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In this introductory review, we focus on applications of quantum computation to problems of interest in physics and chemistry.
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Simulating Ising spin glasses on a quantum computer, Physical Review E
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Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer, SIAM Journal on Computing
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Quantum lower bounds by polynomials, Proceedings of FOCS’ 98
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Quantum Algorithm Providing Exponential Speed Increase for Finding Eigenvalues and Eigenvectors, Physical Review Letters
[] Abrams, D. & Lloyd, S. (1999) · 1999
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Nobel Lecture: Electronic structure of matter—wave functions and density functionals, Reviews of Modern Physics
[] Kohn, W. (1999) · 1999
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Calculating the thermal rate constant with exponential speedup on a quantum computer, Physical Review E
[] Lidar, D. & Wang, H. (1999) · 1999
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Nobel Lecture: Quantum chemical models, Reviews of Modern Physics
[] Pople, J. (1999) · 1999
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Quantum Simulations on a Quantum Computer, Physical Review Letters
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Mapping from Densities to Potentials in Time-Dependent Density-Functional Theory, Phys. Rev. Lett
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Quantum Computation by Adiabatic Evolution, arXiv:quant-ph/0001106v1
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Molecular Electronic-Structure Theory
[] Helgaker, T., Jorgensen, P. & Olsen, J. (2000) · 2000
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Problem of equilibration and the computation of correlation functions on a quantum computer, Physical Review A
[] Terhal, B. M. & DiVincenzo, D. P. (2000) · 2000
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Universal simulation of Markovian quantum dynamics, Physical Review A
[] Bacon, D., Childs, A., Chuang, I., Kempe, J., Leung, D. & Zhou, X. (2001) · 2001
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Quantum algorithms for fermionic simulations, Physical Review A
[] Ortiz, G., Gubernatis, J., Knill, E. & Laflamme, R. (2001) · 2001
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Quantum NP - A Survey, arXiv:quant-ph/0210077
[] Aharonov, D. & Naveh, T. (2002) · 2002
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Algorithmic cooling and scalable NMR quantum computers., Proceedings of the National Academy of Sciences of the United States of America
[] Boykin, P. O., Mor, T., Roychowdhury, V., Vatan, F. & Vrijen, R. (2002) · 2002
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The theory of open quantum systems
[] Breuer, H.-P. & Petruccione, F. (2002) · 2002
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Creating superpositions that correspond to efficiently integrable probability distributions, arXiv:quant-ph/0208112
[] Grover, L. & Rudolph, T. (2002) · 2002
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Classical and quantum computation
[] Kitaev, A., Shen, A. & Vyalyi, M. (2002) · 2002
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Simulating physical phenomena by quantum networks, Physical Review A
[] Somma, R., Ortiz, G., Gubernatis, J. E., Knill, E. & Laflamme, R. (2002) · 2002
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Error Sensitivity of a Quantum Simulator I: a First Example, Fortschritte der Physik
[] Strini, G. (2002) · 2002
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Polynomial-Time Simulation of Pairing Models on a Quantum Computer, Physical Review Letters
[] Wu, L.-a., Byrd, M. & Lidar, D. (2002) · 2002
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Adiabatic quantum state generation and statistical zero knowledge, Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
[] Aharonov, D. & Ta-Shma, A. (2003) · 2003
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Quantum computing with an always-on heisenberg interaction, Phys. Rev. Lett
[] Benjamin, S. C. & Bose, S. (2003) · 2003
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Eigenvector Approximation Leading to Exponential Speedup of Quantum Eigenvalue Calculation, Physical Review Letters
[] Jaksch, P. & Papageorgiou, A. (2003) · 2003
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Efficiency of free-energy calculations of spin lattices by spectral quantum algorithms, Physical Review A
[] Master, C., Yamaguchi, F. & Yamamoto, Y. (2003) · 2003
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Quantum Simulations of Physics Problems, Proceedings of SPIE
[] Somma, R., Ortiz, G., Knill, E. & Gubernatis, J. (2003) · 2003
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Quantum computing in arrays coupled by “always-on” interactions, Phys. Rev. A
[] Benjamin, S. C. & Bose, S. (2004) · 2004
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Quantum information processing in continuous time
[] Childs, A. M. (2004) · 2004
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Quantum networks for generating arbitrary quantum states
[] Kaye, P. & Mosca, M. (2004) · 2004
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Quantum Speed-Up of Markov Chain Based Algorithms, 45th Annual IEEE Symposium on Foundations of Computer Science
[] Szegedy, M. (2004) · 2004
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Simulated quantum computation of molecular energies., Science (New York, N.Y.)
[] Aspuru-Guzik, A., Dutoi, A. D., Love, P. J. & Head-Gordon, M. (2005) · 2005
Cited alongside, same era.
Experimental implementation of heat-bath algorithmic cooling using solid-state nuclear magnetic resonance., Nature
[] Baugh, J., Moussa, O., Ryan, C. a., Nayak, A. & Laflamme, R. (2005) · 2005
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Finding exponential product formulas of higher orders, in
[] Hatano, N. & Suzuki, M. (2005) · 2005
Cited alongside, same era.
