Quantum repeaters pave the way for long-distance quantum communications and quantum Internet, and the idea of quantum repeaters is based on entanglement swapping which requires the implementation of controlled quantum gates. Frequently measuring a quantum system affects its dynamics which is known as the quantum Zeno effect (QZE). Beyond slowing down its evolution, QZE can be used to control the dynamics of a quantum system by introducing a carefully designed set of operations between measurements. Here, we propose an entanglement swapping protocol based on QZE, which achieves almost unit fidelity. Implementation of our protocol requires only simple frequent threshold measurements and single particle rotations. We extend the proposed entanglement swapping protocol to a series of repeater stations for constructing quantum Zeno repeaters which also achieve almost unit fidelity regardless of the number of repeaters. Requiring no controlled gates, our proposal reduces the quantum circuit complexity of quantum repeaters. Our work has potential to contribute to long distance quantum communications and quantum computing via quantum Zeno effect.
Quantum repeaters pave the way for long-distance quantum communications and quantum Internet, and the idea of quantum repeaters is based on entanglement swapping which requires the implementation of controlled quantum gates. Frequently measuring a quantum system affects its dynamics which is known as the quantum Zeno effect (QZE). Beyond slowing down its evolution, QZE can be used to control the dynamics of a quantum system by introducing a carefully designed set of operations between measurements. Here, we propose an entanglement swapping protocol based on QZE, which achieves almost unit fidelity. Implementation of our protocol requires only simple frequent threshold measurements and single particle rotations. We extend the proposed entanglement swapping protocol to a series of repeater stations for constructing quantum Zeno repeaters which also achieve almost unit fidelity regardless of the number of repeaters. Requiring no controlled gates, our proposal reduces the quantum circuit complexity of quantum repeaters. Our work has potential to contribute to long distance quantum communications and quantum computing via quantum Zeno effect.
When built, quantum repeater networks will require classical network protocols to control the quantum operations. However, existing work on repeaters has focused on the quantum operations themselves, with less attention paid to the contents, semantics, ordering and reliability of the classical control messages. In this work we define and describe our implementation of the classical control protocols. The state machines and packet sequences for the three protocol layers are presented, and operation confirmed by running the protocols over simulations of the physical network. We also show that proper management of the resources in a bottleneck link allows the aggregate throughput of two end-to-end flows to substantially exceed that of a single flow. Our layered architectural framework will support independent evolution of the separate protocol layers. Networks of quantum repeaters utilize three concepts to execute a distributed algorithm that creates entangled quantum states between nodes that are far apart: a basic entanglement mechanism which depends on the physical implementation, error management (in this work, we study a method known as purification), and finally a quantum state propagation layer (here we implement entanglement swapping, which builds multi-hop connections from single-hop connections). Some researchers are investigating approaches that are substantially different from entanglement swapping [30, 24, 19]. Here we focus on swapping, but the layered architecture approach is broadly applicable, allowing other implementations to replace only a single layer in the protocol stack. Previous work primarily focused on the physical and mathematical tools for building repeaters. Classical information is also needed to enable teleportation and swapping, as many quantum operations are not deterministic, and results of quantum measurements need to be reported to distant partners before further operations can proceed. Also, operations in the middle of the network must be coordinated to route and swap properly. This requires classical messages to make operations robust, but message propagation times penalize performance. Even though this delay is usually included in repeater simulations, prior work has not defined the protocols in detail, especially with respect to how all of the nodes make consistent decisions in a timely fashion. In this work, we introduce a protocol stack for networks of quantum repeaters that considers all the necessary classical messages and which can be easily adapted for different approaches at all three protocol layers. We run simulations of competing flows on a dumbbell topology in order to increase our confidence in the behavior of our network protocols. By adjusting the fidelity thresholds required for entanglement swapping, we show that some configurations boost the aggregate throughput for multiple flows significantly above the maximum for a single flow, taking advantage of resources that would otherwise sit idle. The operation of such complex networks and such delicate tuning of the system without formal protocol definitions would not be possible. Previous work has also concentrated almost exclusively on the dedicated use of a single line or chain of repeaters, delivering Bell pairs only to the two nodes at the ends of the chain. Networks, however, typically have more than two end points, and allow any pair of these end nodes to communicate. More topologically complex networks, with numerous end nodes, are obviously much more scalable than connecting every possible pair of nodes using a dedicated line of repeaters. we investigate how classical multiplexing schemes translate to the domain of quantum repeaters, in order to manage shared resources and active communication flows of data from different stations. We simulate four sharing protocols in a complex network with competing traffic. Circuit switching gives any individual flow the best performance, but makes poor use of the overall network and is inflexible. We use circuit switching as our baseline case to compare time division multiplexing, buffer space multiplexing, and statistical multiplexing, and show that all multiplexing schemes are better than circuit switching. For the particular network simulated, we find that statistical multiplexing outperforms time division multiplexing by 28% and buffer space multiplexing by 13%. We find that all three multiplexing schemes are fair; each flow is penalized a similar percentage of its throughput as the the total number of users in the network increases. Finally, statistical multiplexing requires no network-wide coordination of the use of quantum memory or channels, and is easier to implement than a robust, scalable scheme for the other protocols. Our current results suggest that the best strategy for quantum repeater networks is statistical multiplexing. (This is in fact the quantum analogue of the basis on which the Internet works.) However, our current simulations are done with no degradation of memory over time, using the assumption of quantum error-corrected memory at each repeater; inclusion of decoherence and a finite qubit lifetime remains as future work.
