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Quantum computation appears to offer significant advantages over classical computation and this has generated a tremendous interest in the field.
Upper and lower bounds for eigenvalues by finite difference methods
Weinberger, H. F · 1956
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Lower bounds for higher eigenvalues by finite difference methods
Weinberger, H. F · 1958
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Eigenfunction Expansions: Associated with Second-Order Differential Equations
Titchmarsh, E · 1962
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Inhomogeneous electron gas
Hohenberg, P., and Kohn, W · 1964
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Lectures on physics, vol. iii, 1965
Feynman, R. P., Leighton, R. B., and Sands, M · 1965
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Self-consistent molecular-orbital methods. i. Use of Gaussian expansions of Slater-type atomic orbitals
Hehre, W. J., Stewart, R. F., and Pople, J. A · 1969
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The complexity of theorem-proving procedures
Cook, S. A · 1971
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Gaussian basis functions for use in molecular calculations. iii. contraction of (10s6p) atomic basis sets for the first-row atoms
Dunning, T., et al · 1971
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Ab initio calculations on large molecules
Christoffersen, R. E · 1972
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Computation of large molecules with the Hartree-Fock model
Clementi, E · 1972
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Reducibility among combinatorial problems
Karp, R. M · 1972
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The Design and Analysis of Computer Algorithms
Aho, A. V., Hopcroft, J. E., and Ullman, J · 1974
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Finding a maximum cut of a planar graph in polynomial time
Hadlock, F · 1975
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Worst-case analysis of a new heuristic for the travelling salesman problem
Christofides, N · 1976
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P-complete approximation problems
Sahni, S., and Gonzalez, T · 1976
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Generalized Trotter’s formula and systematic approximants of exponential operators and inner derivations with applications to many-body problems
Suzuki, M · 1976
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Complexity of machine scheduling problems
Lenstra, J. K., Kan, A. R., and Brucker, P · 1977
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Node-and edge-deletion NP–complete problems
Yannakakis, M · 1978
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Computers and Intractability: A Guide to the Theory of NP–Completeness
Garey, M. R., and Johnson, D. S · 1979
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A graph coloring algorithm for large scheduling problems
Leighton, F. T · 1979
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The Symmetric Eigenvalue Problem
Parlett, B. N · 1980
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How well can a graph be n-colored?
Vitányi, P. M · 1981
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Principles for a direct SCF approach to LICAO–MO ab-initio calculations
Almlöf, J., Faegri, K., and Korsell, K · 1982
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Register allocation & spilling via graph coloring
Chaitin, G. J · 1982
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Simulating physics with computers
Feynman, R · 1982
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A polynomial algorithm for constructing a large bipartite subgraph, with an application to a satisfiability problem
Poljak, S., and Turzik, D · 1982
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Iterative Methods for the Solution of Equations
Traub, J. F · 1982
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The Max–Cut problem on graphs not contractible to K5
Barahona, F · 1983
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Quantum theory, the Church-Turing principle and the universal quantum computer
Deutsch, D · 1985
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An application of combinatorial optimization to statistical physics and circuit layout design
Barahona, F., Grötschel, M., Jünger, M., and Reinelt, G · 1988
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The influence of variables on Boolean functions
Kahn, J., Kalai, G., and Linial, N · 1988
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Time/space trade-offs for reversible computation
Bennett, C. H · 1989
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Quantum computational networks
Deutsch, D · 1989
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A note on Bennett’s time-space tradeoff for reversible computation
Levine, R. Y., and Sherman, A. T · 1990
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On approximation preserving reductions: Complete problems and robust measures (revised version)
Orponen, P., and Mannila, H · 1990
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Quantifiers and approximation
Panconesi, A., and Ranjan, D · 1990
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Fractal decomposition of exponential operators with applications to many-body theories and Monte Carlo simulations
Suzuki, M · 1990
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Eigenvalue problems
Babuška, I., and Osborn, J · 1991
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Approximation and intractability results for the maximum cut problem and its variants
Haglin, D. J., and Venkatesan, S. M · 1991
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Optimization, approximation, and complexity classes
Papadimitriou, C. H., and Yannakakis, M · 1991
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General theory of fractal path integrals with application to many-body theories and statistical physics
Suzuki, M · 1991
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The algorithmic aspects of the regularity lemma
Alon, N · 1992
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The polynomial method in circuit complexity
Beigel, R · 1993
