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arXiv:2211.06069 · IEEE Network

Quantum Routing for Emerging Quantum Networks

Wenbo Shi, Robert Malaney

Published Oct 3, 2023• 16 citations
arXivHTMLPDF

Abstract

Quantum routing, the entanglement of an input quantum signal over multiple output paths, will be an important aspect of future quantum networks. Implementation of such routing in near-term quantum networks via the noisy quantum devices currently under development is a distinct possibility. Quantum error correction, suitable for the arbitrary noisy quantum channels experienced in the routing process, will be required. In this work, we design a combined circuit for quantum routing and quantum error correction, and carry out an implementation of such a circuit on a noisy real-world quantum device. Under the assumption of statistical knowledge on the channel, we experimentally verify the quantum nature of the error-corrected quantum routing by determining the path-entanglement through quantum state tomography, measuring also its probability of success. The quantum error correction deployed is identified as successful in terms of improving the routing. Our experiments validate, for the first time, that error-corrected quantum routing in near-term quantum networks is feasible, provided enough statistical information on the noise intrinsic to the routing device isa prioriknown.

DOI
10.1109/mnet.2023.3317821

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Quantum routing, the entanglement of an input quantum signal over multiple output paths, will be an important aspect of future quantum networks. Implementation of such routing in near-term quantum networks via the noisy quantum devices currently under development is a distinct possibility. Quantum error correction, suitable for the arbitrary noisy quantum channels experienced in the routing process, will be required. In this work, we design a combined circuit for quantum routing and quantum error correction, and carry out an implementation of such a circuit on a noisy real-world quantum device. Under the assumption of statistical knowledge on the channel, we experimentally verify the quantum nature of the error-corrected quantum routing by determining the path-entanglement through quantum state tomography, measuring also its probability of success. The quantum error correction deployed is identified as successful in terms of improving the routing. Our experiments validate, for the first time, that error-corrected quantum routing in near-term quantum networks is feasible, provided enough statistical information on the noise intrinsic to the routing device isa prioriknown.
Quantum routers will provide for important functionality in emerging quantum networks, and the deployment of quantum routing in real networks will initially be realized on low-complexity (few-qubit) noisy quantum devices. A true working quantum router will represent a new application for quantum entanglement-the coherent superposition of multiple communication paths traversed by the same quantum signal. Most end-user benefits of this application are yet to be discovered, but a few important use-cases are now known. In this work, we investigate the deployment of quantum routing on low-complexity superconducting quantum devices. In such devices, we verify the quantum nature of the routing process as well as the preservation of the routed quantum signal. We also implement quantum random access memory, a key application of quantum routing, on these same devices. Our experiments then embed a five-qubit quantum error-correcting code within the router, outlining the pathway for error-corrected quantum routing. We detail the importance of the qubit-coupling map for a superconducting quantum device that hopes to act as a quantum router, and experimentally verify that optimizing the number of controlled-X gates decreases hardware errors that impact routing performance. Our results indicate that near-term realization of quantum routing using noisy superconducting quantum devices within real-world quantum networks is possible.
With sub-threshold quantum error correction on quantum hardware still out of reach, quantum error mitigation methods are currently deemed an attractive option for implementing certain applications on near-term noisy quantum devices. One such application is quantum routing - the ability to map an incoming quantum signal into a superposition of paths. In this work, we use a 7-qubit IBM quantum device to experimentally deploy two promising quantum error mitigation methods, Zero-Noise Extrapolation (ZNE) and Probabilistic Error Cancellation (PEC), in the context of quantum routing. Importantly, beyond investigating the improved performance of quantum routing via ZNE and PEC separately, we also investigate the routing performance provided by the concatenation of these two error-mitigation methods. Our experimental results demonstrate that such concatenation leads a very significant performance improvement relative to implementation with no error mitigation. Indeed, an almost perfect performance in terms of fidelity of the output entangled paths is found. These new results reveal that with concatenated quantum error-mitigation embedded, useful quantum routing becomes feasible on current devices without the need for quantum error correction - opening up a potential implementation pathway to other applications that utilize a superposition of communication links.
Quantum error correction (QEC) remains a critical challenge for the realization of fault-tolerant quantum computation. A significant bottleneck in QEC performance stems from the propagation of errors through entangled states. This paper introduces a novel algorithm, Entanglement Routing Algorithm (ERA), designed to optimize the routing of entangled states within a quantum circuit, thereby minimizing error propagation. The core idea revolves around leveraging quantum decoherence theory and implementing a path optimization strategy to identify the most resilient routes. The algorithm constructs a network representation of the quantum circuit and employs a cost function that quantifies the potential for information loss along each path, considering decoherence rates and connectivity. The optimization process then seeks the route that minimizes this cost function. Simulation results demonstrate that ERA can significantly reduce error propagation compared to naive routing strategies, paving the way for more robust and efficient QEC protocols.
The use of quantum teleportation in future quantum networks creates a completely new way for communication. As the quantum link length increased, the fidelity decreased, owing to the loss of quantum information between distant quantum nodes. This paper conducts an exploration of quantum fidelity routing design that is intended to specifically focus on the applicability of quantum error correction (QEC) as the scale of the network expands. Our research involves proposing a novel Quantum-maximum Fidelity miNimum Dijkstra's (Q-FIND) algorithm incorporated with QEC, which is designed to not only improve the long-distance link fidelity, but also to further reduce the network latency under the conditions of a noisy quantum channel. By using Qiskit, we examine the performance of proposed routing algorithm. Our simulation result reveals that the significance of QEC becomes more prominent in long-distance quantum networks.
Near-term quantum communication protocols suffer inevitably from channel noises, whose alleviation has been mostly attempted with resources such as multiparty entanglement or sophisticated experimental techniques. Generation of multiparty higher dimensional entanglement is not easy. This calls for exploring realistic solutions which are implementable with current devices. Motivated particularly by the difficulty in generation of multiparty entangled states, in this paper, we have investigated error-free information transfer with minimal requirements. For this, we have proposed a new information encoding scheme for communication purposes. The encoding scheme is based on the fact that most noisy channels leave some quantities invariant. Armed with this fact, we encode information in these invariants. These invariants are functions of expectation values of operators. This information passes through the noisy channel unchanged. Pertinently, this approach is not in conflict with other existing error correction schemes. In fact, we have shown how standard quantum error-correcting codes emerge if suitable restrictions are imposed on the choices of logical basis states. As applications, for illustration, we propose a quantum key distribution protocol and an error-immune information transfer protocol.
Finding a path with the least overall noise from quantum memories, fibers, and gate operations in a quantum network involves the challenge of acquiring knowledge of these noises, their sources, and the time of occurrences. In this paper, we propose a reinforcement learning-based route selection approach that uses a multi-arm bandit algorithm to find the least noisy path from a transmitter (Tx) to a receiver (Rx), without considering any information on qubit decoherence due to probabilistic noises inherent in quantum memories and imperfect gate operations. It only uses network deployment knowledge to find a set of feasible paths from Tx to Rx. We provide a key finding from a network design perspective which says that performing entanglement swapping on nodes within a path in a non-synchronized and parallel manner not always reduces the decoherence experienced in achieving the end-to-end entanglement on that path. Further, we design and open-source a new simulator for simulating probabilistic noises encountered during entanglement distribution between Tx-Rx on a path, which has supporting callable functions for connecting the unknown network environment required for interaction with the multi-arm bandit agent. The simulation results demonstrate that our proposed route selection approach provides a path up to ~ 33% better fidelity (less noise) compared to conventional, distance-based route selection approach for the considered quantum network.