We introduce the concept of quantum time/utility functions (TUF) to enable effective scheduling decisions when executing quantum applications. The quantum TUF captures the relationship between the projected execution quality of an application and its execution time, enabling real-time, noise-aware scheduling. We consider different strategies for computing the TUF while addressing practical constraints, and introduce the Haar TUF, a simple, application-agnostic formula for random circuits. We implement the Haar TUF for a delegated quantum computing application, where we showcase both its ability to capture meaningful behaviour and its limitations in describing application-specific instances.

Consider two parties who want to agree on a common frequency band for communication in the presence of independent jammers. Such jammers block a different subset of bands at each site, where each party can observe only its own set of unjammed bands. Yet, they must agree on a common band without communicating. We first establish the optimal classical strategy, maximizing the probability they output a common frequency band in a single shot. We proceed to show that sharing an entangled pair of local dimension d allows the parties to coordinate strictly better, provided both the number of safe bands d and the spectrum size n are sufficiently large. We study explicit quantum strategies offering a pathway to near-term demonstrations, including an explicit strategy for d = 2 that outperforms the classical optimum for all spectrum sizes, achieving a 5.4

Architectures have been proposed to control entanglement generation in multi-user quantum networks. To allow time for local operations and classical communication at end nodes, these architectures insert fixed separations between consecutive batches of entanglement generation attempts. This reduces network utilization when attempts fail, leaving the network idle during the scheduled separation. To address this limitation, we propose a novel method to reclaim this idle time by shortening the scheduled separation between attempts while respecting hardware constraints. The method uses an analytical execution model to optimize the separation and reduce the total network service time of an application. Evaluations within the Arqon architecture show network service time reductions of up to 42 minutes (7.6

Quantum internet applications coordinate classical control, local quantum operations, and entanglement/communication across independent nodes under strict protocol ordering constraints. While Qoala and QNodeOS provide programming and execution abstractions for such applications, there is no compiler infrastructure that systematically lowers Qoala programs to executable node-level code while enabling optimization. We present the first multi-level compiler pipeline for Qoala quantum internet programs. The compiler lowers programs through three MLIR-based IRs that progressively expose hybrid control flow, explicit quantum memory, and Qoala block structure. On top of this pipeline, we implement (i) local peephole rewrites, and (ii) a block-reordering pass formulated as a MILP to reduce qubit lifetimes under precedence and resource constraints. We also provide static analyses for gate counts, qubit lifetimes, fidelity estimation, and quantum-memory efficiency. We evaluate on rotation-merging and blind quantum computing benchmarks using density-matrix simulation and IRderived estimates, showing that block reordering improves fidelity and memory reuse in latency-dominated regimes with modest compilation overhead.

Entanglement buffers are systems that maintain high-quality entanglement, ensuring it is readily available for consumption when needed. We study the performance of a two-node buffer, where each node has one long-lived quantum memory for entanglement storage and multiple short-lived memories for generation. Freshly generated entanglement may be used to purify stored entanglement, which degrades over time. Stored entanglement may be removed due to consumption or failed purification. We derive analytical expressions for the entanglement availability and the average fidelity upon consumption. Our solutions are computationally efficient and provide fundamental bounds to the performance of purification-based entanglement buffers. We also show that purification must be performed as frequently as possible to maximise the average fidelity of entanglement upon consumption, even if this often leads to the loss of high-quality entanglement due to purification failures. Moreover, we obtain heuristics for the design of good purification policies in practical systems.

Remote state preparation (RSP) allows one party to remotely prepare a known quantum state on another party's qubit using entanglement. This can be used in quantum networks to perform applications such as blind quantum computing or long-distance quantum key distribution (QKD) with quantum repeaters. Devices to perform RSP, referred to as a client, ideally have low hardware requirements, such as only sending photonic qubits. A weak coherent pulse source offers a practical alternative to true single-photon sources and is already widely used in QKD. Here, we introduce two new protocols to the previously known protocol for RSP with a weak-coherent-pulse-based device. The known technique uses a double-click (DC) protocol, where a photon from both the server and the client needs to reach an intermediate Bell state measurement. Here, we add to that a single-click (SC) RSP protocol, which requires only one photon to reach the Bell state measurement, allowing for better performance in certain regimes. In addition, we introduce a double-single-click (DSC) protocol, where the SC protocol is repeated twice, and a CNOT gate is applied between the resulting qubits. DSC mitigates the need for phase stabilization in certain regimes, lowering technical complexity while still improving performance compared to DC in some regimes. We compare these protocols in terms of fidelity and rate, finding that SC consistently achieves higher rates than DC and, interestingly, does not suffer from an inherently lower fidelity than the DC, as is the case for entanglement generation. Although SC provides stronger performance, DSC can still show performance improvements over DC, and it may have reduced technical complexity compared to SC. Lastly, we show how these protocols can be used in long-distance QKD using quantum repeaters.

