Paramount for performances of quantum network applications are the structure and quality of distributed entanglement. Here we propose a scalable and efficient approach to reveal the topological information of unknown quantum networks, and quantify entanglement simultaneously. The scheme exploits entropic uncertainty, an operationally meaningful measure of correlation, by performing only two local measurements on each qubit. Moreover, when measurement outcomes in each node are collectively evaluated, integrating uncertainty and mutual information enables a direct count of the number of bipartite sources between any two nodes. This surpasses what is possible via applying either approach solely. Moreover, quantum error mitigation techniques including probabilistic error cancellation (PEC) and virtual distillation (VD), which have been widely applied to suppress biases in single expectation value, are further incorporated to mitigate errors in entropic quantities. We find that PEC successfully removes deviations in correlation estimations. Meanwhile, VD extends the depolarizing noise strength that allows for valid bipartite entanglement certification from 8.8% to 26.4%, thus substantially enhancing robustness against bias-inducing noise in practical situations. The proposal is applicable to a broad variety of platforms and helps to spur future studies toward harnessing the advantages of quantum networks.
Paramount for performances of quantum network applications are the structure and quality of distributed entanglement. Here we propose a scalable and efficient approach to reveal the topological information of unknown quantum networks, and quantify entanglement simultaneously. The scheme exploits entropic uncertainty, an operationally meaningful measure of correlation, by performing only two local measurements on each qubit. Moreover, when measurement outcomes in each node are collectively evaluated, integrating uncertainty and mutual information enables a direct count of the number of bipartite sources between any two nodes. This surpasses what is possible via applying either approach solely. Moreover, quantum error mitigation techniques including probabilistic error cancellation (PEC) and virtual distillation (VD), which have been widely applied to suppress biases in single expectation value, are further incorporated to mitigate errors in entropic quantities. We find that PEC successfully removes deviations in correlation estimations. Meanwhile, VD extends the depolarizing noise strength that allows for valid bipartite entanglement certification from 8.8% to 26.4%, thus substantially enhancing robustness against bias-inducing noise in practical situations. The proposal is applicable to a broad variety of platforms and helps to spur future studies toward harnessing the advantages of quantum networks.
Statistical correlations that can be generated across the nodes in a quantum network depend crucially on its topology.However, this topological information might not be known a priori, or it may need to be verified.In this paper, we propose an efficient protocol for distinguishing and inferring the topology of a quantum network.We leverage entropic quantities-namely, the von Neumann entropy and the measured mutual information-as well as measurement covariance to uniquely characterize the topology.We show that the entropic quantities are sufficient to distinguish two networks that prepare GHZ states.Moreover, if qubit measurements are available, both entropic quantities and covariance can be used to infer the network topology without state-preparation assumptions.We show that the protocol can be entirely robust to noise and can be implemented via quantum variational optimization.Numerical experiments on both classical simulators and quantum hardware show that covariance is generally more reliable for accurately and efficiently inferring the topology, whereas entropy-based methods are often better at identifying the absence of entanglement in the low-shot regime.
Distributed quantum information in networks is paramount for global secure quantum communication. Moreover, it finds applications as a resource for relevant tasks, such as clock synchronization, magnetic field sensing, and blind quantum computation. For quantum network analysis and benchmarking of implementations, however, it is crucial to characterize the topology of networks in a way that reveals the nodes between which entanglement can be reliably distributed. Here, we demonstrate an efficient scheme for this topology certification. Our scheme allows for distinguishing, in a scalable manner, different networks consisting of bipartite and multipartite entanglement sources. It can be applied to semi-device-independent scenarios also, where the measurement devices and network nodes are not well characterized and trusted. We experimentally demonstrate our approach by certifying the topology of different six-qubit networks generated with polarized photons, employing active feed-forward and time multiplexing. Our methods can be used for general simultaneous tests of multiple hypotheses with few measurements, being useful for other certification scenarios in quantum technologies.