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A still better performance guarantee for approximate graph coloring
Halldórsson, M. M · 1993
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Constant depth circuits, Fourier transform, and learnability
Linial, N., Mansour, Y., and Nisan, N · 1993
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The traveling salesman problem with distances one and two
Papadimitriou, C. H., and Yannakakis, M · 1993
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Quantum circuit complexity
Yao, A. C.-C · 1993
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Applications of cut polyhedra–ii
Deza, M., and Laurent, M · 1994
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On the degree of Boolean functions as real polynomials
Nisan, N., and Szegedy, M · 1994
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The hardness of approximation: gap location
Petrank, E · 1994
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Adapted Wavelet Analysis from Theory to Software
Wickerhauser, M. V · 1994
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Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming
Goemans, M. X., and Williamson, D. P · 1995
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Approximating discrete collections via local improvements
Halldórsson, M. M · 1995
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Modern Quantum Mechanics (revised edition)
Sakurai, J. J · 1995
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A quantitative study of the scaling properties of the Hartree-Fock method
Strout, D. L., and Scuseria, G. E · 1995
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Bipartite subgraphs
Alon, N · 1996
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Efficient networks for quantum factoring
Beckman, D., Chari, A. N., Devabhaktuni, S., and Preskill, J · 1996
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Introduction to Spectral Theory: With Applications to Schrödinger Operators
Hislop, P. D., and Sigal, I. M · 1996
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A combinatorial design approach to maxcut
Hofmeister, T., and Lefmann, H · 1996
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Universal quantum simulators
Lloyd, S · 1996
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Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory
Szabo, A., and Ostlund, N. S · 1996
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Quantum networks for elementary arithmetic operations
Vedral, V., Barenco, A., and Ekert, A · 1996
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On unapproximable versions of NP–complete problems
Zuckerman, D · 1996
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Simulation of many-body Fermi systems on a universal quantum computer
Abrams, D. S., and Lloyd, S · 1997
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Quantum complexity theory
Bernstein, E., and Vazirani, U · 1997
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A short guide to approximation preserving reductions
Crescenzi, P · 1997
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Applied Numerical Linear Algebra
Demmel, J. W · 1997
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Improved approximation algorithms for max–k–cut and max bisection
Frieze, A., and Jerrum, M · 1997
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Quantum mechanics helps in searching for a needle in a haystack
Grover, L. K · 1997
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Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer
Shor, P. W · 1997
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Bipartite subgraphs of integer weighted graphs
Alon, N., and Halperin, E · 1998
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Simulating quantum mechanics on a quantum computer
Boghosian, B. M., and Taylor, W · 1998
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Quantum annealing in the transverse Ising model
Kadowaki, T., and Nishimori, H · 1998
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On syntactic versus computational views of approximability
Khanna, S., Motwani, R., Sudan, M., and Vazirani, U · 1998
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Lecture notes for physics 229: Quantum information and computation
Preskill, J · 1998
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Efficient simulation of quantum systems by quantum computers
Zalka, C · 1998
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Simulating quantum systems on a quantum computer
Zalka, C · 1998
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Quantum algorithm providing exponential speed increase for finding eigenvalues and eigenvectors
Abrams, D. S., and Lloyd, S · 1999
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Real Analysis: Modern Techniques and Their Applications
Folland, G. B · 1999
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Linear scaling electronic structure methods
Goedecker, S · 1999
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Quantum computation over continuous variables
Lloyd, S., and Braunstein, S. L · 1999
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Reversible arithmetic coding for quantum data compression
Chuang, I., and Modha, D. S · 2000
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Addition on a quantum computer
Draper, T. G · 2000
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Quantum computation by adiabatic evolution
Farhi, E., Goldstone, J., Gutmann, S., and Sipser, M · 2000
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Quantum optimization
Hogg, T., and Portnov, D · 2000
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Error bounds for exponential operator splittings
Jahnke, T., and Lubich, C · 2000
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Quantum Computation and Quantum Information
Nielsen, M., and Chuang, I · 2000
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Quantum lower bounds by polynomials
Beals, R., Buhrman, H., Cleve, R., Mosca, M., and De Wolf, R · 2001
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A quantum adiabatic evolution algorithm applied to random instances of an NP–complete problem
Farhi, E., Goldstone, J., Gutmann, S., Lapan, J., Lundgren, A., and Preda, D · 2001
Cited alongside, same era.