A single photon in a superposition of d modes naturally encode a d-dimensional quantum system, a so-called qudit. We show that such superpositions can be leveraged to achieve a quantum speed-up of remote remote state preparation (RSP): a primitive for several quantum network protocols. For a superposition over d≥ 2 modes, the photon state can encode up to Log_2(d) qubits, which we exploit in a proposed reflection based RSP protocol with multiple variations. For single qubit RSP, we achieve a performance comparable to the best known existing schemes but with reduced requirements for phase stabilization. For many qubit RSP the achievable success rates remain high despite needing exponentially many temporal modes, since only one photon needs to be transmitted and detected to prepare multiple qubits. By simultaneously preparing many qubits at once, we bypass limited qubit lifetimes limited qubit lifetimes and improve fidelities beyond what is achievable with existing RSP protocols.

We investigate the hardware requirements for quantum teleportation in an intercity-scale network topology consisting of two metropolitan-scale networks connected via a long-distance backbone link. Specifically, we identify the minimal improvements required beyond the state-of-the-art to achieve an end-to-end expected teleportation fidelity of $2/3$, which represents the classical limit. To this end, we formulate the hardware requirements computation as optimisation problems, where the hardware parameters representing the underlying device capabilities serve as decision variables. Assuming a simplified noise model, we derive closed-form analytical expressions for the teleportation fidelity and rate when the network is realised using heterogeneous quantum hardware, including a quantum repeater chain with a memory cut-off. Our derivations are based on events defined by the order statistics of link generation durations in both the metropolitan networks and the backbone, and the resulting expressions are validated through simulations on the NetSquid platform. The analytical expressions facilitate efficient exploration of the optimisation parameter space without resorting to computationally intensive simulations. We then apply this framework to a representative realisation in which the metropolitan nodes are based on trapped-ion processors and the backbone is composed of ensemble-based quantum memories. Our results suggest that teleportation across metropolitan distances is already achievable with state-of-the-art hardware when the data qubit is prepared after end-to-end entanglement has already been established, whereas extending teleportation to intercity scales requires additional, though plausibly achievable, improvements in hardware performance.

We consider a multiplexed quantum repeater that distributes entanglement between two end nodes. Multiplexing is achieved through optical integration of many quantum chips. Each chip hosts an optically addressable communication qubit and a separate memory qubit. The communication qubit serves as an entanglement generation interface between different quantum chips, and the memory qubit can be used to store entanglement. The quantum chips on the repeater are interconnected using a reconfigurable router, which makes it possible to dynamically assign quantum chips for entanglement generation with either of the two end nodes in every end-to-end communication cycle. We propose a dynamic multiplexing policy in which after an entangled link has been established with one of the end nodes, all remaining quantum chips are assigned to the opposite end node. We compare this dynamic policy to a policy in which the assignment of quantum chips to end nodes is fixed. We consider a parameter regime where on average less than one entangled link is generated per end-to-end communication cycle, which is the relevant regime for near-term quantum networks. We show that in this regime, the dynamic multiplexing policy can lead to a significant improvement in fidelity over a fixed policy, while marginally improving the rate. Moreover, even though the dynamic multiplexing policy requires a deeper, and hence, more lossy, router than the fixed policy, it can still achieve higher secret key rates in the parameter regime studied. This makes dynamic multiplexing with a many-quantum-chip repeater especially relevant for the development of near-term quantum networks.

