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The quantum circuit model is the most widely used model of quantum computation.
On the convergence of the perturbation method. I
Tosio Kato · 1949
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Sur la théorie des perturbations des états liés
Claude Bloch · 1958
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Theorie der normalflachen, ein isotopiekriterium für den kreisknoten
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Quantum Mechanics
Albert Messiah · 1961
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Group Theory and its Application to Physical Problems
Morton Hamermesh · 1962
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Representation of Groups
H. Boerner · 1963
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Relationships between nondeterministic and deterministic tape complexities
W. J. Savitch · 1970
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On computing the minima of quadratic forms
Andrew Yao · 1975
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Quantum Mechanics
Claude Cohen-Tannoudji, Bernard Diu, and Franck Laloë · 1977
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Computers and Intractability: A Guide to the Theory of NP-Completeness
M. R. Garey and D. S. Johnson · 1979
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A simplification of the computation of the natural representation of the symmetric group S n S_{n}
Joseph M. Clifton · 1981
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Simulating physics with computers
Richard P. Feynman · 1982
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Braid groups, Hecke algebras and type II 1 \mathrm{II}_{1} factors
Vaughan F. R. Jones · 1983
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Quantum theory, the Church-Turing principle, and the universal quantum computer
David Deutsch · 1985
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Algorithms for the character theory of the symmetric group
Ömer Eǧecioǧlu · 1985
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A polynomial invariant for knots via von Neumann algebras
Vaughan F. R. Jones · 1985
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Quantum mechanical computers
Richard Feynman · 1986
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The Complexity of Boolean Functions
Ingo Wegener · 1987
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Bounded-width polynomial-size brancing programs recognize exactly those languages in NC 1 \mathrm{NC}^{1}
David A. Barrington · 1989
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Quantum field theory and the Jones polynomial
Edward Witten · 1989
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On the computational complexity of the Jones and Tutte polynomials
F. Jaeger, D. L. Vertigan, and D. J. A. Welsh · 1990
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Rapid solution of problems by quantum computation
David Deutsch and Richard Josza · 1992
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An efficient algorithm for evaluating the standart Young-Yamanouchi orthogonal representation with two-column Young tableaux for symmetric groups
Wei Wu and Qianer Zhang · 1992
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Quantum complexity theory
Ethan Bernstein and Umesh Vazirani · 1993
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Quantum Theory: Concepts and Methods
Asher Peres · 1993
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On the complexity of computing characters of finite groups
Charles Thomas Hepler · 1994
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Computational Complexity
Christos H. Papadimitriou · 1994
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Natural proofs
Alexander A. Razborov and Steven Rudich · 1994
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Modern Quantum Mechanics
J. J. Sakurai · 1994
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The orthogonal and the natural representation for symmetric groups
Wi Wu and Qianer Zhang · 1994
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Quantum cryptoanalysis of hidden linear functions
D. Boneh and R. J. Lipton · 1995
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Quantum measurements and the Abelian stabilizer problem
Alexei Kitaev · 1995
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Approximate quantum Fourier transform and decoherence
Adriano Barenco, Artur Ekert, Kalle-Antti Suominen, and Päivi Törmä · 1996
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A quantum algorithm for finding the minimum
Christoph Dürr and Peter Høyer · 1996
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Simulations of many-body quantum systems by a quantum computer
Stephen Wiesner · 1996
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Efficient simulation of quantum systems by quantum computers
Christof Zalka · 1996
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Simulation of many-body Fermi systems on a universal quantum computer
Daniel S. Abrams and Seth Lloyd · 1997
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The strengths and weaknesses of quantum computation
Charles H. Bennet, Ethan Bernstein, Gilles Brassard, and Umesh Vazirani · 1997
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Quantum algorithm for the collision problem
Gilles Brassard, Peter Høyer, and Alain Tapp · 1997
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Stabilizer Codes and Quantum Error Correction
Daniel Gottesman · 1997
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Quantum mechanics helps in searching for a needle in a haystack
Lov K. Grover · 1997
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Quantum computations: algorithms and error correction
Alexei Yu. Kitaev · 1997
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Quantum lower bounds by polynomials
R. Beals, H. Buhrmann, R. Cleve, M. Mosca, and R. de Wolf · 1998
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Tight bounds on quantum searching
M. Boyer, G. Brassard, P. Høyer, and A. Tapp · 1998
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Quantum counting
G. Brassard, P. Høyer, and A. Tapp · 1998
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Limit on the speed of quantum computation in determining parity
