Here we consider the speed at which quantum information can be transferred between the nodes of a linear network. Because such nodes are linear oscillators, this speed is also important in the cooling and state preparation of mechanical oscillators, as well as in frequency conversion. We show that if there is no restriction on the size of the linear coupling between two oscillators, then there exist control protocols that will swap their respective states with high fidelity within a time much shorter than a single oscillation period. Standard gradient search methods fail to find these fast protocols. We were able to do so by augmenting standard search methods with a path-tracing technique, demonstrating that this technique has remarkable power to solve time-optimal control problems, as well as confirming the highly challenging nature of these problems. As a further demonstration of the power of path tracing, first introduced by Moore Tibbets et al. ( Phys. Rev. A , 86 (2012) 062309), we apply it to the generation of entanglement in a linear network.
Here we consider the speed at which quantum information can be transferred between the nodes of a linear network. Because such nodes are linear oscillators, this speed is also important in the cooling and state preparation of mechanical oscillators, as well as in frequency conversion. We show that if there is no restriction on the size of the linear coupling between two oscillators, then there exist control protocols that will swap their respective states with high fidelity within a time much shorter than a single oscillation period. Standard gradient search methods fail to find these fast protocols. We were able to do so by augmenting standard search methods with a path-tracing technique, demonstrating that this technique has remarkable power to solve time-optimal control problems, as well as confirming the highly challenging nature of these problems. As a further demonstration of the power of path tracing, first introduced by Moore Tibbets et al. ( Phys. Rev. A , 86 (2012) 062309), we apply it to the generation of entanglement in a linear network.
A fully-quantum network implies the creation of quantum entanglement between a given source node and some other destination node, with a number of quantum repeaters in between. This paper tackles the problem of quantum entanglement distribution by solving the routing problem over an infrastructure based on quantum repeaters and with a finite number of pairs of entangled qubits available in each link. The network model considers that link purification is available such that a nested purification protocol can be applied at each link to generate entangled qubits with higher fidelity than the original ones. A low-complexity multi-objective routing algorithm to find the shortest path between any two given nodes is proposed and assessed for random networks, using a fairly general path extension mechanism that can fit a large family of particular technological requirements. Different types of quantum protocols require different levels of fidelity for the entangled qubit pairs. For that reason, the proposed algorithm identifies the shortest path between two nodes that assures an end-to-end fidelity above a specified threshold. The minimum requirements for the end-to-end entanglement fidelity depend on the whole extension of the paths, and cannot be looked at as a local property of each link. Moreover, one needs to keep track not only of the shortest path, but also of longer paths holding more entangled qubits than the shorter paths in order to satisfy the fidelity criterion. Thus, standard single parameter shortest-path algorithms do not necessarily converge to the optimal solution. The problem of finding the best path in a network subject to multiple criteria (known as multi-objective routing) is, in general, an NP-hard problem due to the rapid growth of the number of stored paths. This work proposes a metric that identifies and discards paths that are objectively worse than others. By doing so, the time complexity of the proposed algorithm scales near-to-linearly with respect to the number of nodes in the network, showing that the shortest-path problem in quantum networks can be solved with a complexity very close to the one of the classical counterparts. That is analytically proved for the case where all the links of a path have the same fidelity (homogeneous model). The algorithm is also adapted to a particular type of path extension, where different links along a path can be purified to different degrees, asserting its flexibility and near-to-linearity even when heterogeneous fidelities along the sections of a path are considered.
We present an approach to purification and entanglement routing on complex quantum network architectures, that is, how a quantum network equipped with imperfect channel fidelities and limited memory storage time can distribute entanglement between users. We explore how network parameters influence the performance of path-finding algorithms necessary for optimizing routing and, in particular, we explore the interplay between the bandwidth of a quantum channels and the choice of purification protocol. Finally, we demonstrate multi-path routing on various network topologies with resource constraints, in an effort to inform future design choices for quantum network configurations. Our work optimizes both the choice of path over the quantum network and the choice of purification schemes used between nodes. We consider not only pair-production rate, but optimize over the fidelity of the delivered entangled state. We introduce effective heuristics enabling fast path-finding algorithms for maximizing entanglement shared between two nodes on a quantum network, with performance comparable to that of a computationally-expensive brute-force path search.
