We investigate resource allocation for quantum entanglement distribution over an optical network. We characterize and model a network architecture that employs a single broadband quasi-deterministic time-frequency heralded Einstein-Podolsky-Rosen (EPR) pair source, and develop a routing and spectrum allocation scheme for distributing entangled photon pairs over such a network. As our setting allows separately solving the routing and spectrum allocation problems, we first find an optimal polynomial-time routing algorithm. We then employ max-min fairness criterion for spectrum allocation, which presents an NP-hard problem. Thus, we focus on approximately-optimal schemes. We compare their performance by evaluating the max-min and median number of EPR-pair rates assigned by them, and the associated Jain index. We identify two polynomial-time approximation algorithms that perform well, or better than others under these metrics. We also investigate scalability by analyzing how the network size and connectivity affect performance using Watts-Strogatz random graphs. We find that a spectrum allocation approach that achieves higher minimum EPR-pair rate can perform significantly worse when the median EPR-pair rate, Jain index, and computational resources are considered. Additionally, we evaluate the effect of the source node placement on the performance.
We investigate resource allocation for quantum entanglement distribution over an optical network. We characterize and model a network architecture that employs a single broadband quasi-deterministic time-frequency heralded Einstein-Podolsky-Rosen (EPR) pair source, and develop a routing and spectrum allocation scheme for distributing entangled photon pairs over such a network. As our setting allows separately solving the routing and spectrum allocation problems, we first find an optimal polynomial-time routing algorithm. We then employ max-min fairness criterion for spectrum allocation, which presents an NP-hard problem. Thus, we focus on approximately-optimal schemes. We compare their performance by evaluating the max-min and median number of EPR-pair rates assigned by them, and the associated Jain index. We identify two polynomial-time approximation algorithms that perform well, or better than others under these metrics. We also investigate scalability by analyzing how the network size and connectivity affect performance using Watts-Strogatz random graphs. We find that a spectrum allocation approach that achieves higher minimum EPR-pair rate can perform significantly worse when the median EPR-pair rate, Jain index, and computational resources are considered. Additionally, we evaluate the effect of the source node placement on the performance.
We investigate resource allocation for quantum entanglement distribution over an optical network. We characterize and model a network architecture that employs a single quasi-deterministic time-frequency heralded EPR-pair source, and develop a routing scheme for distributing entangled photon pairs over such a network. We focus on max-min fairness in entanglement distribution and compare the performance of various spectrum allocation schemes by examining both the max-min number of EPR pairs assigned by them and the Jain index associated with this assignment.
Entanglement routing plays a vital role in distributed quantum computing and quantum networks. Previous works on entanglement routing have addressed several design challenges due to limited quantum resources, failures to establish entanglement, and decoherence of established entanglement, but considered neither the limitations imposed by having a limited number of entangled photon sources (EPSes), nor the benefits of using all-optical (or quantum) switching to distribute entangled photons. In this paper, we first explore the problem of jointly optimizing entanglement routing and EPS assignment, assuming no all-optical switching capability. In other words, a pair of entangled photons generated by one EPS can be distributed to two neighboring quantum nodes. We then relax the above assumption so as to allow a pair of entangled photons generated by one EPS to be distributed to non-adjacent nodes using all-optical switching. We propose two corresponding solutions, namely, entanglement routing and EPS assignment (or ERSA), and ERSA with all-optical switching-based distribution (or ERSA+D) that aim to maximize the number of entanglement connections between the given set of source-destination (SD) pairs while avoiding starvation and achieving fairness among the SD pairs. In order to obtain efficient solutions in a large discrete solution space in a timely manner, we first formulate each optimization problem as an Integer Linear Programming (ILP), and then propose efficient algorithms to derive near-optimal solutions based on relaxation, Lagrangian decomposition, duality iteration, and rounding techniques. Extensive simulations show that ERSA+D can increase network throughput by up to 1652% and 113%, respectively, thanks to EPS assignment optimization, and all-optical switching based entanglement distribution.