Edward Farhi, Jeffrey Goldstone, Sam Gutmann, and Michael Sipser · 1998
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Quantum computation and decision trees
Edward Farhi and Sam Gutmann · 1998
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Theory of fault-tolerant quantum computation
Daniel Gottesman · 1998
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Power of one bit of quantum information
E. Knill and R. Laflamme · 1998
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Quantum searching, counting, and amplitude amplification by eigenvector analysis
M. Mosca · 1998
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Polynomial-time solution to the hidden subgroup problem for a class of non-abelian groups
Martin Roetteler and Thomas Beth · 1998
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Invariant quantum algorithms for insertion into an ordered list
Edward Farhi, Jeffrey Goldstone, Sam Gutmann, and Michael Sipser · 1999
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Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations
Daniel Gottesman and Isaac Chuang · 1999
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The computational complexity of knot and link problems
Joel Hass, Jeffrey Lagarias, and Nicholas Pippenger · 1999
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Calculating the thermal rate constant with exponential speedup on a quantum computer
Daniel A. Lidar and Haobin Wang · 1999
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Quantum Computer Algorithms
Michele Mosca · 1999
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The quantum query complexity of approximating the median and related statistics
Ashwin Nayak and Felix Wu · 1999
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Quantum algorithms which accept hot qubit inputs
Xinlan Zhou, Debbie W. Leung, and Isaac L. Chuang · 1999
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Quantum lower bounds by quantum arguments
Andris Ambainis · 2000
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Integer relation detection
David H. Bailey · 2000
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Fast parallel circuits for the quantum Fourier transform
Richard Cleve and John Watrous · 2000
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Addition on a quantum computer
Thomas Draper · 2000
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Quantum computation by adiabatic evolution
Edward Farhi, Jeffrey Goldstone, Sam Gutmann, and Michael Sipser · 2000
Cited alongside, same era.
A modular functor which is universal for quantum computation
Michael Freedman, Michael Larsen, and Zhenghan Wang · 2000
Cited alongside, same era.
Introduction to Quantum Mechanics
Applications of coherent classical communication and the Schur transform to quantum information theory
Aram W. Harrow · 2005
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Quantum algorithm for commutativity testing of a matrix set
Yuki Kelly Itakura · 2005
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Fast quantum algorithm for numerical gradient estimation
Stephen P. Jordan · 2005
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Noise resistance of adiabatic quantum computation using random matrix theory
Jeremie Roland and Nicolas J. Cerf · 2005
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Characterization of complex quantum dynamics with a scalable NMR information processor
C. A. Ryan, J. Emerson, D. Poulin, C. Negrevergne, and R. Laflamme · 2005
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Adiabatic quantum computation in open systems
M. S. Sarandy and D. A. Lidar · 2005
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David J. Griffiths · 2000
Cited alongside, same era.
Quantum Computation and Quantum Information
Michael A. Nielsen and Isaac L. Chuang · 2000
Cited alongside, same era.
Efficient quantum algorithms for shifted quadratic character problems
Wim van Dam and Sean Hallgren · 2000
Cited alongside, same era.
Coherence-preserving quantum bits
Dave Bacon, Kenneth R. Brown, and K. Birgitta Whaley · 2001
Cited alongside, same era.
Quantum algorithms for element distinctness
Harry Burhrman, Christoph Dürr, Mark Heiligman, Peter Høyer, Fr’ed’eric Magniez, Miklos Santha, and Ronald de Wolf · 2001
Cited alongside, same era.
Robustness of adiabatic quantum computation
Andrew Childs, Edward Farhi, and John Preskill · 2001
Cited alongside, same era.
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Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer
Peter W. Shor · 2005
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The BQP-hardness of approximating the Jones polynomial
Dorit Aharonov and Itai Arad · 2006
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A polynomial quantum algorithm for approximating the Jones polynomial
Dorit Aharonov, Vaughan Jones, and Zeph Landau · 2006
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Simple proof of fault tolerance in the graph-state model
Panos Aliferis and Debbie Leung · 2006
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Computing with highly mixed states
Andris Ambainis, Leonard Schulman, and Umesh Vazirani · 2006
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Quantum verification of matrix products
Harry Buhrman and Robert Špalek · 2006
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Notes on the hidden subgroup problem on some semi-direct product groups
Dong Pyo Chi, Jeong San Kim, and Soojoon Lee · 2006
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Quantum query complexity of some graph problems
Christoph Dürr, Mark Heiligman, Peter Høyer, and Mehdi Mhalla · 2006
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BQP-complete problems concerning mixing properties of classical random walks on sparse graphs
Dominik Janzing and Pawel Wocjan · 2006
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q-deformed spin networks knot polynomials and anyonic topological quantum computation
Louis H. Kauffman and Samuel J. Lomonaco Jr · 2006
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Quantum computation of zeta functions of curves
Kirin S. Kedlaya · 2006
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Consistency of local density matrices is QMA-complete
