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Springer Science and Business Media LLC
Communications in Mathematical Physics (297)
References
54
Referenced
264
-
Aaronson, S., Shi, Y.: Quantum lower bounds for the collision and the element distinctness problems. J. ACM 51 (4) 595–605 (2004), preliminary versions in STOC 2002 and FOCS 2002
(
10.1145/1008731.1008735
) - Aharonov, D., Ambainis, A., Kempe, J., Vazirani, U.: Quantum walks on graphs. In: Proc. 33rd ACM Symposium on Theory of Computing, pp. 50–59, 2001, available at http://arxiv.org/abs/quant-ph/0012090 , 2000
- Aharonov, D., Ta-Shma, A.: Adiabatic quantum state generation and statistical zero knowledge. In: Proc. 35th ACM Symposium on Theory of Computing, pp. 20–29, 2003, available at http://arxiv.org/abs/quant-ph/0301023 , 2003
- Aldous, D., Fill, J.A.: Reversible Markov chains and random walks on graphs (in preparation), http://www.stat.berkeley.edu/~aldous/RWG/book.html
-
Ambainis A.: Quantum walk algorithm for element distinctness. SIAM J. Comput. 37(1), 210–239 (2007)
(
10.1137/S0097539705447311
) / SIAM J. Comput. by A. Ambainis (2007) - Ambainis, A., Bach, E., Nayak, A., Vishwanath, A., Watrous, J.: One-dimensional quantum walks. Proc. 33rd ACM Symposium on Theory of Computing, pp. 37–49, 2001, available at http://arxiv.org/abs/quant-ph/0010117 , 2000
- Ambainis, A., Childs, A.M., Reichardt, B.W., Špalek, R., Zhang S.: Any AND-OR formula of size N can be evaluated in time N 1/2+o(1) on a quantum computer. In: Proc. 48th IEEE Symposium on Foundations of Computer Science, pp. 363–372, 2007, available at http://arxiv.org/abs/quant-ph/0703015 and http://arxiv.org/abs/0704.3628 , 2007
- Ambainis, A., Kempe, J., Rivosh, A.: Coins make quantum walks faster. In: Proc. 16th ACM-SIAM Symposium on Discrete Algorithms, pp. 1099–1108, 2005, available at http://arxiv.org/abs/quant-ph/0402107 , 2004
-
Berry D.W., Ahokas G., Cleve R., Sanders B.C.: Efficient quantum algorithms for simulating sparse Hamiltonians. Commun. Math. Phys. 270(2), 359–371 (2007)
(
10.1007/s00220-006-0150-x
) / Commun. Math. Phys. by D.W. Berry (2007) - Buhrman, H., Špalek, R.: Quantum verification of matrix products. In: Proc. 17th ACM-SIAM Symposium on Discrete Algorithms, pp. 880–889, 2006, available at http://arxiv.org/abs/quant-ph/0409035 , 2004
-
Bužek V., Derka R., Massar S.: Optimal quantum clocks. Phys. Rev. Lett. 82(10), 2207–2210 (1999)
(
10.1103/PhysRevLett.82.2207
) / Phys. Rev. Lett. by V. Bužek (1999) - Childs, A.M.: Quantum information processing in continuous time. Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA, 2004
- Childs, A.M., Cleve, R., Deotto, E., Farhi, E., Gutmann, S., Spielman, D.A.: Exponential algorithmic speedup by quantum walk. In: Proc. 35th ACM Symposium on Theory of Computing, pp. 59–68, 2003, available at http://arxiv.org/abs/quant-ph/0209131 , 2002
- Childs A.M., Eisenberg J.M.: Quantum algorithms for subset finding. Quant. Inf. Comp. 5(7), 593–604 (2005) / Quant. Inf. Comp. by A.M. Childs (2005)
-
Childs A.M., Farhi E., Gutmann S.: An example of the difference between quantum and classical random walks. Quant. Inf. Proc. 1(1-2), 35–43 (2002)
(
10.1023/A:1019609420309
) / Quant. Inf. Proc. by A.M. Childs (2002) -
Childs A.M., Goldstone J.: Spatial search by quantum walk. Phys. Rev. A 70(2), 022314 (2004)
(
10.1103/PhysRevA.70.022314
) / Phys. Rev. A by A.M. Childs (2004) -
Childs A.M., Goldstone J.: Spatial search and the Dirac equation. Phys. Rev. A 70(4), 042312 (2004)
(
10.1103/PhysRevA.70.042312
) / Phys. Rev. A by A.M. Childs (2004) - Childs, A.M., Schulman, L.J., Vazirani, U.V.: Quantum algorithms for hidden nonlinear structures. In: Proc. 48th IEEE Symposium on Foundations of Computer Science, pp. 395–404, 2007, available at http://arxiv.org/abs/0705.2784 , 2007
