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The problem of sampling outputs of quantum circuits has been proposed as a candidate for demonstrating a quantum computational advantage (sometimes referred to as quantum "supremacy").
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PP is as hard as the polynomial-time hierarchy
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Universal quantum simulators
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Persistent entanglement in arrays of interacting particles
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A one-way quantum computer
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Decomposing Finite Abelian Groups
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Classical and quantum computation
Alexei Yu Kitaev, Alexander Shen, and Mikhail N Vyalyi · 2002
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Quantum search by measurement
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Simulating physical phenomena by quantum networks
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Measuring 4-local n-qubit observables could probabilistically solve PSPACE
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Adaptive quantum computation, constant depth quantum circuits and arthur-merlin games
B. M. Terhal and D. P. DiVincenzo · 2004
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Frustrated Spin Systems
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Beyond NP: The work and legacy of Larry Stockmeyer
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Quantum computing, postselection, and probabilistic polynomial-time
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Several natural bqp-complete problems
Pawel Wocjan and Shengyu Zhang · 2006
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Effective method to compute franck-condon integrals for optical spectra of large molecules in solution
Fabrizio Santoro, Roberto Improta, Alessandro Lami, Julien Bloino, and Vincenzo Barone · 2007
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A single-shot measurement of the energy of product states in a translation invariant spin chain can replace any quantum computation
Dominik Janzing, Pawel Wocjan, and Shengyu Zhang · 2008
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Temporally unstructured quantum computation
Dan Shepherd and Michael J. Bremner · 2008
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Adiabatic quantum computation is equivalent to standard quantum computation
Dorit Aharonov, Wim Van Dam, Julia Kempe, Zeph Landau, Seth Lloyd, and Oded Regev · 2008
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The complexity of quantum spin systems on a two-dimensional square lattice
Roberto Oliveira and Barbara M Terhal · 2008
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Classical simulation of commuting quantum computations implies collapse of the polynomial hierarchy
Michael J. Bremner, Richard Jozsa, and Dan J. Shepherd · 2010
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The computational complexity of linear optics
Scott Aaronson and Alex Arkhipov · 2011
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Quantum Phase Transitions
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Probing the relaxation towards equilibrium in an isolated strongly correlated one-dimensional Bose gas
S. Trotzky, Y.-A. Chen, A. Flesch, I. P. McCulloch, U. Schollwöck, J. Eisert, and I. Bloch · 2012
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Computational Strategies for Spectroscopy: from Small Molecules to Nano Systems
Vincenzo Barone (Editor) · 2012
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VS Shchesnovich · 2013
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Commuting quantum circuits: efficient classical simulations versus hardness results
Xiaotong Ni and Maarten Van Den Nest · 2013
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Hardness of classically simulating the one-clean-qubit model
Tomoyuki Morimae, Keisuke Fujii, and Joseph F. Fitzsimons · 2014
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Measuring entanglement entropy in a quantum many-body system
Rajibul Islam, Ruichao Ma, Philipp M. Preiss, M. Eric Tai, Alexander Lukin, Matthew Rispoli, and Markus Greiner · 2015
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Characterizing quantum supremacy in near-term devices
Sergio Boixo, Sergei V. Isakov, Vadim N. Smelyanskiy, Ryan Babbush, Nan Ding, Zhang Jiang, Michael J. Bremner, John M. Martinis, and Hartmut Neven · 2018
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Architectures for quantum simulation showing a quantum speedup
Juan Bermejo-Vega, Dominik Hangleiter, Martin Schwarz, Robert Raussendorf, and Jens Eisert · 2018
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Quantum Computing in the NISQ era and beyond
John Preskill · 2018
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Dynamical Phase Transitions in Sampling Complexity
Abhinav Deshpande, Bill Fefferman, Minh C. Tran, Michael Foss-Feig, and Alexey V. Gorshkov · 2018
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Mathematical foundations of quantum mechanics: New edition
John Von Neumann · 2018
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Anticoncentration theorems for schemes showing a quantum speedup
Dominik Hangleiter, Juan Bermejo-Vega, Martin Schwarz, and Jens Eisert · 2018
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S. Braun, M. Friesdorf, J. S. Hodgman, M. Schreiber, J. P. Ronzheimer, A. Riera, M. del Rey, I. Bloch, J. Eisert, and U. Schneider · 2015
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Boson sampling for molecular vibronic spectra
Joonsuk Huh, Gian Giacomo Guerreschi, Borja Peropadre, Jarrod R McClean, and Alán Aspuru-Guzik · 2015
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Hamiltonian simulation with nearly optimal dependence on all parameters
D. W. Berry, A. M. Childs, and R. Kothari · 2015
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Quantum circuit complexity of one-dimensional topological phases
Yichen Huang and Xie Chen · 2015
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Universal adiabatic quantum computation via the space-time circuit-to-hamiltonian construction
David Gosset, Barbara M. Terhal, and Anna Vershynina · 2015
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Quantum hamiltonian complexity
Sevag Gharibian, Yichen Huang, Zeph Landau, and Seung Woo Shin · 2015
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How hard is it to approximate the jones polynomial?
Greg Kuperberg · 2015
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Clocks in feynman’s computer and kitaev’s local hamiltonian: Bias, gaps, idling, and pulse tuning
Libor Caha, Zeph Landau, and Daniel Nagaj · 2018
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Quantum simulation of partially distinguishable boson sampling
Alexandra E. Moylett and Peter S. Turner · 2018
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Universal quantum Hamiltonians
Toby S. Cubitt, Ashley Montanaro, and Stephen Piddock · 2018
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Ramis Movassagh · 2018
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Post hoc verification of quantum computation
Joseph F. Fitzsimons, Michal Hajdušek, and Tomoyuki Morimae · 2018
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Classical verification of quantum computations
Urmila Mahadev · 2018
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Quantum supremacy using a programmable superconducting processor
Frank Arute, Kunal Arya, Ryan Babbush, Dave Bacon, Joseph C Bardin, Rami Barends, Rupak Biswas, Sergio Boixo, Fernando GSL Brandao, David A Buell, et al · 2019
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Quantum critical behaviour at the many-body localization transition
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Probing scrambling using statistical correlations between randomized measurements
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A quantum-inspired classical algorithm for recommendation systems
Ewin Tang · 2019
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Quantum supremacy and the complexity of random circuit sampling
A. Bouland, B. Fefferman, C. Nirkhe, and U. Vazirani · 2019
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Quantum computational supremacy in the sampling of bosonic random walkers on a one-dimensional lattice
Gopikrishnan Muraleedharan, Akimasa Miyake, and Ivan H. Deutsch · 2019
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Complexity phase diagram for interacting and long-range bosonic Hamiltonians
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Quantum eigenvalue estimation via time series analysis
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Hamiltonian Simulation by Qubitization
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Sample complexity of device-independently certified “quantum supremacy”
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Quantum non-demolition measurement of a many-body hamiltonian
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