Fetching the paper…
Reading the bibliography…
Quantum walk is one of the main tools for quantum algorithms.
A. Weil, On some exponential sums , Proc. Natl. Acad. Sci. 34
1948
Earlier work this paper cites.
I. B. Damgård, On the randomness of Legendre and Jacobi sequences , Advances in Cryptology - CRYPTO ’88, Lecture Notes in Computer Science, vol. 403, pp. 163–172, 1990
1990
Earlier work this paper cites.
N. Linial, Locality in distributed graph algorithms , SIAM J. Comput. 21
1992
Earlier work this paper cites.
L. K. Grover, Quantum mechanics helps in searching for a needle in a haystack , Phys. Rev. Lett. 79
1996
Earlier work this paper cites.
S. Lloyd, Universal quantum simulators , Science 273
1996
Earlier work this paper cites.
A. Luis and J. Peřina, Optimum phase-shift estimation and the quantum description of the phase difference , Phys. Rev. A 54
1996
Earlier work this paper cites.
D. A. Meyer, From quantum cellular automata to quantum lattice gasses , J. Stat. Phys. 85
1996
Earlier work this paper cites.
P. W. Shor, Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer , SIAM J. Comput. 26
1997
Earlier work this paper cites.
E. Farhi and S. Gutmann, Analog analogue of a digital quantum computation , Phys. Rev. A 57
1998
Earlier work this paper cites.
V. Bužek, R. Derka, and S. Massar, Optimal quantum clocks , Phys. Rev. Lett. 82
1999
Earlier work this paper cites.
D. Aharonov, A. Ambainis, J. Kempe, and U. Vazirani, Quantum walks on graphs , Proc. 33rd ACM Symposium on Theory of Computing, pp. 50–59, 2001, quant-ph/0012090
2001
Earlier work this paper cites.
A. Ambainis, E. Bach, A. Nayak, A. Vishwanath, and J. Watrous, One-dimensional quantum walks , Proc. 33rd ACM Symposium on Theory of Computing, pp. 37–49, 2001, quant-ph/0010117
2001
Earlier work this paper cites.
W. van Dam, M. Mosca, and U. Vazirani, How powerful is adiabatic quantum computation? , Proc. 42nd IEEE Symposium on Foundations of Computer Science, pp. 279–287, 2001, quant-ph/0206003
2001
Earlier work this paper cites.
J. Watrous, Quantum simulations of classical random walks and undirected graph connectivity , J. Comput. System Sci. 62
2001
Earlier work this paper cites.
S. Aaronson and Y. Shi, Quantum lower bounds for the collision and the element distinctness problems , J. ACM 51
2002
Earlier work this paper cites.
A. M. Childs, E. Farhi, and S. Gutmann, An example of the difference between quantum and classical random walks , Quantum Information Processing 1
2002
Earlier work this paper cites.
W. van Dam, S. Hallgren, and L. Ip, Quantum algorithms for some hidden shift problems , Proc. 14th ACM-SIAM Symposium on Discrete Algorithms, pp. 489–498, 2002, quant-ph/0211140
2002
Cited alongside, same era.
C. Moore and A. Russell, Quantum walks on the hypercube , Proc. 6th International Workshop on Randomization and Approximation Techniques in Computer Science, Lecture Notes in Computer Science, vol. 2483, pp. 164–178, 2002, quant-ph/0104137
2002
Cited alongside, same era.
J. Roland and N. J. Cerf, Quantum search by local adiabatic evolution , Phys. Rev. A 65
2002
Cited alongside, same era.
D. Aharonov and A. Ta-Shma, Adiabatic quantum state generation and statistical zero knowledge , Proc. 35th ACM Symposium on Theory of Computing, pp. 20–29, 2003, quant-ph/0301023
2003
Cited alongside, same era.
F. Magniez and A. Nayak, Quantum complexity of testing group commutativity , Algorithmica 48
2005
Later among the works it cites.
F. Magniez, M. Santha, and M. Szegedy, Quantum algorithms for the triangle problem , Proc. 16th ACM-SIAM Symposium on Discrete Algorithms, pp. 1109–1117, 2005, quant-ph/0310134
2005
Later among the works it cites.
H. Buhrman and R. Špalek, Quantum verification of matrix products , Proc. 17th ACM-SIAM Symposium on Discrete Algorithms, pp. 880–889, 2006, quant-ph/0409035
2006
Later among the works it cites.
K. S. Kedlaya, Quantum computation of zeta functions of curves , Comput. Complex. 15
2006
Later among the works it cites.
F. W. Strauch, Connecting the discrete- and continuous-time quantum walks , Phys. Rev. A 74
2006
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
A. M. Childs, R. Cleve, E. Deotto, E. Farhi, S. Gutmann, and D. A. Spielman, Exponential algorithmic speedup by quantum walk , Proc. 35th ACM Symposium on Theory of Computing, pp. 59–68, 2003, quant-ph/0209131
2003
Cited alongside, same era.
W. van Dam and G. Seroussi, Quantum algorithms for estimating Gauss sums and calculating discrete logarithms , manuscript, 2003
2003
Cited alongside, same era.
S. Severini, On the digraph of a unitary matrix , SIAM J. Matrix Anal. Appl. 25
2003
Cited alongside, same era.
N. Shenvi, J. Kempe, and K. B. Whaley, A quantum random walk search algorithm , Phys. Rev. A 67
2003
Cited alongside, same era.
A. Ambainis, Quantum walk algorithm for element distinctness , SIAM J. Comput. 37
2004
Cited alongside, same era.
A. M. Childs, Quantum information processing in continuous time , Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA, 2004
2004
Cited alongside, same era.
A. M. Childs and J. Goldstone, Spatial search by quantum walk , Phys. Rev. A 70
2004
Cited alongside, same era.
W. M. Schmidt, Equations Over Finite Fields: An Elementary Approach , 2nd ed., Kendrick Press, 2004
2004
Cited alongside, same era.
2007
Later among the works it cites.
D. W. Berry, G. Ahokas, R. Cleve, and B. C. Sanders, Efficient quantum algorithms for simulating sparse Hamiltonians , Commun. Math. Phys. 270
2007
Later among the works it cites.
2007
Later among the works it cites.
2007
Later among the works it cites.
F. Magniez, A. Nayak, J. Roland, and M. Santha, Search via quantum walk , Proc. 39th ACM Symposium on Theory of Computing, pp. 575–584, 2007, quant-ph/0608026
2007
Later among the works it cites.
C. Mochon, Hamiltonian oracles , Phys. Rev. A 75
2007
Later among the works it cites.
E. Farhi, J. Goldstone, and S. Gutmann, A quantum algorithm for the Hamiltonian NAND tree , Theory of Computing 4
2008
Closest in time.
2008
Closest in time.