We introduce measurement-based quantum repeaters, where small-scale measurement-based quantum processors are used to perform entanglement purification and entanglement swapping in a long-range quantum communication protocol. In the scheme, preprepared entangled states stored at intermediate repeater stations are coupled with incoming photons by simple Bell measurements, without the need of performing additional quantum gates. We show how to construct the required resource states, and how to minimize their size. We analyze the performance of the scheme under noise and imperfections, with focus on small-scale implementations involving entangled states of few qubits. We find measurement-based purification protocols with significantly improved noise thresholds. Furthermore we show that resource states of small size suffice to significantly increase the maximal communication distance. We also discuss possible advantages of our scheme for different setups.
Quantum repeaters are essential for scalable long-distance quantum networking. As quantum information processing moves toward fault-tolerant and error-corrected operations, it becomes increasingly important to study quantum repeaters that also move beyond raw physical entanglement and towards logical entanglement. In this paper, we implement and simulate the quantum repeater with encoding and classical error correction (QRE-CEC) protocol in SeQUeNCe, a discrete-event simulator of quantum networks. The protocol distributes logical Bell pairs, performs encoded entanglement swapping, and uses classical error correction for the decoding of entanglement swapping measurement outcomes to determine Pauli-frame corrections. For this study, we extend SeQUeNCe with a stabilizer-based backend, add support for CSS code-based encoded operations, and integrate gate, measurement, idle decoherence, and state-initialization noise models. Our simulation results show that QRE-CEC suppresses all modeled errors to the second order. Also, QRE-CEC can distribute logical Bell pairs with 0.91 fidelity over a distance of 2000 km under the parameter regimes we study. Beyond protocol-level performance evaluation, our implementation exposes practical simulator and control-plane challenges that are typically abstracted away in theoretical studies.
Long-distance transfer of quantum information is an essential ability for many applications of quantum science. A natural choice to distribute quantum information is to encode it into photons and transfer it through optical fibers. However, due to the unavoidable transmission losses present in every communication channel, the distances for efficient quantum communication via direct-state transfer are limited to a few hundred kilometers. To overcome this limitation, the use of quantum repeaters has been suggested. A quantum repeater protocol aims to establish entanglement (i.e., quantum correlation) between remote nodes by first generating entanglement over shorter distance pieces, storing it in quantum memories, and finally extending it to the whole distance using entanglement swapping. The main goal of this thesis is to design quantum repeater architectures using single solid-state quantum emitters and to develop the two-qubit gates required for performing entanglement swapping. We first explain the basic ideas of quantum repeaters and introduce potential material candidates, single erbium (168Er) and europium (151Eu) ions doped yttrium orthosilicate photonic crystals. Next, we propose a quantum repeater scheme combing erbium and europium ions to generate and distribute entanglement over long distances. We study the entanglement generation rate of the protocol and compare it with the rate of a well-known ensemble-based quantum repeater. Then, using cavity assisted interactions, we propose three different schemes to perform high fidelity two-qubit gates between single quantum systems. We quantify their expected performance in detail by taking into account many realistic imperfections and compare their strengths and weaknesses. The ability to perform local two-qubits gates is especially crucial in terms of distributing entanglement. Finally, based on our gained knowledge through these projects, we propose our second quantum repeater architecture based on erbium (167Er) ions, which outperforms the first scheme. We study two possibilities for distributing entanglement and calculate the overall fidelity as well as the distribution rate of the protocol.
The quantum Zeno effect (QZE) is the phenomenon in which the unitary evolution of a quantum state is suppressed, e.g., due to frequent measurements. Here, we investigate the use of the QZE in a class of communication complexity problems (CCPs). Quantum entanglement is known to solve certain CCPs beyond classical constraints. However, recent developments have yielded CCPs for which superclassical results can be obtained using only communication of a single d-level quantum state (qudit) as a resource. In the class of CCPs considered here, we show quantum reduction of complexity in three ways: using (i) entanglement and the QZE, (ii) a single qudit and the QZE, and (iii) a single qudit. We have performed a proof of concept experimental demonstrations of three party CCP protocol based on single-qubit communication with and without QZE.