Yi-Kai Liu · 2006
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The complexity of quantum spin systems in a two-dimensional square lattice
Roberto Oliveira and Barbara M. Terhal · 2006
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Computation with unitaries and one pure qubit
Dan Shepherd · 2006
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A quantum circuit for Shor’s factoring algorithm using 2 n + 2 2n+2 qubits
Yasuhiro Takahashi and Noburu Kunihiro · 2006
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Quantum algorithms for some hidden shift problems
Wim van Dam, Sean Hallgren, and Lawrence Ip · 2006
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The Jones polynomial: quantum algorithms and applications in quantum complexity theory
Pawel Wocjan and Jon Yard · 2006
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Polynomial quantum algorithms for additive approximations of the Potts model and other points of the Tutte plane
Dorit Aharonov, Itai Arad, Elad Eban, and Zeph Landau · 2007
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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 · 2007
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Quantum walk algorithm for element distinctness
Andris Ambainis · 2007
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Andris Ambainis, Andrew M. Childs, Ben W.Reichardt, Robert Špalek, and Shengyu Zheng · 2007
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Quantum search in an ordered list via adaptive learning
Michael Ben-Or and Avinatan Hassidim · 2007
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Efficient quantum algorithms for simulating sparse Hamiltonians
D.W. Berry, G. Ahokas, R. Cleve, and B. C. Sanders · 2007
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Realizable Hamiltonians for universal adiabatic quantum computers
Jacob D. Biamonte and Peter J. Love · 2007
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Quantum algorithms for hidden nonlinear structures
A. M. Childs, L. J. Schulman, and U. V. Vazirani · 2007
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Optimal quantum adversary lower bounds for ordered search
Andrew Childs and Troy Lee · 2007
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Discrete-query quantum algorithm for NAND trees
Andrew M. Childs, Richard Cleve, Stephen P. Jordan, and David Yeung · 2007
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Quantum algorithm for a generalized hidden shift problem
Andrew M. Childs and Wim van Dam · 2007
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Quantum algorithms for evaluating MIN-MAX trees
Richard Cleve, Dmitry Gavinsky, and David L. Yeung · 2007
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Codeword stabilized quantum codes
Andrew Cross, Graeme Smith, John A. Smolin, and Bei Zeng · 2007
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Quantum algorithm for identifying hidden polynomial function graphs
Thomas Decker, Jan Draisma, and Pawel Wocjan · 2007
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A quantum algorithm for the Hamiltonian NAND tree
Edward Farhi, Jeffrey Goldstone, and Sam Gutmann · 2007
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A note on cyclotomic cosets, an algorithm for finding coset representatives and size, and a theorem on the quantum evaluation of weight enumerators for a certain class of cyclic codes
Joseph Geraci and Frank Van Bussel · 2007
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On the exact evaluation of certain instances of the Potts partition function by quantum computers
Joseph Geraci and Daniel A. Lidar · 2007
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Efficient quantum algorithms for the hidden subgroup problem over a class of semi-direct product groups
Yoshifumi Inui and Francois Le Gall · 2007
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An efficient quantum algorithm for the hidden subgroup problem in extraspecial groups
Gábor Ivanyos, Luc Sanselme, and Miklos Santha · 2007
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An efficient quantum algorithm for the hidden subgroup problem in nil-2 groups
Gábor Ivanyos, Luc Sanselme, and Miklos Santha · 2007
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A promiseBQP-complete string rewriting problem
Dominik Janzing and Pawel Wocjan · 2007
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A simple promiseBQP-complete matrix problem
Dominik Janzing and Pawel Wocjan · 2007
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Quantum algorithms for the triangle problem
Frederic Magniez, Miklos Santha, and Mario Szegedy · 2007
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Quantum algorithm for the hidden subgroup problem on a class of semidirect product groups
Carlos Magno, M. Cosme, and Renato Portugal · 2007
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New construction for a QMA complete 3-local Hamiltonian
Daniel Nagaj and Shay Mozes · 2007
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Non-abelian anyons and topological quantum computation
Chetan Nayak, Steven H. Simon, Ady Stern, Michael Freedman, and Sankar Das Sarma · 2007
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Matrix product state representations
David Perez-Garcia, Frank Verstraete, Michael M. Wolf, and J. Ignacio Cirac · 2007
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Span-program-based quantum algorithm for evaluating formulas
Ben Reichardt and Robert Špalek · 2007
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Computational complexity of PEPS
N. Schuch, M. M. Wolf, F. Verstraete, and J. I. Cirac · 2007
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R. D. Somma, S. Boixo, and H. Barnum · 2007
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Nonadditive quantum error-correcting code
Sixia Yu, Qing Chen, C. H. Lai, and C. H. Oh · 2007
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Joseph Geraci · 2008
Closest in time.
Quantum algorithms for the simulation of chemical dynamics
Ivan Kassal, Stephen P. Jordan, Peter J. Love, Masoud Mohseni, and Alán Aspuru-Guzik · 2008
Closest in time.
Local Hamiltonians in quantum computation
Daniel Nagaj · 2008
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