In recent years, quantum communication networks have emerged as a promising alternative to classical communication networks for the transmission of quantum information. One of the challenges for achieving optimal performance in quantum communication networks is the efficient routing of quantum signals across multiple paths. To address this, a variety of routing protocols have been proposed, including multi-path routing protocols. Multi-path routing involves sending a quantum signal through multiple distinct paths simultaneously to reduce delays in the transmission of quantum information. By distributing the quantum information over multiple paths, this approach can provide significant performance improvements, including reduced latency and higher throughput. In addition, multi-path routing can enable new possibilities for the security of quantum communication networks, such as more secure entanglement swapping protocols and improved protection against eavesdropping. In this paper, we investigate the performance of multi-path routing protocols in multi-node quantum communication networks. We consider two approaches to multi-path routing, a basic routing approach based on shortest path optimization, and a more advanced approach based on graph partitions. We evaluate the performance of these protocols in a range of multi-node networks, with focus on the trade-off between latency and throughput. The results show that multi-path routing yields significant performance improvements in such networks and provides an efficient way for routing quantum signals across multiple paths.
It is essential to establish precise times in future communication networks. Any real-time task's function depends on the system's ability to synchronise time. Time synchronisation is critical in the current communication network and must be maintained to transmit data packets. The functionality of 6G, the Tactile Internet, Time-Sensitive Networking, and ultra-reliable low-latency communications is highly susceptible to time synchronisation. We investigated the idea of employing time synchronisation across different communication network nodes. The current state-of-the-art employs network protocols like Precision-Time Protocol for synchronising clocks across different nodes. These network protocols are not robust and can generate jitters in data transmission. In this paper, we suggested synchronising the time of the node clocks at three different places using quantum technology. Notably, the oscillation frequencies of each qubit (or oscillator) located at these nodes can be synchronised using the quantum synchronisation technique. This set of three oscillators will work as a single clock and will be the master clock of the network. We propose distributing precise time and frequency standards using quantum synchronisation on node clocks. We can synchronise the three qubits (each placed at one node) to oscillate at an identical frequency by applying an external field of a wavelength of 813.32 nm. We analysed our model for different coupling constants and dissipation rates to provide an analysis of the behaviour of the amount of synchronisation in different experimental configurations. The optimal accuracy for our system is 1.6×1015 signals per second. Further, we used the Allan deviation to examine the stability of our system for various noise strengths.
Efficiently controlling linear Gaussian quantum (LGQ) systems is a significant task in both the study of fundamental quantum theory and the development of modern quantum technology. Here, we propose a general quantum-learning-control method for optimally controlling LGQ systems based on the gradient-descent algorithm. Our approach flexibly designs the loss function for diverse tasks by utilizing first- and second-order moments that completely describe the quantum state of LGQ systems. We demonstrate both deep optomechanical cooling and large optomechanical entanglement using this approach. Our approach enables the fast and deep ground-state cooling of a mechanical resonator within a short time, surpassing the limitations of sideband cooling in the continuous-wave driven strong-coupling regime. Furthermore, optomechanical entanglement could be generated remarkably fast and surpass several times the corresponding steady-state entanglement, even when the thermal phonon occupation reaches one hundred. This work will not only broaden the application of quantum learning control, but also open an avenue for optimal control of LGQ systems.
Future communication systems are expected to integrate quantum networks to enable highly secure communication and enhance computational capabilities. In quantum networks, communication is accomplished by sharing entanglement between remote locations, which is the basis for most known quantum protocols. Entanglement is a correlation between qubits that is not reproducible with classical means. However, as entanglement is susceptible to noise limiting its range, quantum repeaters can enable entanglement over more considerable distances. Using the entanglement swapping protocol, quantum repeaters can be placed between remote locations to establish entanglement. This requires each repeater to first generate entanglement with its neighboring nodes, named entanglement generation. However, as the size of current quantum networks is limited, the development and evaluation of quantum networks and quantum protocols is based on simulations. To simulate quantum networks accurately, accurate and high-performance models of the entanglement generation process must be employed. This paper proposes two new models for generating entanglement in simulations and develops quantum protocols for generating and purifying entanglement. The protocols are evaluated in thorough simulations under perfect and realistic conditions regarding delay and fidelity. Furthermore, the accuracy and runtime of the models are evaluated. The results show the models are accurate, with delay primarily influenced by the source duration, while longer coherence times significantly enhance fidelity. The model runtimes are consistently shorter than the simulation runtimes across all protocols, averaging about 2% of the total simulation time.