Some optimal inapproximability results
Håstad, J · 2001
Cited alongside, same era.
Discrete cosine transforms on quantum computers
Klappenecker, A., and Rötteler, M · 2001
Cited alongside, same era.
Quantum algorithms for fermionic simulations
Ortiz, G., Gubernatis, J., Knill, E., and Laflamme, R · 2001
Cited alongside, same era.
Approximation Algorithms
Vazirani, V. V · 2001
Cited alongside, same era.
Black-box Hamiltonian simulation and unitary implementation
Berry, D. W., and Childs, A. M · 2012
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Hamiltonian simulation using linear combinations of unitary operations
Childs, A. M., and Wiebe, N · 2012
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Matrix Computations
Golub, G. H., and Van Loan, C. F · 2012
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Boolean Methods in Operations Research and Related Areas
Hammer, P. L., and Rudeanu, S · 2012
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Matrix Analysis
Horn, R. A., and Johnson, C. R · 2012
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Faster quantum chemistry simulation on fault-tolerant quantum computers
Jones, N. C., Whitfield, J. D., McMahon, P. L., Yung, M.-H., Van Meter, R., Aspuru-Guzik, A., and Yamamoto, Y · 2012
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Aharonov, D., and Naveh, T · 2002
Cited alongside, same era.
Pseudo-Boolean optimization
Boros, E., and Hammer, P. L · 2002
Cited alongside, same era.
Quantum amplitude amplification and estimation
Brassard, G., Hoyer, P., Mosca, M., and Tapp, A · 2002
Cited alongside, same era.
Fermionic quantum computation
Bravyi, S. B., and Kitaev, A. Y · 2002
Cited alongside, same era.
Finding cliques by quantum adiabatic evolution
Childs, A. M., Farhi, E., Goldstone, J., and Gutmann, S · 2002
Cited alongside, same era.
Lanczos Algorithms for Large Symmetric Eigenvalue Computations: Vol. 1: Theory
Cullum, J. K., and Willoughby, R. A · 2002
Cited alongside, same era.
Quantum algorithms
Mosca, M · 2012
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On the efficiency of quantum algorithms for Hamiltonian simulation
Papageorgiou, A., and Zhang, C · 2012
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Quantum computing and the entanglement frontier
Preskill, J · 2012
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Quantum-circuit design for efficient simulations of many-body quantum dynamics
Raeisi, S., Wiebe, N., and Sanders, B. C · 2012
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The Bravyi-Kitaev transformation for quantum computation of electronic structure
Seeley, J. T., Richard, M. J., and Love, P. J · 2012
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Principles of Quantum Mechanics
Shankar, R · 2012
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Quantum Ising Phases and Transitions in Transverse Ising Models
Suzuki, S., Inoue, J.-i., and Chakrabarti, B. K · 2012
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Exponential improvement in precision for Hamiltonian-evolution simulation
Berry, D. W., Cleve, R., and Somma, R. D · 2013
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Quantum algorithm and circuit design solving the Poisson equation
Cao, Y., Papageorgiou, A., Petras, I., Traub, J. F., and Kais, S · 2013
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Quantum Error Correction
Lidar, D. A., and Brun, T. A · 2013
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Measures of quantum computing speedup
Papageorgiou, A., and Traub, J. F · 2013
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Synthesis and optimization of reversible circuits - a survey
Saeedi, M., and Markov, I. L · 2013
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Inverting well conditioned matrices in quantum logspace
Ta-Shma, A · 2013
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Quantum algorithms for quantum chemistry based on the sparsity of the CI-matrix
Toloui, B., and Love, P. J · 2013
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Exponential improvement in precision for simulating sparse Hamiltonians
Berry, D. W., Childs, A. M., Cleve, R., Kothari, R., and Somma, R. D · 2014
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Evidence for quantum annealing with more than one hundred qubits
Boixo, S., Rønnow, T. F., Isakov, S. V., Wang, Z., Wecker, D., Lidar, D. A., Martinis, J. M., and Troyer, M · 2014
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QMA-complete problems
Bookatz, A. D · 2014
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The Bose-Hubbard model is QMA-complete
Childs, A. M., Gosset, D., and Webb, Z · 2014
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A quantum approximate optimization algorithm
Farhi, E., Goldstone, J., and Gutmann, S · 2014
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A quantum approximate optimization algorithm applied to a bounded occurrence constraint problem
Farhi, E., Goldstone, J., and Gutmann, S · 2014
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Quantum simulation
Georgescu, I., Ashhab, S., and Nori, F · 2014
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Molecular Electronic-Structure Theory
Helgaker, T., Jorgensen, P., and Olsen, J · 2014
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Quantum algorithms for fermionic quantum field theories
Jordan, S. P., Lee, K. S., and Preskill, J · 2014
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Quantum computation of scattering in scalar quantum field theories
Jordan, S. P., Lee, K. S., and Preskill, J · 2014
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Back to the Future: A roadmap for quantum simulation from vintage quantum chemistry