- Cleve, R., Gottesman, D., Mosca, M., Somma, R.D., Yonge-Mallo, D.L.: Efficient discrete-time simulations of continuous-time quantum query algorithms. In: Proc. 41st ACM Symposium on Theory of Computing, pp. 409–416, 2009, available at http://arxiv.org/abs/0811.4428 , 2008
-
van Dam W., D’Ariano G.M., Ekert A., Macchiavello C., Mosca M.: Optimal phase estimation in quantum networks. J. Phys. A 40(28), 7971–7984 (2007)
(
10.1088/1751-8113/40/28/S07
) / J. Phys. A by W. Dam van (2007) - van Dam, W., Hallgren, S., Ip, L.: Quantum algorithms for some hidden shift problems. In: Proc. 14th ACM-SIAM Symposium on Discrete Algorithms, pp. 489–498, 2002, available at http://arxiv.org/abs/quant-ph/0211140 , 2002
- van Dam, W., Mosca, M., Vazirani, U.: How powerful is adiabatic quantum computation?. In: Proc. 42nd IEEE Symposium on Foundations of Computer Science, pp. 279–287, 2001, available at http://arxiv.org/abs/quant-ph/0206003 , 2002
- van Dam, W., Seroussi, G.: Quantum algorithms for estimating Gauss sums and calculating discrete logarithms. Manuscript, 2003, available at http://www.cs.ucsb.edu/~vandam/gausssumdlog.pdf
- Damgård, I.B.: On the randomness of Legendre and Jacobi sequences. Advances in Cryptology - CRYPTO ’88, Lecture Notes in Computer Science, vol. 403, New York: Springer, 1990, pp. 163–172
-
Farhi E., Goldstone J., Gutmann S.: A quantum algorithm for the Hamiltonian NAND tree. Theory of Computing 4(1), 169–190 (2008)
(
10.4086/toc.2008.v004a008
) / Theory of Computing by E. Farhi (2008) -
Farhi E., Gutmann S.: Analog analogue of a digital quantum computation. Phys. Rev. A 57(4), 2403–2406 (1998)
(
10.1103/PhysRevA.57.2403
) / Phys. Rev. A by E. Farhi (1998) -
Farhi E., Gutmann S.: Quantum computation and decision trees. Phys. Rev. A 58(2), 915–928 (1998)
(
10.1103/PhysRevA.58.915
) / Phys. Rev. A by E. Farhi (1998) - Godsil, C.: Association schemes. Lecture notes, available at http://quoll.uwaterloo.ca/pstuff/assoc.pdf , 2004
- Grover, L., Rudolph, T.: Creating superpositions that correspond to efficiently integrable probability distributions, available at http://arxiv.org/abs/quant-ph/0208112v1 , 2002
-
Grover, L.K.: Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79(2), 325–328 (1997), preliminary version in STOC 1996
(
10.1103/PhysRevLett.79.325
) -
Kedlaya K.S.: Quantum computation of zeta functions of curves. Comput. Complex. 15(1), 1–19 (2006)
(
10.1007/s00037-006-0204-7
) / Comput. Complex. by K.S. Kedlaya (2006) -
Linial N.: Locality in distributed graph algorithms. SIAM J. Comput. 21(1), 193–201 (1992)
(
10.1137/0221015
) / SIAM J. Comput. by N. Linial (1992) -
Lloyd S.: Universal quantum simulators. Science 273(5278), 1073–1078 (1996)
(
10.1126/science.273.5278.1073
) / Science by S. Lloyd (1996) -
Luis A., Peřina J.: Optimum phase-shift estimation and the quantum description of the phase difference. Phys. Rev. A 54(5), 4564–4570 (1996)
(
10.1103/PhysRevA.54.4564
) / Phys. Rev. A by A. Luis (1996) -
Magniez, F., Nayak, A.: Quantum complexity of testing group commutativity. Algorithmica 48(3), 221–232 (2007), preliminary version in ICALP 2005
(
10.1007/s00453-007-0057-8
) - Magniez, F., Nayak, A., Roland, J., Santha, M.: Search via quantum walk. In: Proc. 39th ACM Symposium on Theory of Computing, pp. 575–584, 2007, available at http://arvix.org/abs/quant-ph/0608026 , 2006
- Magniez, F., Santha, M., Szegedy, M.: Quantum algorithms for the triangle problem. In: Proc. 16th ACM-SIAM Symposium on Discrete Algorithms, pp. 1109–1117, 2005, available at http://arxiv.org/abs/quant-ph/0310134 , 2003
-
Meyer D.A.: From quantum cellular automata to quantum lattice gasses. J. Stat. Phys. 85(5/6), 551–574 (1996)
(
10.1007/BF02199356
) / J. Stat. Phys. by D.A. Meyer (1996) -