Until fault-tolerance becomes implementable at scale, quantum computing will heavily rely on noise mitigation techniques. While methods such as zero noise extrapolation with probabilistic error amplification (ZNE-PEA) and probabilistic error cancellation (PEC) have been successfully tested on hardware recently, their scalability to larger circuits may be limited. Here, we introduce the tensor-network error mitigation (TEM) algorithm, which acts in post-processing to correct the noise-induced errors in estimations of physical observables. The method consists of the construction of a tensor network representing the inverse of the global noise channel affecting the state of the quantum processor, and the consequent application of the map to informationally complete measurement outcomes obtained from the noisy state. TEM does therefore not require additional quantum operations other than the implementation of informationally complete POVMs, which can be achieved through randomised local measurements. The key advantage of TEM is that the measurement overhead is quadratically smaller than in PEC. We test TEM extensively in numerical simulations in different regimes. We find that TEM can be applied to circuits of twice the depth compared to what is achievable with PEC under realistic conditions with sparse Pauli-Lindblad noise, such as those in [E. van den Berg et al., Nat. Phys. (2023)]. By using Clifford circuits, we explore the capabilities of the method in wider and deeper circuits with lower noise levels. We find that in the case of 100 qubits and depth 100, both PEC and ZNE fail to produce accurate results by using ∼105 shots, while TEM succeeds.
Virtual distillation is a promising error-mitigation technique that exploits multiple copies of a noisy quantum state to estimate observables as if measured on a purified state. Although originally introduced in the context of bosonic many-body systems under the name of virtual cooling, its development and applications have largely focused on qubit-based quantum computation. Here, we establish a framework for virtual distillation in bosonic quantum information processing and continuous-variable quantum computing. Building on a diagonalization of cyclic shift operators implemented with passive linear-optical interferometers, we derive experimentally accessible protocols for estimating virtually distilled expectation values of observables relevant to bosonic architectures. In particular, we show how to recover noise-mitigated expectation values of number operators, phase-shift operators, and arbitrary quadratures from multi-copy measurements. For number operators, we further demonstrate the estimation of virtually distilled correlators of arbitrary order through the characteristic function of the photon-number distribution. We apply the framework to states affected by photon loss and dephasing, two of the dominant noise mechanisms in bosonic quantum computation, and quantify the resulting suppression of noise contributions. Our results extend virtual distillation beyond its original setting and provide a practical route toward error-mitigated measurements in bosonic quantum processors using experimentally available linear-optical resources.
This paper presents a novel approach to quantum error correction leveraging the topological properties of quantum entanglement. Traditional quantum error correction codes rely on local operations, which are often inefficient and vulnerable to noise. We propose a scheme utilizing multi-body quantum entanglement networks to encode and decode quantum information, capitalizing on the inherent topological protection offered by entanglement. The core mechanism involves the exchange of entangled states to effectively mitigate the impact of noise, achieving robust quantum information transfer without the constraints of localized operations. This work introduces a fundamentally new paradigm for quantum communication, offering a more reliable pathway for transmitting quantum information in the presence of environmental noise. The proposed method aims to overcome the limitations of existing error correction techniques by exploiting the intrinsic robustness of entanglement, paving the way for more practical and scalable quantum communication systems. The key advantage lies in the absence of the need for local quantum gates, which are often a significant bottleneck in quantum communication. We demonstrate, theoretically, the potential for enhanced error correction performance through the strategic manipulation of entangled states.
Long-distance quantum networks are far more than mere channels for data transfer; they are sophisticated systems that harness the counterintuitive features of quantum mechanics to enable secure and high-performance communication over vast distances. In our study, we explore the underlying mechanisms of quantum connectivity by investigating phenomena such as superposition and entanglement, and their roles in sustaining robust information propagation. We focus on the interaction between these quantum effects and routing protocols strategies that, while inspired by classical networks, must overcome challenges associated with quantum decoherence and measurement uncertainty. To evaluate these interactions, we simulated distributed quantum networks with node counts ranging from 10 to 100 using novel routing strategies including Q-Learning, Bell State, and Entanglement Swapping protocols. Our analysis centers on key performance metrics that capture both quantum fidelity and operational efficiency. Notably, our results show that high quantum state fidelity is maintained across all network configurations, confirming the efficacy of entangled states in preserving the integrity of quantum information over long distances. Simultaneously, we observe that increased network complexity introduces trade-offs, such as higher computational overhead and amplified susceptibility to decoherence and error propagation. These findings underscore the necessity for advanced error-correction techniques and adaptive routing strategies to ensure scalability and robustness in long-distance quantum communication. Overall, our work provides critical insights into optimizing quantum superposition and entanglement in practical routing implementations, thereby paving the way for the future realization of a global quantum communication infrastructure.