Physical Limits of Heat-Bath Algorithmic Cooling, Physical Review Letters
[] Schulman, L., Mor, T. & Weinstein, Y. (2005) · 2005
Cited alongside, same era.
Efficient Quantum Algorithms for Simulating Sparse Hamiltonians, Communications in Mathematical Physics
[] Berry, D. W., Ahokas, G., Cleve, R. & Sanders, B. C. (2006) · 2006
Cited alongside, same era.
Discrete Single-Photon Quantum Walks with Tunable Decoherence, Physical Review Letters
[] Broome, M. A., Fedrizzi, A., Lanyon, B. P., Kassal, I., Aspuru-Guzik, A. & White, A. G. (2010) · 2010
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Using Quantum Computers for Quantum Simulation, Entropy
[] Brown, K. L., Munro, W. J. & Kendon, V. M. (2010) · 2010
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On the relationship between continuous- and discrete-time quantum walk, Comm. Math. Phys
[] Childs, A. M. (2010) · 2010
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Simulating sparse Hamiltonians with star decompositions, Theory of Quantum Computation Communication and Cryptography TQC 2010
[] Childs, A. M. & Kothari, R. (2011) · 2010
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NMR Implementation of a Molecular Hydrogen Quantum Simulation with Adiabatic State Preparation, Physical Review Letters
[] Du, J., Xu, N., Peng, X., Wang, P., Wu, S. & Lu, D. (2010) · 2010
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Limitations of quantum simulation examined by simulating a pairing Hamiltonian using nuclear magnetic resonance., Physical Review Letters
[] Brown, K. R., Clark, R. J. & Chuang, I. L. (2006) · 2006
Cited alongside, same era.
Simulating lattice gauge theories on a quantum computer, Physical Review A
[] Byrnes, T. & Yamamoto, Y. (2006) · 2006
Cited alongside, same era.
Positive definite matrices
[] Bhatia, R. (2007) · 2007
Cited alongside, same era.
An introduction to computer simulation methods: applications to physical systems
[] Gould, H., Tobochnik, J. & Christian, W. (2007) · 2007
Cited alongside, same era.
An Introduction to Quantum Computing
[] Kaye, P., Laflamme, R. & Mosca, M. (2007) · 2007
Cited alongside, same era.
Optimal quantum measurements of expectation values of observables, Physical Review A (Atomic, Molecular, and Optical Physics)
[] Knill, E., Ortiz, G. & Somma, R. D. (2007) · 2007
Cited alongside, same era.
Quantum speedup of classical mixing processes, Physical Review A
[] Richter, P. (2007) · 2007
Cited alongside, same era.
Towards superconductor-spin ensemble hybrid quantum systems, Physics
[] Duty, T. (2010) · 2010
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[] Knysh, S. & Smelyanskiy, V. (2010) · 2010
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Quantum computers., Nature
[] Ladd, T. D., Jelezko, F., Laflamme, R., Nakamura, Y., Monroe, C. & O’Brien, J. L. (2010) · 2010
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Towards quantum chemistry on a quantum computer, Nature Chemistry
[] Lanyon, B. P., Whitfield, J. D., Gillett, G. G., Goggin, M. E., Almeida, M. P., Kassal, I., Biamonte, J. D., Mohseni, M., Powell, B. J., Barbieri, M., Aspuru-Guzik, A. & White, A. G. (2010) · 2010
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On the efficiency of quantum algorithms for hamiltonian simulation, Quantum Information Processing
[] Papageorgiou, A. & Zhang, C. (2010) · 2010
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Interacting Boson Problems Can Be QMA Hard, Physical Review Letters
[] Wei, T.-C., Mosca, M. & Nayak, A. (2010) · 2010
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Explorations in Quantum Computing
[] Williams, C. P. (2010) · 2010
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First-Order Phase Transition in the Quantum Adiabatic Algorithm, Physical Review Letters
[] Young, a. P. & Smelyanskiy, V. N. (2010) · 2010
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Simulation of classical thermal states on a quantum computer: A transfer-matrix approach, Physical Review A
[] Yung, M.-H., Nagaj, D., Whitfield, J. & Aspuru-Guzik, A. (2010) · 2010
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Why Philosophers Should Care About Computational Complexity, arXiv:1108.1791
[] Aaronson, S. (2011) · 2011
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An open-system quantum simulator with trapped ions, Nature
[] Barreiro, J. T., Müller, M., Schindler, P., Nigg, D., Monz, T., Chwalla, M., Hennrich, M., Roos, C. F., Zoller, P. & Blatt, R. (2011) · 2011
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Optical Pumping into Many-Body Entanglement, Physical Review Letters
[] Cho, J., Bose, S. & Kim, M. (2011) · 2011
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Can One Trust Quantum Simulators?, arXiv:1109.6457
[] Hauke, P., Cucchietti, F. M., Tagliacozzo, L., Deutsch, I. & Lewenstein, M. (2011) · 2011
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Exponential complexity of the quantum adiabatic algorithm for certain satisfiability problems, Physical Review E
[] Hen, I. & Young, A. P. (2011) · 2011
Later among the works it cites.