Quantum network implementations using single spontaneous parametric downconversion (SPDC)-based broadband entangled photon pair source (EPPS) have been reported recently. Here, leveraging the wavelength-correlation between entangled photon pairs, the traditional wavelength division multiplexing (WDM) method is utilized to route photons based on their wavelengths. From single EPPS, entangled photon pairs are distributed in a centralized way to different node pairs in the network. However, the number of nodes pairs that can be entangled in a network is limited by the number of entangled wavelength pairs that an EPPS can generate. To entangle a higher number of node pairs in a network, multiple EPPSs can be employed. In this work, we present a WDM-based entanglement distribution approach using multiple EPPSs in multi-hop repeaterless mesh optical networks. We experimentally characterize two EPPSs developed in-house and consider multiple such EPPSs in the network to perform network-level simulations. We consider heterogeneous entanglement demands requiring different entanglement bit (ebit) rates and entanglement visibility. For each entanglement demand, EPPS placement/selection, wavelength-pair assignment, and photon pair routing are performed considering the degradation in both ebit rate and visibility with fiber length and hops in the network. Two main findings of this study include: (i) a hybrid approach of one-photon (OP) and both-photon (BP) entanglement distribution provides higher flexibility in multi-EPPS placement and (ii) distributed entanglement distribution using multiple EPPSs enables better entanglement resource utilization and higher entanglement demand acceptance as compared to centralized entanglement distribution.
Quantum networks are designed to transmit quantum bits (qubits) among quantum devices to enable new network resources for the applications. Entanglement distribution and entanglement swapping are fundamental procedures that are required in several network operations. However, they are probabilistic operations, which can lead to severe network performance degradation. This article investigates the engineering problem of resource allocation in quantum networks, considering factors like entanglement distribution probability, quantum memory characteristics, and fidelity. We model this as an optimization model to obtain an optimal solution. In particular, we formulate an integer linear programming (ILP) and develop a heuristic algorithm, aiming to minimize the number of required entangled qubit pairs (Bell pairs or EPR pairs) in any adjacent pair in the quantum network. Extensive simulations are performed to compare the performance of proposed ILP and heuristic. In all the cases, the heuristic produces a comparable solution to the optimal one. Simulation results ensure that the value of maximum utilized Bell pairs in a quantum network highly depends on the value of the probability of entangled pairs established, considering the time in the quantum memory besides the number of incoming requests.
Entanglement-based networks provide a scalable framework for multiuser quantum communication by passively routing spectrally correlated photon pairs across interconnected nodes. Several wavelength-allocation schemes have already been demonstrated experimentally, but these designs do not yet provide a general way to determine how spectral use, receiver load, repeated connections, fan-out, and optical loss constrain one another. Motivated by a field-deployed four-node network, we formulate wavelength assignment as an exact resource-optimization problem on the network connectivity graph. We consider uniquely paired wavelength channels and require that no user receive both channels of a pair. For one-sided fan-out, we obtain an exact optimization for arbitrary networks, and closed-form resource laws for complete networks and for networks with one excluded partner per user. Allowing both conjugate wavelengths to fan out changes the resource landscape. In complete networks, a balanced binary hierarchy uses the minimum number of spectral layers among nonredundant assignments while reducing the maximum receiver wavelength load to a quantity that grows logarithmically with the number of users. For eight users, the source-cost ordering depends on splitter transmission: changing the transmission can change which architecture requires less pair generation. We formulate a BBM92 rate model for evaluating the corresponding architectures. For a single continuous-wave broadband source, the occupied wavelength pairs are generated with fixed relative weights, while detector singles and accidental coincidences couple the link rates. The same resource laws can therefore be evaluated using the measured parameters of the hardware that implements the network.
As practical quantum networks approach large-scale deployment, the need for efficient user-to-user frequency allocation is increasing, yet current approaches only provide partial solutions to the routing and spectrum allocation problem for an arbitrary quantum network. We address this challenge for repeater-less flex-grid quantum networks based on hyperentangled photons using an efficient three-stage pipeline combining leading tools in classical networking with recent advances in numerical optimization. First, double instantiations of Yen's algorithm obtain low-loss route candidates between each pair of users and the entanglement sources. Second, the advanced process optimizer (APOPT) obtains frequency channel allocations that maximize distribution rates under fidelity constraints. Finally, the constraint programming solver using satisfiability methods (CP-SAT) assigns specific frequency bins to each link, ensuring that there is no contention between frequencies from different sources. We numerically demonstrate this approach on a representative ring network and a Manhattan incumbent local exchange carrier topology, realizing significant improvements over prior genetic algorithm approaches in speed, accuracy, and scalability. Overall, this pipeline provides an efficient heuristic workflow for optimizing broadband entanglement distribution, applicable to arbitrarily connected quantum networks integrated within the existing lightwave infrastructure.