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Quantum computers are designed to outperform standard computers by running quantum algorithms.
Experimental realization of quantum algorithm for solving linear systems of equations
J. Pan, Y. Cao, X. Yao, Z. Li, C. Ju, X. Peng, S. Kais, and J. Du · 1946
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A method for obtaining digital signatures and public-key cryptosystems
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Simulating physics with computers
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Factoring integers with the number field sieve
J. Buhler, H. W. Lenstra Jr., and C. Pomerance · 1993
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Computational Complexity
C. Papadimitriou · 1994
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Quantum cryptanalysis of hidden linear functions
D. Boneh and R. Lipton · 1995
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On the Monte Carlo boolean decision tree complexity of read-once formulae
M. Santha · 1995
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A quantum algorithm for finding the minimum, 1996
C. Dürr and P. Høyer · 1996
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Universal quantum simulators
S. Lloyd · 1996
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An exact quantum polynomial-time algorithm for Simon’s problem
G. Brassard and P. Høyer · 1997
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Quantum mechanics helps in searching for a needle in a haystack
L. Grover · 1997
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Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer
P. W. Shor · 1997
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Tight bounds on quantum searching
M. Boyer, G. Brassard, P. Høyer, and A. Tapp · 1998
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Quantum entanglement and the communication complexity of the inner product function
R. Cleve, W. van Dam, M. Nielsen, and A. Tapp · 1998
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A probabilistic algorithm for k-SAT and constraint satisfaction problems
U. Schöning · 1999
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Quantum simulations on a quantum computer
S. Somaroo, C. Tseng, T. Havel, R. Laflamme, and D. Cory · 1999
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Grover’s quantum searching algorithm is optimal
C. Zalka · 1999
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Quantum computation by adiabatic evolution
E. Farhi, J. Goldstone, S. Gutmann, and M. Sipser · 2000
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Implementation of a three-quantum-bit search algorithm
L. Vandersypen, M. Steffen, M. Sherwood, C. Yannoni, G. Breyta, and I. Chuang · 2000
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Quantum walks on graphs
D. Aharonov, A. Ambainis, J. Kempe, and U. Vazirani · 2001
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Quantum lower bounds by polynomials
R. Beals, H. Buhrman, R. Cleve, M. Mosca, and R. de Wolf · 2001
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A quantum adiabatic evolution algorithm applied to random instances of an NP-complete problem
E. Farhi, J. Goldstone, S. Gutmann, J. Lapan, A. Lundgren, and D. Preda · 2001
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How powerful is adiabatic quantum computation?
W. van Dam, M. Mosca, and U. Vazirani · 2001
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Quantum amplitude amplification and estimation
G. Brassard, P. Høyer, M. Mosca, and A. Tapp · 2002
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An example of the difference between quantum and classical random walks
A. Childs, E. Farhi, and S. Gutmann · 2002
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A modular functor which is universal for quantum computation
M. Freedman, M. Larsen, and Z. Wang · 2002
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Classical and Quantum Computation
A. Yu. Kitaev, A. H. Shen, and M. N. Vyalyi · 2002
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The quantum communication complexity of sampling
A. Ambainis, L. J. Schulman, A. Ta-Shma, U. Vazirani, and A. Wigderson · 2003
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Exponential algorithmic speedup by a quantum walk
A. Childs, R. Cleve, E. Deotto, E. Farhi, S. Gutmann, and D. Spielman · 2003
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Shor’s discrete logarithm quantum algorithm for elliptic curves
J. Proos and C. Zalka · 2003
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Both Toffoli and controlled-NOT need little help to do universal quantum computing
Y. Shi · 2003
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Quantum query complexity of some graph problems
C. Dürr, M. Heiligman, P. Høyer, and M. Mhalla · 2004
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Quantum computation and lattice problems
O. Regev · 2004
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A subexponential time algorithm for the dihedral hidden subgroup problem with polynomial space, 2004
O. Regev · 2004
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Quantum speed-up of Markov chain based algorithms
M. Szegedy · 2004
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Quantum random walks hit exponentially faster
J. Kempe · 2005
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A subexponential-time quantum algorithm for the dihedral hidden subgroup problem
G. Kuperberg · 2005
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A survey of recent advances in SAT-based formal verification
M. Prasad, A. Biere, and A. Gupta · 2005
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Polynomial-time quantum algorithms for Pell’s equation and the principal ideal problem
S. Hallgren · 2007
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Experimental realisation of Shor’s quantum factoring algorithm using qubit recycling
E. Martín-López, A. Laing, T. Lawson, R. Alvarez, X.-Q. Zhou, and J. O’Brien · 2012
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M. Mosca · 2012
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S. Trotzky, Y-A. Chen, A. Flesch, I. McCulloch, U. Schollwöck, J. Eisert, and I. Bloch · 2012
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Quantum algorithm for data fitting
N. Wiebe, D. Braun, and S. Lloyd · 2012
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Entanglement-free Heisenberg-limited phase estimation
B. Higgins, D. Berry, S. Bartlett, H. Wiseman, and G. Pryde · 2007
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How to make the quantum adiabatic algorithm fail
E. Farhi, J. Goldstone, S. Gutmann, and D. Nagaj · 2008
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A quantum algorithm to solve nonlinear differential equations, 2008
S. Leyton and T. Osborne · 2008
Cited alongside, same era.