We study quantum repeater chains in which entangled links between neighbouring nodes are created through heralded entanglement generation and adjacent links are swapped as soon as possible. Since heralded entanglement generation attempts succeed only probabilistically, some links will have to be stored in quantum memories at the nodes of the chain while waiting for adjacent links to be generated. The fidelity of these stored links decreases with time due to decoherence, and if they are stored for too long then this can lead to low end-to-end fidelity. Previous work has shown that the end-to-end fidelity can be improved by deterministically discarding links when their ages exceed some cutoff value. Such deterministic cutoff policies provide strict control of the fidelity of all links, but they come at the expense of having to track link ages. In this work, we introduce a probabilistic cutoff policy that does not require tracking link ages, at the cost of abandoning strict control of the fidelity. We benchmark this new probabilistic cutoff policy against a deterministic cutoff policy. We compare the policies in terms of the end-to-end rate and fidelity, and the secret-key rate. We find that even though the probabilistic cutoff policy keeps track of less state, it can provide secret-key rates of the same order of magnitude as the deterministic cutoff policy in chains with few nodes or high elementary link generation probabilities. Moreover, we identify a scenario in which the probabilistic cutoff policy can deliver end-to-end links that are required to have some minimum threshold fidelity at a higher rate than the deterministic cutoff policy.

Coordination in distributed systems is often hampered by communication latency, which degrades performance. Quantum entanglement offers fundamentally stronger correlations than classically achievable without communication. Crucially, these correlations manifest instantaneously upon measurement, irrespective of the physical distance separating the systems. We investigate the application of shared entanglement to a dualwork optimization problem in a distributed system comprising two servers. The system must process both a continuously available, preemptible baseline task and incoming customer requests arriving in pairs. System performance is characterized by the trade-off between baseline task throughput and customer waiting time. We present a rigorous analytical model demonstrating that when the baseline task throughput function is strictly convex, rewarding longer uninterrupted processing periods, entanglement-assisted routing strategies achieve Pareto-superior performance compared to optimal communication-free classical strategies. We prove this advantage through queueing-theoretic analysis, nonlocal game formulation, and computational certification of classical bounds. We complement these formal results with simulations indicating that the advantage persists when arrivals are independent across routers and grows under bursty traffic. Our results suggest distributed scheduling and coordination as a candidate application domain for near-term entanglement-based quantum networks.

A quantum network's purpose is to enable users to execute applications on end nodes. This requires the network to provide the service of creating entangled links between those nodes. Users of mature networks, such as the internet or the telephone network expect accepted service demands to be met reliably. We first define reliability requirements that extend classical computer network concepts to quantum network service delivery. We then introduce Arqon, a suite of control applications designed to deliver reliable service in centrally controlled quantum networks. We demonstrate through both analytic and numerical evaluation that Arqon satisfies all reliability requirements for accepted demands. These evaluations consider static network topologies. We provide a complete Python implementation and perform complexity analysis showing that admission control scales as O(k^3) in the number of incoming demands k and schedule computation scales as O(N^3) in the number of accepted demands to schedule N.

Execution of quantum network applications requires a software stack for nodes. Recently, the first designs and demonstrations have been proposed for such software stacks, including QNodeOS and its extension, Qoala. The latter enables compilation strategies previously not possible in QNodeOS. Here, we show how the extensions provided by Qoala can be used by a compiler to improve the performance of quantum network applications. We define new compilation strategies that allow the compiler to influence the scheduling and execution of quantum programs on a quantum network node. Through simulation, we demonstrate that our compilation strategies can reduce the execution time by up to 29.53% and increase the success probability by up to 25.12%. Our work highlights the potential of compiler optimizations for quantum network programs.

The aim of a quantum network is to enable the generation of end-to-end entangled links between end nodes of the network, so that they can execute quantum network applications. To facilitate this, it is desirable to have robust control of the network in order to be able to provide a reliable service to the end nodes. In recent work arXiv:2503.12582, we proposed a modular control architecture for a generate-when-request type network. This control architecture enables quantum network applications to be executed on end nodes running a modern operating system such as QNodeOS arXiv:2407.18306. In that work, we performed an evaluation of our architecture based on a proof-of-concept implementation. In the course of performing this evaluation, we discovered many outstanding questions and challenges. These relate not only to implementing our specific control architecture, but also to the design of any quantum network control architecture. Here, we describe some outstanding questions and challenges, discuss possible solutions, and identify where existing protocols require adaptation or new protocols must be designed.

The aim of a quantum network is to enable users to successfully execute applications on their quantum end nodes. Users of mature networks, such as the internet, the postal network, or the telephone network expect their demands for service to be satisfied reliably. Here, we present an extended abstract introducing Arqon, a suite of control applications capable of delivering reliable service to end nodes. We define a full set of reliability requirements and demonstrate through a numeric evaluation that Arqon is capable of simultaneously satisfying all requirements.