Meyer D.A.: On the absence of homogeneous scalar unitary cellular automata. Phys. Lett. A 223, 337–340 (1996)
(
10.1016/S0375-9601(96)00745-1
) / Phys. Lett. A by D.A. Meyer (1996) -
Mochon C.: Hamiltonian oracles. Phys. Rev. A 75(4), 042313 (2007)
(
10.1103/PhysRevA.75.042313
) / Phys. Rev. A by C. Mochon (2007) -
Moore, C., Russell, A.: Quantum walks on the hypercube. In: Proc. 6th International Workshop on Randomization and Approximation Techniques in Computer Science, Lecture Notes in Computer Science, Vol. 2483, Berlin: Springer, 2002 pp. 164–178
(
10.1007/3-540-45726-7_14
) - Regev, O.: Witness-preserving amplification of QMA. Lecture notes, http://www.cs.tau.ac.il/~odedr/teaching/quantum_fall_2005/ln/qma.pdf , 2006
- Reichardt, B.W., Špalek, R.: Span-program-based quantum algorithm for evaluating formulas. In: Proc. 40th ACM Symposium on Theory of Computing, pp. 103–112, 2008, available at http://arxiv.org/abs/0710.2630 , 2007
-
Roland J., Cerf N.J.: Quantum search by local adiabatic evolution. Phys. Rev. A 65(4), 042308 (2002)
(
10.1103/PhysRevA.65.042308
) / Phys. Rev. A by J. Roland (2002) -
Roland J., Cerf N.J.: Quantum-circuit model of Hamiltonian search algorithms. Phys. Rev. A 68(6), 062311 (2003)
(
10.1103/PhysRevA.68.062311
) / Phys. Rev. A by J. Roland (2003) - Schmidt W.M.: Equations over Finite Fields: An Elementary Approach. 2nd ed. Kendrick Press, Hebercity, UT (2004) / Equations over Finite Fields: An Elementary Approach by W.M. Schmidt (2004)
-
Severini S.: On the digraph of a unitary matrix. SIAM J. Matrix Anal. Appl. 25(1), 295–300 (2003)
(
10.1137/S0895479802410293
) / SIAM J. Matrix Anal. Appl. by S. Severini (2003) -
Shenvi N., Kempe J., Whaley K.B.: A quantum random walk search algorithm. Phys. Rev. A 67(5), 052307 (2003)
(
10.1103/PhysRevA.67.052307
) / Phys. Rev. A by N. Shenvi (2003) -
Shor P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26(5), 1484–1509 (1997)
(
10.1137/S0097539795293172
) / SIAM J. Comput. by P.W. Shor (1997) -
Strauch F.W.: Connecting the discrete- and continuous-time quantum walks. Phys. Rev. A 74(3), 030301 (2006)
(
10.1103/PhysRevA.74.030301
) / Phys. Rev. A by F.W. Strauch (2006) - Szegedy, M.: Quantum speed-up of Markov chain based algorithms. In: Proc. 45th IEEE Symposium on Foundations of Computer Science, pp. 32–41, 2004, available at http://arxiv.org/abs/quant-ph/0401053 , 2004
-
Tulsi A.: Faster quantum-walk algorithm for the two-dimensional spatial search. Phys. Rev. A 78(1), 012310 (2008)
(
10.1103/PhysRevA.78.012310
) / Phys. Rev. A by A. Tulsi (2008) -
Watrous J.: Quantum simulations of classical random walks and undirected graph connectivity. J. Comput. System Sci. 62(2), 376–391 (2001)
(
10.1006/jcss.2000.1732
) / J. Comput. System Sci. by J. Watrous (2001) -
Weil A.: On some exponential sums. Proc. Natl. Acad. Sci. 34(5), 204–207 (1948)
(
10.1073/pnas.34.5.204
) / Proc. Natl. Acad. Sci. by A. Weil (1948)
Dates
Type | When |
---|---|
Created | 15 years, 10 months ago (Oct. 9, 2009, 4:59 p.m.) |
Deposited | 6 years, 3 months ago (May 24, 2019, 6:56 a.m.) |
Indexed | 2 weeks, 3 days ago (Aug. 19, 2025, 6:22 a.m.) |
Issued | 15 years, 10 months ago (Oct. 10, 2009) |
Published | 15 years, 10 months ago (Oct. 10, 2009) |
Published Online | 15 years, 10 months ago (Oct. 10, 2009) |
Published Print | 15 years, 6 months ago (March 1, 2010) |
@article{Childs_2009, title={On the Relationship Between Continuous- and Discrete-Time Quantum Walk}, volume={294}, ISSN={1432-0916}, url={http://dx.doi.org/10.1007/s00220-009-0930-1}, DOI={10.1007/s00220-009-0930-1}, number={2}, journal={Communications in Mathematical Physics}, publisher={Springer Science and Business Media LLC}, author={Childs, Andrew M.}, year={2009}, month=oct, pages={581–603} }