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1. Emergent complex quantum networks in continuous-variables non-Gaussian states

   Mattia Walschaers, Nicolas Treps (July 2021, ArXivorg)

   Large multipartite quantum systems tend to rapidly reach extraordinary levels of complexity as their number of constituents and entanglement links grow. Here we use complex network theory to study a class of continuous variables quantum states that present both multipartite entanglement and non-Gaussian statistics. In particular, the states are built from an initial imprinted cluster state created via Gaussian entangling operations according to a complex network structure. To go beyond states that can be easily simulated via classical computers we engender non-Gaussian statistics via multiple photon subtraction operations. We then use typical networks measures, the degree and clustering, to characterize the emergent complex network of photon-number correlations after photon subtractions. We show that, in contrast to regular clusters, in the case of imprinted complex network structures the emergent correlations are strongly affected by photon subtraction. On the one hand, we unveil that photon subtraction universally increases the average photon-number correlations, regardless of the imprinted network structure. On the other hand, we show that the shape of the distributions in the emergent networks after subtraction is greatly influenced by the structure of the imprinted network, as witnessed by their higher-moments. Thus for the field of network theory, we introduce a new class of networks to study. At the same time for the field of continuous variable quantum states, this work presents a new set of practical tools to benchmark systems of increasing complexity. 

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2. Response of quantum spin networks to attacks

   https://doi.org/10.1088/2632-072X/abf5c2  

   Sundar, Bhuvanesh; Walschaers, Mattia; Parigi, Valentina; Carr, Lincoln D. (May 2021, Journal of Physics: Complexity)

   Abstract We investigate the ground states of spin models defined on networks that we imprint (e.g., non-complex random networks like Erdos–Renyi, or complex networks like Watts–Strogatz, and Barabasi–Albert), and their response to decohering processes which we model with network attacks. We quantify the complexity of these ground states, and their response to the attacks, by calculating distributions of network measures of an emergent network whose link weights are the pairwise mutual information between spins. We focus on attacks which projectively measure spins. We find that the emergent networks in the ground state do not satisfy the usual criteria for complexity, and their average properties are captured well by a single dimensionless parameter in the Hamiltonian. While the response of classical networks to attacks is well-studied, where classical complex networks are known to be more robust to random attacks than random networks, we find counter-intuitive results for our quantum networks. We find that the ground states for Hamiltonians defined on different classes of imprinted networks respond similarly to all our attacks, and the attacks rescale the average properties of the emergent network by a constant factor. Mean field theory explains these results for relatively dense networks, but we also find the simple rescaling behavior away from the regime of validity of mean field theory. Our calculations indicate that complex spin networks are not more robust to projective measurement attacks, and presumably also other quantum attacks, than non-complex spin networks, in contrast to the classical case. Understanding the response of the spin networks to decoherence and attacks will have applications in understanding the physics of open quantum systems, and in designing robust complex quantum systems—possibly even a robust quantum internet in the long run—that is maximally resistant to decoherence. 

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3. A Simulator of Atom-Atom Entanglement with Atomic Ensembles and Quantum Optics

   https://doi.org/10.1109/QCE57702.2023.00143  

   Zhou, Ruilin; Lai, Xuanying; Gan, Yuhang; Obraczka, Katia; Du, Shengwang; Qian, Chen (September 2023, IEEE)

   One fundamental goal of quantum networks is to provide node-to-node entanglement distribution. In this work, we develop a simulator, called A 2 Tango, for entanglement generation between two remote atom-ensemble nodes in a quantum network following Briegel, Dur, Cirac and Zoller (BDCZ) protocol. We encode quantum information to the two spatial modes of local atomic-ensemble spin waves and polarization states of single photons. The basic operations include atom-photon entanglement generation, quantum memory write-read operations, two-photon Bell-state measurement, and quantum state tomography. We model multi-photon events during the local excitation and propagation to account for their induced error in entanglement generation and distribution. We investigate the entanglement generation rate and fidelity as functions of the parameters which are realizable in experiments. Our work improves the open-sourced SeQUeNCe simulator and inspires the development of future quantum networks. 

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4. Measurement-based generation and preservation of cat and grid states within a continuous-variable cluster state

   https://doi.org/10.22331/q-2022-07-20-769  

   Eaton, Miller; González-Arciniegas, Carlos; Alexander, Rafael N.; Menicucci, Nicolas C.; Pfister, Olivier (July 2022, Quantum)

   We present an algorithm to reliably generate various quantum states critical to quantum error correction and universal continuous-variable (CV) quantum computing, such as Schrödinger cat states and Gottesman-Kitaev-Preskill (GKP) grid states, out of Gaussian CV cluster states. Our algorithm is based on the Photon-counting-Assisted Node-Teleportation Method (PhANTM), which uses standard Gaussian information processing on the cluster state with the only addition of local photon-number-resolving measurements. We show that PhANTM can apply polynomial gates and embed cat states within the cluster. This method stabilizes cat states against Gaussian noise and perpetuates non-Gaussianity within the cluster. We show that existing protocols for breeding cat states can be embedded into cluster state processing using PhANTM. 

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5. Non-Gaussian and Gottesman–Kitaev–Preskill state preparation by photon catalysis

   https://doi.org/10.1088/1367-2630/ab5330  

   Eaton, Miller; Nehra, Rajveer; Pfister, Olivier (November 2019, New Journal of Physics)

   Abstract Continuous-variable quantum-computing is the most scalable implementation of QC to date but requires non-Gaussian resources to allow exponential speedup and quantum correction, using error encoding such as Gottesman–Kitaev–Preskill (GKP) states. However, GKP state generation is still an experimental challenge. We show theoretically that photon catalysis, the interference of coherent states with single-photon states followed by photon-number-resolved detection, is a powerful enabler for non-Gaussian quantum state engineering such as exactly displaced single-photon states andM-symmetric superpositions of squeezed vacuum (SSV), including squeezed cat states (M= 2). By including photon-counting based state breeding, we demonstrate the potential to enlarge SSV states and produce GKP states. 

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