Bosonsampling is far from uniform

Quantum Information and Computation

Volumn 14, Issue 15-16, 2014, Pages 1383-1423

  Aaronson, Scott ^a   Arkhipov, Alex ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Linear optics; Permanent; Sampling problems; Testing distributions

Indexed keywords

POLYNOMIAL APPROXIMATION; QUANTUM THEORY; SAMPLING;

HIGH PROBABILITY; LINEAR OPTICS; PERMANENT; PRIORI KNOWLEDGE; QUANTUM ALGORITHMS; RESEARCH QUESTIONS; SAMPLING PROBLEMS; UNIFORM DISTRIBUTION;

PROBABILITY DISTRIBUTIONS;

EID: 84906808881     PISSN: 15337146     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (19)

1. S. Aaronson and A. Arkhipov. The computational complexity of linear optics. Theory of Computing, 9(4):143-252, 2013. Conference version in Proceedings of ACM STOC'2011. ECCC TR10-170, arXiv:1011.3245.
2. M. A. Broome, A. Fedrizzi, S. Rahimi-Keshari, J. Dove, S. Aaronson, T. C. Ralph, and A. G. White. Photonic boson sampling in a tunable circuit. Science, (10.1126/science.1231440), 2012. arXiv:1212.2234.
3. K. P. Costello and V. H. Vu. Concentration of random determinants and permanent estimators. SIAM J. Discrete Math, 23(3).
4. A. Crespi, R. Osellame, R. Ramponi, D. J. Brod, E. F. Galv ao, N. Spagnolo, C. Vitelli, E. Maiorino, P. Mataloni, and F. Sciarrino. Experimental boson sampling in arbitrary integrated photonic circuits. Nature Photonics, 7:545-549, 2013. arXiv:1212.2783.
5. B. T. Gard, R. M. Cross, M. B. Kim, H. Lee, and J. P. Dowling. Classical computers very likely can not efficiently simulate multimode linear optical interferometers with arbitrary Fock-state inputs-an elementary argument. arXiv:1304.4206, 2013.
6. V. L. Girko. A refinement of the Central Limit Theorem for random determinants. Teor. Veroyatnost. i Primenen, 42:63-73, 1997. Translation in Theory Probab. Appl 42 (1998), 121-129.
7. C. Gogolin, M. Kliesch, L. Aolita, and J. Eisert. Boson-Sampling in the light of sample complexity. arXiv:1306.3995, 2013.
8. M. Jerrum, A. Sinclair, and E. Vigoda. A polynomial-time approximation algorithm for the permanent of a matrix with non-negative entries. J. ACM, 51(4):671-697, 2004. Earlier version in STOC'2001.
9. T. Jiang. How many entries of a typical orthogonal matrix can be approximated by independent normals? Ann. Probab., 34(4):1497-1529, 2006.
10. E. Knill. Fermionic linear optics and matchgates. quant-ph/0108033, 2001.
11. E. Knill, R. Laflamme, and G. J. Milburn. A scheme for efficient quantum computation with linear optics. Nature, 409:46-52, 2001. See also quant-ph/0006088.
12. N. Linial, A. Samorodnitsky, and A. Wigderson. A deterministic strongly polynomial algorithm for matrix scaling and approximate permanents. Combinatorica, 20(4):545-568, 2000.
13. R. Renner and S. Wolf. Smooth rényi entropy and applications. In Proc. IEEE International Symposium on Information Theory (ISIT), page 233, 2004.
14. J. B. Spring, B. J. Metcalf, P. C. Humphreys, W. S. Kolthammer, X.-M. Jin, M. Barbieri, A. Datta, N. Thomas-Peter, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley. Boson sampling on a photonic chip. Science, (10.1126/science.1231692), 2012. arXiv:1212.2622.
15. T. Tao. Determinantal processes, 2009. Blog post. http://terrytao.wordpress.com/2009/08/23/determinantal-processes/.
16. B. M. Terhal and D. P. DiVincenzo. Classical simulation of noninteracting-fermion quantum circuits. Phys. Rev. A, 65(032325), 2002. quant-ph/0108010.
17. M. Tillmann, B. Dakić, R. Heilmann, S. Nolte, A. Szameit, and P. Walther. Experimental boson sampling. Nature Photonics, 7:540-544, 2013. arXiv:1212.2240.
18. L. Trevisan, M. Tulsiani, and S. Vadhan. Regularity, boosting, and efficiently simulating every high-entropy distribution. In Proc. IEEE Conference on Computational Complexity, pages 126-136, 2009. ECCC TR08-103.
19. L. G. Valiant. Quantum circuits that can be simulated classically in polynomial time. SIAM J. Comput., 31(4):1229-1254, 2002. Earlier version in STOC'2001.