Quantum walk based search algorithms
M. Santha · 2008
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Quantum simulators
I. Bulata and F. Nori · 2009
Cited alongside, same era.
Quantum algorithm for linear systems of equations
A. Harrow, A. Hassidim, and S. Lloyd · 2009
Cited alongside, same era.
S. Aaronson and A. Arkhipov · 2013
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Experimental quantum computing to solve systems of linear equations
X.-D. Cai, C. Weedbrook, Z.-E. Su, M.-C. Chen, M. Gu, M.-J. Zhu, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan · 2013
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Preconditioned quantum linear system algorithm
B. Clader, B. Jacobs, and C. Sprouse · 2013
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Quantum algorithms for supervised and unsupervised machine learning, 2013
S. Lloyd, M. Mohseni, and P. Rebentrost · 2013
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Experimental evaluation of an adiabiatic quantum system for combinatorial optimization
C. McGeoch and C. Wang · 2013
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Quantum computation: Boson sampling on a chip
T. Ralph · 2013
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Oversimplifying quantum factoring
J. Smolin, G. Smith, and A. Vargo · 2013
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Quantum Information Theory
M. Wilde · 2013
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Improving exhaustive search implies superpolynomial lower bounds
R. Williams · 2013
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Solving systems of linear equations on a quantum computer
S. Barz, I. Kassal, M. Ringbauer, Y. Ole Lipp, B. Dakic, A. Aspuru-Guzik, and P. Walther · 2014
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Quantum algorithms for learning symmetric juntas via adversary bound
A. Belovs · 2014
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High-order quantum algorithm for solving linear differential equations
D. Berry · 2014
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A. Bookatz · 2014
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E. Farhi, J. Goldstone, and S. Gutmann · 2014
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I. Georgescu, S. Ashhab, and F. Nori · 2014
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Boson sampling for molecular vibronic spectra, 2014
J. Huh, G. Guerreschi, B. Peropadre, J. McClean, and A. Aspuru-Guzik · 2014
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Improved quantum algorithm for triangle finding via combinatorial arguments
F. Le Gall · 2014
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Defining and detecting quantum speedup
T. Rønnow, Z. Wang, J. Job, S. Boixo, S. Isakov, D. Wecker, J. Martinis, D. Lidar, and M. Troyer · 2014
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Gate count estimates for performing quantum chemistry on small quantum computers
D. Wecker, B. Bauer, B. Clark, M. Hastings, and M. Troyer · 2014
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Quantum machine learning algorithms: Read the fine print
S. Aaronson · 2015
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Beating the random assignment on constraint satisfaction problems of bounded degree, 2015
B. Barak, A. Moitra, R. O’Donnell, P. Raghavendra, O. Regev, D. Steurer, L. Trevisan, A. Vijayaraghavan, D. Witmer, and J. Wright · 2015
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Hamiltonian simulation with nearly optimal dependence on all parameters, 2015
D. Berry, A. Childs, and R. Kothari · 2015
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Improving quantum algorithms for quantum chemistry
M. Hastings, D. Wecker, B. Bauer, and M. Troyer · 2015
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Benchmarking a quantum annealing processor with the time-to-target metric, 2015
J. King, S. Yarkoni, M. Nevisi, J. Hilton, and C. McGeoch · 2015
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Upper bounds on quantum query complexity inspired by the Elitzur-Vaidman bomb tester
C. Lin and H. Lin · 2015
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Simulating molecular vibrations with photons, 2015
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Quantum pattern matching fast on average
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The Trotter step size required for accurate quantum simulation of quantum chemistry
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