focuses on developing optimal techniques to generate and distribute multipartite entanglement states efficiently. Prior works on generating general multipartite entanglement states have focused on the objective of minimizing the number of maximally entangled pairs while ignoring the heterogeneity of the network nodes and links as well as the stochastic nature of underlying processes. In this work, we develop a hypergraph-based linear programming framework that delivers optimal (under certain assumptions) generation schemes for general multipartite entanglement represented by graph states, under the network resources, decoherence, and fidelity constraints, while considering the stochasticity of the underlying processes. We illustrate our technique by developing generation schemes for the special cases of path and tree graph states and discuss optimized generation schemes for more general classes of graph states. Using extensive simulations over a quantum network simulator, we demonstrate the effectiveness of our developed techniques and show that they outperform prior known schemes by up to orders of magnitude.
Remote entanglement distribution plays a crucial role in quantum networks, which can support many essential and exciting quantum applications. As the network scale expands, it is urgent to design a general and efficient remote entanglement distribution protocol. Nowadays, connection-oriented remote entanglement distribution protocols are available to achieve reliable entanglement distribution. However, in memory-limited quantum networks, connection-oriented entanglement distribution protocols cannot utilize entanglement resources fully and increase the delay of End-to-End (E2E) entanglement connection establishment. To overcome these shortcomings of existing entanglement distribution protocols, we design a connectionless remote entanglement distribution protocol to let Source-Destination (S-D) pairs compete for entanglement resources simultaneously. In our protocol, a fair request scheduling algorithm is proposed to reduce the waiting time without entanglement connections between S-D pairs. Furthermore, a fast scheduling trigger mechanism is proposed to perform entanglement swapping timely to reduce the delay of E2E entanglement connection establishment. The simulation results show that the designed protocol has advantages in terms of resource utilization, throughput, the service completion time of S-D pairs, and the maximum waiting time, compared with the existing remote entanglement distribution protocol.