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We propose a quantum-classical hybrid algorithm to simulate the non-equilibrium steady state of an open quantum many-body system, named the dissipative-system Variational Quantum Eigensolver (dVQE).
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Note that it is a NP-hard problem to check whether the condition (II) is satisfied in tensor network methods Kliesch et al. 2014
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2014
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Jian Cui, J. Ignacio Cirac, and Mari Carmen Bañuls, “Variational Matrix Product Operators for the Steady State of Dissipative Quantum Systems,” Phys. Rev. Lett. 114
2015
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Hendrik Weimer, “Variational principle for steady states of dissipative quantum many-body systems,” Phys. Rev. Lett. 114
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2018
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Nicholas C Rubin, Ryan Babbush, and Jarrod McClean, “Application of fermionic marginal constraints to hybrid quantum algorithms,” New Journal of Physics 20
2018
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2019
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Colin D Bruzewicz, John Chiaverini, Robert McConnell, and Jeremy M Sage, “Trapped-ion quantum computing: Progress and challenges,” Applied Physics Reviews 6
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2016
Cited alongside, same era.
A. H. Werner, D. Jaschke, P. Silvi, M. Kliesch, T. Calarco, J. Eisert, and S. Montangero, “Positive tensor network approach for simulating open quantum many-body systems,” Phys. Rev. Lett. 116
2016
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Jiasen Jin, Alberto Biella, Oscar Viyuela, Leonardo Mazza, Jonathan Keeling, Rosario Fazio, and Davide Rossini, “Cluster mean-field approach to the steady-state phase diagram of dissipative spin systems,” Phys. Rev. X 6
2016
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2016
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Aram W. Harrow and Ashley Montanaro, “Quantum computational supremacy,” Nature 549
2017
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Jarrod R. McClean, Mollie E. Kimchi-Schwartz, Jonathan Carter, and Wibe A. de Jong, “Hybrid quantum-classical hierarchy for mitigation of decoherence and determination of excited states,” Phys. Rev. A 95
2017
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Abhinav Kandala, Antonio Mezzacapo, Kristan Temme, Maika Takita, Markus Brink, Jerry M. Chow, and Jay M. Gambetta, “Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets,” Nature 549
2017
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Augustine Kshetrimayum, Hendrik Weimer, and Román Orús, “A simple tensor network algorithm for two-dimensional steady states,” Nat. Commun. 8
2017
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Kristan Temme, Sergey Bravyi, and Jay M. Gambetta, “Error mitigation for short-depth quantum circuits,” Phys. Rev. Lett. 119
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2019
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Tyson Jones, Suguru Endo, Sam McArdle, Xiao Yuan, and Simon C. Benjamin, “Variational quantum algorithms for discovering hamiltonian spectra,” Phys. Rev. A 99
2019
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Oscar Higgott, Daochen Wang, and Stephen Brierley, “Variational Quantum Computation of Excited States,” Quantum 3
2019
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Robert M. Parrish, Edward G. Hohenstein, Peter L. McMahon, and Todd J. Martánez, “Quantum computation of electronic transitions using a variational quantum eigensolver,” Phys. Rev. Lett. 122
2019
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Nobuyuki Yoshioka and Ryusuke Hamazaki, “Constructing neural stationary states for open quantum many-body systems,” Phys. Rev. B 99
2019
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Michael J. Hartmann and Giuseppe Carleo, “Neural-network approach to dissipative quantum many-body dynamics,” Phys. Rev. Lett. 122
2019
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Alexandra Nagy and Vincenzo Savona, “Variational quantum monte carlo method with a neural-network ansatz for open quantum systems,” Phys. Rev. Lett. 122
2019
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Filippo Vicentini, Alberto Biella, Nicolas Regnault, and Cristiano Ciuti, “Variational neural-network ansatz for steady states in open quantum systems,” Phys. Rev. Lett. 122
2019
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