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1. Quantum spacetime on a quantum simulator

   https://doi.org/10.1038/s42005-019-0218-5  

   Li, Keren; Li, Youning; Han, Muxin; Lu, Sirui; Zhou, Jie; Ruan, Dong; Long, Guilu; Wan, Yidun; Lu, Dawei; Zeng, Bei; et al (December 2019, Communications Physics)
2. Variational quantum unsampling on a quantum photonic processor

   https://doi.org/10.1038/s41567-019-0747-6  

   Carolan, Jacques; Mohseni, Masoud; Olson, Jonathan P.; Prabhu, Mihika; Chen, Changchen; Bunandar, Darius; Niu, Murphy Yuezhen; Harris, Nicholas C.; Wong, Franco N.; Hochberg, Michael; et al (March 2020, Nature Physics)
3. Training of quantum circuits on a hybrid quantum computer

   https://doi.org/10.1126/sciadv.aaw9918  

   Zhu, D.; Linke, N. M.; Benedetti, M.; Landsman, K. A.; Nguyen, N. H.; Alderete, C. H.; Perdomo-Ortiz, A.; Korda, N.; Garfoot, A.; Brecque, C.; et al (October 2019, Science Advances)

   Generative modeling is a flavor of machine learning with applications ranging from computer vision to chemical design. It is expected to be one of the techniques most suited to take advantage of the additional resources provided by near-term quantum computers. Here, we implement a data-driven quantum circuit training algorithm on the canonical Bars-and-Stripes dataset using a quantum-classical hybrid machine. The training proceeds by running parameterized circuits on a trapped ion quantum computer and feeding the results to a classical optimizer. We apply two separate strategies, Particle Swarm and Bayesian optimization to this task. We show that the convergence of the quantum circuit to the target distribution depends critically on both the quantum hardware and classical optimization strategy. Our study represents the first successful training of a high-dimensional universal quantum circuit and highlights the promise and challenges associated with hybrid learning schemes. 

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4. Simulating Large Quantum Circuits on a Small Quantum Computer

   https://doi.org/10.1103/PhysRevLett.125.150504  

   Peng, Tianyi; Harrow, Aram W.; Ozols, Maris; Wu, Xiaodi (October 2020, Physical Review Letters)

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5. 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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