Quantum computing with NMR., Progress in nuclear magnetic resonance spectroscopy
[] Jones, J. A. (2011) · 2011
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Simulating chemistry using quantum computers., Annual review of physical chemistry
[] Kassal, I., Whitfield, J. D., Perdomo-Ortiz, A., Yung, M.-H. & Aspuru-Guzik, A. (2011) · 2011
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[] Kitagawa, T., Broome, M. A., Fedrizzi, A., Rudner, M. S., Berg, E., Kassal, I., Aspuru-Guzik, A., Demler, E. & White, A. G. (2011) · 2011
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Dissipative Quantum Church-Turing Theorem, Physical Review Letters
[] Kliesch, M., Barthel, T., Gogolin, C., Kastoryano, M. & Eisert, J. (2011) · 2011
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Entanglement Generated by Dissipation and Steady State Entanglement of Two Macroscopic Objects, Physical Review Letters
[] Krauter, H., Muschik, C., Jensen, K., Wasilewski, W., Petersen, J., Cirac, J. & Polzik, E. (2011) · 2011
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Universal Digital Quantum Simulation with Trapped Ions, Science
[] Lanyon, B. P., Hempel, C., Nigg, D., Muller, M., Gerritsma, R., Zahringer, F., Schindler, P., Barreiro, J. T., Rambach, M., Kirchmair, G., Hennrich, M., Zoller, P., Blatt, R. & Roos, C. F. (2011) · 2011
Later among the works it cites.
Solving Quantum Ground-State Problems with Nuclear Magnetic Resonance, Scientific Reports
[] Li, Z., Yung, M.-H., Chen, H., Lu, D., Whitfield, J. D., Peng, X., Aspuru-Guzik, A. & Du, J. (2011) · 2011
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Simulation of Chemical Isomerization Reaction Dynamics on a NMR Quantum Simulator, Physical Review Letters
[] Lu, D., Xu, N., Xu, R., Chen, H., Gong, J., Peng, X. & Du, J. (2011) · 2011
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Simulating open quantum systems: from many-body interactions to stabilizer pumping, New Journal of Physics
[] Müller, M., Hammerer, K., Zhou, Y. L., Roos, C. F. & Zoller, P. (2011) · 2011
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Dissipatively driven entanglement of two macroscopic atomic ensembles, Physical Review A
[] Muschik, C., Polzik, E. & Cirac, J. (2011) · 2011
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Quantum Computation and Quantum Information: 10th Anniversary Edition
[] Nielsen, M. A. & Chuang, I. L. (2011) · 2011
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Quantum Annealing: An Introduction and New Developments, Journal of Computational and Theoretical Nanoscience
[] Ohzeki, M. & Nishimori, H. (2011) · 2011
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Hamiltonian complexity, arXiv:1106.5875
[] Osborne, T. J. (2011) · 2011
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Quantum memories based on engineered dissipation, Physical Review A
[] Pastawski, F., Clemente, L. & Cirac, J. (2011) · 2011
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Designing Quantum Circuits for Efficient Many-Body Quantum Simulation, Arxiv:1108.4318
[] Raesi, S., Wiebe, N. & Sanders, B. C. (2011) · 2011
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Thermalization in nature and on a quantum computer, arXiv:1102.2389
[] Riera, A., Gogolin, C. & Eisert, J. (2011) · 2011
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Quantum Metropolis sampling., Nature
[] Temme, K., Osborne, T. J., Vollbrecht, K. G., Poulin, D. & Verstraete, F. (2011) · 2011
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[] Tempel, D. G. & Aspuru-Guzik, A. (2011) · 2011
Later among the works it cites.
Quantum algorithm for simulating the dynamics of an open quantum system, Physical Review A
[] Wang, H., Ashhab, S. & Nori, F. (2011) · 2011
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Simulation of electronic structure Hamiltonians using quantum computers, Molecular Physics
[] Whitfield, J. D., Biamonte, J. & Aspuru-Guzik, A. (2011) · 2011
Later among the works it cites.
Algorithmic quantum cooling via random walk, under preparation
[] Yung, M.-H., Boixo, S. & Aspuru-Guzik, A. (2011) · 2011
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Digital Quantum Simulation of the Statistical Mechanics of a Frustrated Magnet, arXiv:1108.3270
[] Zhang, J., Yung, M.-H., Laflamme, R., Aspuru-Guzik, A. & Baugh, J. (2011) · 2011
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A Quantum-Quantum Metropolis Algorithm, Proc. Nat. Acad. Sci
[] Yung, M.-H. & Aspuru-Guzik, A. (2012) · 2012
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Time-dependent quantum-mechanical methods for molecular dynamics, The Journal of Physical Chemistry
[] Kosloff, R. (1988) · 2087
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