We propose an architecture for scheduling network operations enabling the end-to-end generation of entanglement according to user demand. The main challenge solved by this architecture is to allow for the integration of a network schedule with the execution of quantum programs running on processing end nodes in order to realise quantum network applications. A key element of this architecture is the definition of an entanglement packet to meet application requirements on near-term quantum networks where the lifetimes of the qubits stored at the end nodes are limited. Our architecture is fully modular and hardware agnostic, and defines a framework for further research on specific components that can now be developed independently of each other. In order to evaluate our architecture, we realise a proof of concept implementation on a simulated 6-node network in a star topology. We show our architecture facilitates the execution of quantum network applications, and that robust admission control is required to maintain quality of service.

Designing and developing future quantum information networks is currently a cutting-edge topic. However, advances made in quantum cryptographic networks and independently in entanglement-based networks create the need for a unified framework for quantum information networking. This work attempts to set a path to a common paradigm for future quantum information networking.

In the performance analysis of quantum networks, it is common to approximate bipartite entangled states as either being Bell-diagonal or Werner states. We refer to these as twirled approximations because it is possible to bring any state to such a form with a twirling map. Although twirled approximations can simplify calculations, they can lead to an inaccuracy in performance estimates. The goal of this work is to quantify this inaccuracy. We consider repeater chains where end-to-end entanglement is achieved by performing an entanglement swap at each repeater in the chain. We consider two scenarios: postselected and non-postselected entanglement swapping, where postselection is performed based on the Bell-state measurement outcomes at the repeaters. We show that, for non-postselected swapping, the Bell-diagonal approximation is exact for the computation of the Bell-diagonal elements of the end-to-end state. We also find that the Werner approximation accurately approximates the end-to-end fidelity when the infidelity of each initial state is small with respect to the number of repeaters in the chain. For postselected swapping, we find bounds on the difference in end-to-end fidelity from what is obtained with the twirled approximation, for initial states with a general noisy form. Finally, for the example of performing quantum key distribution over a repeater chain, we demonstrate how our insights can be used to understand how twirled approximations affect the secret-key rate.

Near-term quantum networks face a bottleneck due to low quantum communication rates. This degrades performance both by lowering operating speeds and increasing qubit storage time in noisy memories, making some quantum internet applications infeasible. One way to circumvent this bottleneck is multiplexing: combining multiple signals into a single signal to improve the overall rate. Standard multiplexing techniques are classical in that they do not make use of coherence between quantum channels nor account for decoherence rates that vary during a protocol's execution. In this paper, we first derive semiclassical limits to multiplexing for many-qubit protocols, and then introduce new techniques: quantum multiplexing and multi-server multiplexing. These can enable beyond-classical multiplexing advantages. We illustrate these techniques through three example applications: 1) entanglement generation between two asymetric quantum network nodes (i.e., repeaters or quantum servers with inequal memories), 2) remote state preparation between many end user devices and a single quantum node, and 3) remote state preparation between one end user device and many internetworked quantum nodes. By utilizing many noisy internetworked quantum devices instead of fewer low-noise devices, our multiplexing strategies enable new paths towards achieving high-speed many-qubit quantum network applications.

Network utility maximization (NUM) addresses the problem of allocating resources fairly within a network and explores the ways to achieve optimal allocation in real-world networks. Although extensively studied in classical networks, NUM is an emerging area of research in the context of quantum networks. In this work, we consider the quantum network utility maximization (QNUM) problem in a static setting, where a user's utility takes into account the assigned quantum quality (fidelity) via a generic entanglement measure, as well as the corresponding rate of entanglement generation. Under certain assumptions, we demonstrate that the QNUM problem can be formulated as an optimization problem with the rate allocation vector as the only decision variable. Using a change-of-variable technique known in the field of geometric programming, we then establish sufficient conditions under which this formulation can be reduced to a convex problem: a class of optimization problems that can be solved efficiently and with certainty even in high dimensions. We further show that this technique preserves convexity, enabling us to formulate convex QNUM problems in networks where some routes have certain entanglement measures that do not readily admit convex formulation while others do. This allows us to compute the optimal resource allocation in networks where heterogeneous applications run over different routes.