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The field of quantum algorithms aims to find ways to speed up the solution of computational problems by using a quantum computer.
Average case complete problems
L. A. Levin · 1986
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Where the really hard problems are
P. Cheeseman, B. Kanefsky, and W. Taylor · 1991
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PP is as hard as the polynomial-time hierarchy
S. Toda · 1991
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Computational Complexity
C. Papadimitriou · 1994
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Algorithms for quantum computation: Discrete logarithms and factoring
P. W. Shor · 1994
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Threshold computation and cryptographic security
Y. Han, L. Hemaspaandra, and T. Thierauf · 1997
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Resilient quantum computation
E. Knill, R. Laflamme, and W. Zurek · 1998
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Quantum computation by adiabatic evolution
E. Farhi, J. Goldstone, S. Gutmann, and M. Sipser · 2000
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On the complexity of k-SAT
R. Impagliazzo and R. Paturi · 2001
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Improved simulation of stabilizer circuits
S. Aaronson and D. Gottesman · 2004
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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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Quantum computing, postselection, and probabilistic polynomial-time
S. Aaronson · 2005
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Quantum computing with realistically noisy devices
E. Knill · 2005
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Threshold values of random k-SAT from the cavity method
S. Mertens, M. Mézard, and R. Zecchina · 2006
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The complexity of stoquastic local Hamiltonian problems
S. Bravyi, D. DiVincenzo, R. Oliveira, and B. Terhal · 2008
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Simulating quantum computation by contracting tensor networks
I. L. Markov and Y. Shi · 2008
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Universal blind quantum computation
A. Broadbent, J. Fitzsimons, and E. Kashefi · 2009
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Temporally unstructured quantum computation
D. Shepherd and M. J. Bremner · 2009
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Quantum computational complexity
J. Watrous · 2009
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Classical simulation of commuting quantum computations implies collapse of the polynomial hierarchy
M. J. Bremner, R. Jozsa, and D. J. Shepherd · 2010
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Goals and opportunities in quantum simulation
J. I. Cirac and P. Zoller · 2012
Cited alongside, same era.
Surface codes: Towards practical large-scale quantum computation
A. Fowler, M. Mariantoni, J. Martinis, and A. Cleland · 2012
Cited alongside, same era.
Quantum computing and the entanglement frontier, 2012, arXiv:1203.5813
J. Preskill · 2012
Cited alongside, same era.
The computational complexity of linear optics
S. Aaronson and A. Arkhipov · 2013
Cited alongside, same era.
D. Aharonov and U. Vazirani · 2013
Cited alongside, same era.
Universal adiabatic quantum computation via the space-time circuit-to-Hamiltonian construction
D. Gosset, B. Terhal, and A. Vershynina · 2015
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Improved classical simulation of quantum circuits dominated by Clifford gates
S. Bravyi and D. Gosset · 2016
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Achieving quantum supremacy with sparse and noisy commuting quantum circuits, 2016, arXiv:1610.01808
M. Bremner, A. Montanaro, and D. Shepherd · 2016
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Average-case complexity versus approximate simulation of commuting quantum computations
M. J. Bremner, A. Montanaro, and D. J. Shepherd · 2016
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Observation of spatial charge and spin correlations in the 2d fermi-hubbard model
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Photonic boson sampling in a tunable circuit
M. A. Broome, A. Fedrizzi, S. Rahimi-Keshari, J. Dove, S. Aaronson, T. C. Ralph, and A. G. White · 2013
Cited alongside, same era.
Integrated multimode interferometers with arbitrary designs for photonic boson sampling
A. Crespi, R. Osellame, R. Ramponi, D. J. Brod, E. F. Galvao, N. Spagnolo, C. Vitelli, E. Maiorino, P. Mataloni, and F. Sciarrino · 2013
Cited alongside, same era.
Thermally assisted quantum annealing of a 16-qubit problem
N. G. Dickson, M. Johnson, M. Amin, R. Harris, F. Altomare, A. Berkley, P. Bunyk, J. Cai, E. Chapple, P. Chavez, et al · 2013
Cited alongside, same era.
General rules for bosonic bunching in multimode interferometers
N. Spagnolo, C. Vitelli, L. Sansoni, E. Maiorino, P. Mataloni, F. Sciarrino, D. Brod, E. Galvaõ, A. Crespi, R. Ramponi, and R. Osellame · 2013
Cited alongside, same era.
Boson sampling on a photonic chip
J. B. Spring, B. J. Metcalf, P. C. Humphreys, W. S. Kolthammer, X.-M. Jin, M. Barbieri, A. Datta, N. Thomas-Peter, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley · 2013
Cited alongside, same era.
M. Tillmann, B. Dakić, R. Heilmann, S. Nolte, A. Szameit, and P. Walther · 2013
Cited alongside, same era.
Bosonsampling is far from uniform
S. Aaronson and A. Arkhipov · 2014
Cited alongside, same era.
L. W. Cheuk, M. A. Nichols, K. R. Lawrence, M. Okan, H. Zhang, E. Khatami, N. Trivedi, T. Paiva, M. Rigol, and M. W. Zwierlein · 2016
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Quantum supremacy through the quantum approximate optimization algorithm, 2016, arXiv:1602.07674
E. Farhi and A. W. Harrow · 2016
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Computational quantum-classical boundary of noisy commuting quantum circuits
K. Fujii and S. Tamate · 2016
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Factoring using 2n + 2 qubits with Toffoli based modular multiplication, 2016, arXiv:1611.07995
T. Häner, M. Roetteler, and K. Svore · 2016
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Direct certification of a class of quantum simulations, 2016, arXiv:1602.00703
D. Hangleiter, M. Kliesch, M. Schwarz, and J. Eisert · 2016
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K. Nishimura, H. Nishimori, A. J. Ochoa, and H. G. Katzgraber · 2016
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The weakness of CTC qubits and the power of approximate counting
R. O’Donnell and A. C. C. Say · 2016
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Sufficient conditions for efficient classical simulation of quantum optics
S. Rahimi-Keshari, T. C. Ralph, and C. M. Caves · 2016
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Multi-photon boson-sampling machines beating early classical computers, 2016, arXiv:1612.06956
H. Wang, Y. He, Y.-H. Li, Z.-E. Su, B. Li, H.-L. Huang, X. Ding, M.-C. Chen, C. Liu, J. Qin, J.-P. Li, Y.-M. He, C. Schneider, M. Kamp, C.-Z. Peng, S. Hoefling, C.-Y. Lu, and J.-W. Pan · 2016
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Complexity-theoretic foundations of quantum supremacy experiments
S. Aaronson and L. Chen · 2017
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Quantum supremacy for simulating a translation-invariant Ising spin model
X. Gao, S.-T. Wang, and L.-M. Duan · 2017
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Quantum sampling problems, bosonsampling and quantum supremacy
A. P. Lund, M. J. Bremner, and T. C. Ralph · 2017
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Characterizing quantum supremacy in near-term devices
S. Boixo, S. V. Isakov, V. N. Smelyanskiy, R. Babbush, N. Ding, Z. Jiang, M. J. Bremner, J. M. Martinis, and H. Neven · 2018
Closest in time.
How many qubits are needed for quantum computational supremacy?, 2018, arXiv:1805.05224
A. M. Dalzell, A. W. Harrow, D. E. Koh, and R. L. La Placa · 2018
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A. W. Harrow and S. Mehraban · 2018
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