Two-Particle Scattering on Non-Translation Invariant Line Lattices

Luna Lima e Silva; Daniel Jost Brod

doi:10.22331/q-2024-04-04-1308

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

Published:	2024-04-04, volume 8, page 1308
Eprint:	arXiv:2303.04342v2
Doi:	https://doi.org/10.22331/q-2024-04-04-1308
Citation:	Quantum 8, 1308 (2024).

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.

Abstract

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.

► BibTeX data

@article{Silva2024twoparticle,
  doi = {10.22331/q-2024-04-04-1308},
  url = {https://doi.org/10.22331/q-2024-04-04-1308},
  title = {Two-{P}article {S}cattering on {N}on-{T}ranslation {I}nvariant {L}ine {L}attices},
  author = {Silva, Luna Lima e and Brod, Daniel Jost},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {8},
  pages = {1308},
  month = apr,
  year = {2024}
}

► References

[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.
https://doi.org/10.1145/380752.380757

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

[3] A. Childs, E. Farhi, and S. Gutmann, Quantum Information Processing 1, 35 (2002).
https://doi.org/10.1023/A:1019609420309

[4] E. Farhi and S. Gutmann, Phys. Rev. A 58, 915 (1998).
https://doi.org/10.1103/PhysRevA.58.915

[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.
https://doi.org/10.1145/780542.780552

[6] A. M. Childs, Phys. Rev. Lett. 102, 180501 (2009).
https://doi.org/10.1103/PhysRevLett.102.180501

[7] A. M. Childs, D. Gosset, and Z. Webb, Science 339, 791 (2013).
https://doi.org/10.1126/science.1229957

[8] M. Valiente and D. Petrosyan, J. Phys. B: At. Mol. Opt. Phys. 41, 161002 (2008).
https://doi.org/10.1088/0953-4075/41/16/161002

[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).
https://doi.org/10.1063/1.4757665

[11] M. Varbanov and T. A. Brun, Phys. Rev. A 80, 052330 (2009).
https://doi.org/10.1103/PhysRevA.80.052330

[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).
arXiv:1608.04820

[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).
https://doi.org/10.1561/0100000006

[15] D. J. Brod and J. Combes, Phys. Rev. Lett. 117, 080502 (2016).
https://doi.org/10.1103/PhysRevLett.117.080502

[16] A. Childs, D. Gosset, D. Nagaj, M. Raha, and Z. Webb, Quantum Information and Computation 15 (2014), 10.26421/QIC15.7-8-5.
https://doi.org/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.
https://doi.org/10.1145/1993636.1993682

[18] D. J. Brod, J. Combes, and J. Gea-Banacloche, Phys. Rev. A 94, 023833 (2016).
https://doi.org/10.1103/PhysRevA.94.023833

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

Cited by

[1] Hao-Yu Guan, Yifei Li, and Xiu-Hao Deng, "Photon-number conserved universal quantum logic employing continuous-time quantum walk on dual-rail qubit arrays", npj Quantum Information 12 1, 17 (2026).

[2] Luna Lima Keller and Daniel Jost Brod, "Two-particle scattering on general graphs", Quantum 10, 2038 (2026).

[3] Ivan M. Burbano and Christian W. Bauer, "Gauge loop-string-hadron formulation on general graphs and applications to fully gauge fixed Hamiltonian lattice gauge theory", Journal of High Energy Physics 2025 12, 60 (2025).

The above citations are from Crossref's cited-by service (last updated successfully 2026-08-10 13:25:51) and SAO/NASA ADS (last updated successfully 2026-08-10 13:25:52). The list may be incomplete as not all publishers provide suitable and complete citation data.

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.