Two-Particle Scattering on Non-Translation Invariant Line Lattices

Luna Lima e Silva and Daniel Jost Brod

Instituto de Física, Universidade Federal Fluminense, Niterói, RJ, 24210-340, Brazil

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Quantum walks have been used to develop quantum algorithms since their inception, and can be seen as an alternative to the usual circuit model; combining single-particle quantum walks on sparse graphs with two-particle scattering on a line lattice is sufficient to perform universal quantum computation. In this work we solve the problem of two-particle scattering on the line lattice for a family of interactions without translation invariance, recovering the Bose-Hubbard interaction as the limiting case. Due to its generality, our systematic approach lays the groundwork to solve the more general problem of multi-particle scattering on general graphs, which in turn can enable design of different or simpler quantum gates and gadgets. As a consequence of this work, we show that a CPHASE gate can be achieved with high fidelity when the interaction acts only on a small portion of the line graph.

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[1] A. Ambainis, E. Bach, A. Nayak, A. Vishwanath, and J. Watrous, in Proceedings of the Thirty-Third Annual ACM Symposium on Theory of Computing, STOC '01 (ACM, New York, 2001) pp. 37–49.

[2] A. Nayak and A. Vishwanath, arXiv:quant-ph/​0010117 (2000).

[3] A. Childs, E. Farhi, and S. Gutmann, Quantum Information Processing 1, 35 (2002).

[4] E. Farhi and S. Gutmann, Phys. Rev. A 58, 915 (1998).

[5] A. M. Childs, R. Cleve, E. Deotto, E. Farhi, S. Gutmann, and D. A. Spielman, in Proceedings of the Thirty-Fifth Annual ACM Symposium on Theory of Computing, STOC '03 (ACM, New York, 2003) pp. 59–68.

[6] A. M. Childs, Phys. Rev. Lett. 102, 180501 (2009).

[7] A. M. Childs, D. Gosset, and Z. Webb, Science 339, 791 (2013).

[8] M. Valiente and D. Petrosyan, J. Phys. B: At. Mol. Opt. Phys. 41, 161002 (2008).

[9] J. J. Sakurai, Modern quantum mechanics (Addison-Wesley, Reading, MA, 1994).

[10] A. M. Childs and D. Gosset, Journal of Mathematical Physics 53, 102207 (2012).

[11] M. Varbanov and T. A. Brun, Phys. Rev. A 80, 052330 (2009).

[12] S. Weinberg, The Quantum Theory of Fields, Volume I Foundations (Cambridge University Press, 1995).

[13] Z. Zhu and M. B. Wakin, arXiv:1608.04820 [cs.IT] (2016).

[14] R. M. Gray, Toeplitz and Circulant Matrices: A review (Foundations and Trends in Communications and Information Theory, Vol 2, Issue 3, pp 155-239, 2006).

[15] D. J. Brod and J. Combes, Phys. Rev. Lett. 117, 080502 (2016).

[16] A. Childs, D. Gosset, D. Nagaj, M. Raha, and Z. Webb, Quantum Information and Computation 15 (2014), 10.26421/​QIC15.7-8-5.

[17] S. Aaronson and A. Arkhipov, in Proceedings of the Forty-Third Annual ACM Symposium on Theory of Computing, STOC '11 (Association for Computing Machinery, New York, NY, USA, 2011) pp. 333–342.

[18] D. J. Brod, J. Combes, and J. Gea-Banacloche, Phys. Rev. A 94, 023833 (2016).

[19] P. F. Byrd and M. D. Friedman, Handbook of Elliptic Integrals for Engineers and Scientists (Springer Berlin, Heidelberg, 1971).

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