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1. Quantum repeaters: From quantum networks to the quantum internet

   https://doi.org/10.1103/RevModPhys.95.045006  

   Azuma, Koji; Economou, Sophia E.; Elkouss, David; Hilaire, Paul; Jiang, Liang; Lo, Hoi-Kwong; Tzitrin, Ilan (December 2023, Reviews of Modern Physics)

   A quantum internet is the holy grail of quantum information processing, enabling the deployment of a broad range of quantum technologies and protocols on a global scale. However, numerous challenges must be addressed before the quantum internet can become a reality. Perhaps the most crucial of these is the realization of a quantum repeater, an essential component in the long-distance transmission of quantum information. As the analog of a classical repeater, extender, or booster, the quantum repeater works to overcome loss and noise in the quantum channels constituting a quantum network. Here the conceptual frameworks and architectures for quantum repeaters, as well as the experimental progress toward their realization, are reviewed. Various near-term proposals to overcome the limits to the communication rates set by point-to-point quantum communication are also discussed. Finally, the manner in which quantum repeaters fit within the broader challenge of designing and implementing a quantum internet is overviewed. 

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2. A quantum walk control plane for distributed quantum computing in quantum networks

   https://doi.org/10.1109/QCE52317.2021.00048  

   de Andrade, Matheus Guedes; Dai, Wenhan; Guha, Saikat; Towsley, Don (November 2021, 2021 IEEE International Conference on Quantum Computing and Engineering (QCE))

   Quantum networks are complex systems formed by the interaction among quantum processors through quantum channels. Analogous to classical computer networks, quantum networks allow for the distribution of quantum computation among quantum computers. In this work, we describe a quantum walk protocol to perform distributed quantum computing in a quantum network. The protocol uses a quantum walk as a quantum control signal to perform distributed quantum operations. We consider a generalization of the discrete-time coined quantum walk model that accounts for the interaction between a quantum walker system in the network graph with quantum registers inside the network nodes. The protocol logically captures distributed quantum computing, abstracting hardware implementation and the transmission of quantum information through channels. Control signal transmission is mapped to the propagation of the walker system across the network, while interactions between the control layer and the quantum registers are embedded into the application of coin operators. We demonstrate how to use the quantum walker system to perform a distributed CNOT operation, which shows the universality of the protocol for distributed quantum computing. Furthermore, we apply the protocol to the task of entanglement distribution in a quantum network. 

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3. A quantum algorithm for evolving open quantum dynamics on quantum computing devices

   https://doi.org/10.1038/s41598-020-60321-x  

   Hu, Zixuan; Xia, Rongxin; Kais, Sabre (February 2020, Scientific Reports)

   Abstract Designing quantum algorithms for simulating quantum systems has seen enormous progress, yet few studies have been done to develop quantum algorithms for open quantum dynamics despite its importance in modeling the system-environment interaction found in most realistic physical models. In this work we propose and demonstrate a general quantum algorithm to evolve open quantum dynamics on quantum computing devices. The Kraus operators governing the time evolution can be converted into unitary matrices with minimal dilation guaranteed by the Sz.-Nagy theorem. This allows the evolution of the initial state through unitary quantum gates, while using significantly less resource than required by the conventional Stinespring dilation. We demonstrate the algorithm on an amplitude damping channel using the IBM Qiskit quantum simulator and the IBM Q 5 Tenerife quantum device. The proposed algorithm does not require particular models of dynamics or decomposition of the quantum channel, and thus can be easily generalized to other open quantum dynamical models. 

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4. Quantum Chaos is Quantum

   https://doi.org/10.22331/q-2021-05-04-453  

   Leone, Lorenzo; Oliviero, Salvatore F.; Zhou, You; Hamma, Alioscia (May 2021, Quantum)

   null (Ed.)

   It is well known that a quantum circuit on N qubits composed of Clifford gates with the addition of k non Clifford gates can be simulated on a classical computer by an algorithm scaling as poly ( N ) exp ⁡ ( k ) \cite{bravyi2016improved}. We show that, for a quantum circuit to simulate quantum chaotic behavior, it is both necessary and sufficient that k = Θ ( N ) . This result implies the impossibility of simulating quantum chaos on a classical computer. 

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5. One-Shot Quantum State Redistribution and Quantum Markov Chains

   https://doi.org/10.1109/ISIT45174.2021.9517813  

   Anshu, Anurag; Hadiashar, Shima Bab; Jain, Rahul; Nayak, Ashwin; Touchette, Dave (July 2021, 2021 IEEE International Symposium on Information Theory (ISIT))

   We revisit the task of quantum state redistribution in the one-shot setting, and design a protocol for this task with communication cost in terms of a measure of distance from quantum Markov chains. More precisely, the distance is defined in terms of quantum max-relative entropy and quantum hypothesis testing entropy. Our result is the first to operationally connect one-shot quantum state redistribution and quantum Markov chains, and can be interpreted as an operational interpretation for a possible one-shot analogue of quantum conditional mutual information. The communication cost of our protocol is lower than all previously known ones and asymptotically achieves the well-known rate of quantum conditional mutual information. Thus, our work takes a step towards the important open question of near-optimal characterization of the one-shot quantum state redistribution. 

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