Love, P. J · 2014
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Ising formulations of many NP problems
Lucas, A · 2014
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Exploiting locality in quantum computation for quantum chemistry
McClean, J. R., Babbush, R., Love, P. J., and Aspuru-Guzik, A · 2014
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Adiabatic quantum computation and quantum annealing: theory and practice
McGeoch, C. C · 2014
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Analysis of Boolean functions
O’Donnell, R · 2014
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Estimating the ground state energy of the Schrödinger equation for convex potentials
Papageorgiou, A., and Petras, I · 2014
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A fast algorithm for approximating the ground state energy on a quantum computer
Papageorgiou, A., Petras, I., Traub, J. F., and Zhang, C · 2014
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Quantum algorithms for continuous problems and their applications
Papageorgiou, A., and Traub, J. F · 2014
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A variational eigenvalue solver on a photonic quantum processor
Peruzzo, A., McClean, J., Shadbolt, P., Yung, M.-H., Zhou, X.-Q., Love, P. J., Aspuru-Guzik, A., and O’Brien, J. L · 2014
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Parametrized Families of Hard Planning Problems from Phase Transitions
Rieffel, E. G., Venturelli, D., Do, M., Hen, I., and Frank, J · 2014
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Gate-count estimates for performing quantum chemistry on small quantum computers
Wecker, D., Bauer, B., Clark, B. K., Hastings, M. B., and Troyer, M · 2014
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Quantum arithmetic and numerical analysis using repeat-until-success circuits
Wiebe, N., and Roetteler, M · 2014
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Read the fine print
Aaronson, S · 2015
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Chemical basis of Trotter-Suzuki errors in quantum chemistry simulation
Babbush, R., McClean, J., Wecker, D., Aspuru-Guzik, A., and Wiebe, N · 2015
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Beating the random assignment on constraint satisfaction problems of bounded degree
Barak, B., Moitra, A., O’Donnell, R., Raghavendra, P., Regev, O., Steurer, D., Trevisan, L., Vijayaraghavan, A., Witmer, D., and Wright, J · 2015
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Simulating Hamiltonian dynamics with a truncated Taylor series
Berry, D. W., Childs, A. M., Cleve, R., Kothari, R., and Somma, R. D · 2015
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Hamiltonian simulation with nearly optimal dependence on all parameters
Berry, D. W., Childs, A. M., and Kothari, R · 2015
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Approximating ground and excited state energies on a quantum computer
Hadfield, S., and Papageorgiou, A · 2015
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Improving quantum algorithms for quantum chemistry
Hastings, M. B., Wecker, D., Bauer, B., and Troyer, M · 2015
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Quantum circuits for 𝔽 2 n \mathbb{F}_{2^{n}} -multiplication with subquadratic gate count
Kepley, S., and Steinwandt, R · 2015
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Reversible circuit compilation with space constraints
Parent, A., Roetteler, M., and Svore, K. M · 2015
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The Trotter step size required for accurate quantum simulation of quantum chemistry
Poulin, D., Hastings, M. B., Wecker, D., Wiebe, N., Doherty, A. C., and Troyer, M · 2015
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A case study in programming a quantum annealer for hard operational planning problems
Rieffel, E. G., Venturelli, D., O’Gorman, B., Do, M. B., Prystay, E. M., and Smelyanskiy, V. N · 2015
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Quantum algorithms for computational nuclear physics
Višňák, J · 2015
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Solving strongly correlated electron models on a quantum computer
Wecker, D., Hastings, M. B., Wiebe, N., Clark, B. K., Nayak, C., and Troyer, M · 2015
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Albash, T., and Lidar, D. A · 2016
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Exponentially more precise quantum simulation of fermions in second quantization
Babbush, R., Berry, D. W., Kivlichan, I. D., Wei, A. Y., Love, P. J., and Aspuru-Guzik, A · 2016
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Quantum algorithms and circuits for scientific computing
Bhaskar, M. K., Hadfield, S., Papageorgiou, A., and Petras, I · 2016
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Biamonte, J., Wittek, P., Pancotti, N., Rebentrost, P., Wiebe, N., and Lloyd, S · 2016
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Characterizing quantum supremacy in near-term devices
Boixo, S., Isakov, S. V., Smelyanskiy, V. N., Babbush, R., Ding, N., Jiang, Z., Martinis, J. M., and Neven, H · 2016
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Computational multiqubit tunnelling in programmable quantum annealers
Boixo, S., Smelyanskiy, V. N., Shabani, A., Isakov, S. V., Dykman, M., Denchev, V. S., Amin, M. H., Smirnov, A. Y., Mohseni, M., and Neven, H · 2016
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Quantum cryptography beyond quantum key distribution
Broadbent, A., and Schaffner, C · 2016
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What is the computational value of finite-range tunneling?
Denchev, V. S., Boixo, S., Isakov, S. V., Ding, N., Babbush, R., Smelyanskiy, V., Martinis, J., and Neven, H · 2016
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Quantum supremacy through the quantum approximate optimization algorithm
Farhi, E., and Harrow, A. W · 2016
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Introduction to Quantum Mechanics
Griffiths, D. J · 2016
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Driver Hamiltonians for constrained optimization in quantum annealing
Hen, I., and Sarandy, M. S · 2016
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Quantum annealing for constrained optimization
Hen, I., and Spedalieri, F. M · 2016
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Quantum algorithms: an overview
Montanaro, A · 2016
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A functional architecture for scalable quantum computing
Sete, E. A., Zeng, W. J., and Rigetti, C. T · 2016
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Training a quantum optimizer
Wecker, D., Hastings, M. B., and Troyer, M · 2016
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Optimizing variational quantum algorithms using Pontryagin’s minimum principle
Yang, Z.-C., Rahmani, A., Shabani, A., Neven, H., and Chamon, C · 2016
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A NASA perspective on quantum computing: opportunities and challenges
Biswas, R., Jiang, Z., Kechezhi, K., Knysh, S., Mandrà, S., O’Gorman, B., Perdomo-Ortiz, A., Petukhov, A., Realpe-Gómez, J., Rieffel, E., et al · 2017
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Quantum algorithms for fixed qubit architectures
Farhi, E., Goldstone, J., Gutmann, S., and Neven, H · 2017
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Practical optimization for hybrid quantum-classical algorithms
Guerreschi, G. G., and Smelyanskiy, M · 2017
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From the quantum approximate optimization algorithm to a quantum alternating operator ansatz
Hadfield, S., Wang, Z., O’Gorman, B., Rieffel, E. G., Venturelli, D., and Biswas, R · 2017
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Quantum approximate optimization with hard and soft constraints
Hadfield, S., Wang, Z., Rieffel, E. G., O’Gorman, B., Venturelli, D., and Biswas, R · 2017
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IBM Q and Quantum Computing
IBM · 2017
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Near-optimal quantum circuit for Grover’s unstructured search using a transverse field
Jiang, Z., Rieffel, E. G., and Wang, Z · 2017
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Commercialize early quantum technologies
Mohseni, M., Read, P., Neven, H., Boixo, S., Denchev, V., Babbush, R., Fowler, A., Smelyanskiy, V., and Martinis, J · 2017
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Elucidating reaction mechanisms on quantum computers
Reiher, M., Wiebe, N., Svore, K. M., Wecker, D., and Troyer, M · 2017
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The multilevel splitting algorithm for graph colouring with application to the potts model
Vaisman, R., Roughan, M., and Kroese, D. P · 2017
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Compiling quantum circuits to realistic hardware architectures using temporal planners
Venturelli, D., Do, M., Rieffel, E., and Frank, J · 2017
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Quantum Theory, Groups and Representations: An Introduction
Woit, P · 2017
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On the representation of Boolean and real functions as Hamiltonians for quantum computing
Hadfield, S · 2018
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Divide and conquer approach to quantum hamiltonian simulation
Hadfield, S., and Papageorgiou, A · 2018
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Quantum approximate optimization algorithm for MaxCut: A fermionic view
Wang, Z., Hadfield, S., Jiang, Z., and Rieffel, E. G · 2018
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