Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
156 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
45 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Solving optimization problems with local light shift encoding on Rydberg quantum annealers (2308.07798v2)

Published 15 Aug 2023 in quant-ph, cond-mat.dis-nn, cond-mat.quant-gas, cs.CC, and physics.atom-ph

Abstract: We provide a non-unit disk framework to solve combinatorial optimization problems such as Maximum Cut (Max-Cut) and Maximum Independent Set (MIS) on a Rydberg quantum annealer. Our setup consists of a many-body interacting Rydberg system where locally controllable light shifts are applied to individual qubits in order to map the graph problem onto the Ising spin model. Exploiting the flexibility that optical tweezers offer in terms of spatial arrangement, our numerical simulations implement the local-detuning protocol while globally driving the Rydberg annealer to the desired many-body ground state, which is also the solution to the optimization problem. Using optimal control methods, these solutions are obtained for prototype graphs with varying sizes at time scales well within the system lifetime and with approximation ratios close to one. The non-blockade approach facilitates the encoding of graph problems with specific topologies that can be realized in two-dimensional Rydberg configurations and is applicable to both unweighted as well as weighted graphs. A comparative analysis with fast simulated annealing is provided which highlights the advantages of our scheme in terms of system size, hardness of the graph, and the number of iterations required to converge to the solution.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (47)
  1. P. W. Shor, Fault-tolerant quantum computation (IEEE, 1996) pp. 56–65.
  2. D. Aharonov and M. Ben-Or, Fault-tolerant quantum computation with constant error, in Proceedings of the twenty-ninth annual ACM symposium on Theory of computing (1997) pp. 176–188.
  3. J. Preskill, Fault-tolerant quantum computation, in Introduction to quantum computation and information (World Scientific, 1998) pp. 213–269.
  4. D. Gottesman, Theory of fault-tolerant quantum computation, Phys. Rev. A 57, 127 (1998).
  5. F. Bova, A. Goldfarb, and R. G. Melko, Commercial applications of quantum computing, EPJ Quant. Techn. 8, 2 (2021).
  6. J. Preskill, Quantum computing in the nisq era and beyond, Quantum 2, 79 (2018).
  7. S. Aaronson, Bqp and the polynomial hierarchy, in Proceedings of the forty-second ACM symposium on Theory of computing (2010) pp. 141–150.
  8. R. M. Karp, On the computational complexity of combinatorial problems (Wiley Online Library, 1975) pp. 45–68.
  9. D. S. Hochbaum and A. Pathria, Analysis of the greedy approach in problems of maximum k-coverage, Naval Research Logistics (NRL) 45, 615 (1998).
  10. S. Butenko, Maximum independent set and related problems, with applications, Ph.D. thesis (2003).
  11. C. Scheideler, A. Richa, and P. Santi, An o (log n) dominating set protocol for wireless ad-hoc networks under the physical interference model, in Proceedings of the 9th ACM international symposium on Mobile ad hoc networking and computing (2008) pp. 91–100.
  12. M. H. Devoret, A. Wallraff, and J. M. Martinis, Superconducting qubits: A short review, arXiv:2004cond.mat.11174D  (2004).
  13. A. Browaeys and T. Lahaye, Many-body physics with individually controlled rydberg atoms, Nat. Phys. 16, 132 (2020).
  14. T. F. Gallagher, Rydberg atoms, Rep. Progr. Phys. 51, 143 (1988).
  15. C. Gross and I. Bloch, Quantum simulations with ultracold atoms in optical lattices, Science 357, 995 (2017).
  16. E. Farhi, J. Goldstone, and S. Gutmann, A quantum approximate optimization algorithm, arXiv:1411.4028  (2014).
  17. L. Bittel and M. Kliesch, Training variational quantum algorithms is np-hard, Phys. Rev. Lett. 127, 120502 (2021).
  18. L. Bittel, S. Gharibian, and M. Kliesch, Optimizing the depth of variational quantum algorithms is strongly qcma-hard to approximate, arXiv:2211.12519  (2022).
  19. F. Glover, G. Kochenberger, and Y. Du, A tutorial on formulating and using qubo models, arXiv:1811.11538  (2018).
  20. A. Lucas, Ising formulations of many np problems, Front. Phys. 2, 5 (2014).
  21. X. Qiu, P. Zoller, and X. Li, Programmable quantum annealing architectures with ising quantum wires, Phys. Rev. X Quantum 1, 020311 (2020).
  22. W. Lechner, P. Hauke, and P. Zoller, A quantum annealing architecture with all-to-all connectivity from local interactions, Science advances 1, e1500838 (2015).
  23. B. N. Clark, C. J. Colbourn, and D. S. Johnson, Unit disk graphs, Discr. Math. 86, 165 (1990).
  24. H. Szu and R. Hartley, Fast simulated annealing, Phys. Lett. A 122, 157 (1987).
  25. A. M. Kaufman and K.-K. Ni, Quantum science with optical tweezer arrays of ultracold atoms and molecules, Nat. Phys. 17, 1324 (2021).
  26. T. Caneva, T. Calarco, and S. Montangero, Chopped random-basis quantum optimization, Phys. Rev. A 84, 022326 (2011).
  27. C. Ferrie and O. Moussa, Robust and efficient in situ quantum control, Phys. Rev. A 91, 052306 (2015).
  28. R. Mukherjee, H. Xie, and F. Mintert, Bayesian optimal control of greenberger-horne-zeilinger states in rydberg lattices, Phys. Rev. Lett. 125, 203603 (2020b).
  29. M. X. Goemans and D. P. Williamson, . 879-approximation algorithms for max cut and max 2sat, in Proceedings of the twenty-sixth annual ACM symposium on Theory of computing (1994) pp. 422–431.
  30. V. V. Vazirani, Approximation algorithms (Springer, 2001) pp. 2–5.
  31. B. Mohar and S. Poljak, Eigenvalues and the max-cut problem, Czech. Math. J. 40, 343 (1990).
  32. M. Saffman, T. G. Walker, and K. Mølmer, Quantum information with rydberg atoms, Rev. Mod. Phys. 82, 2313 (2010).
  33. F. Sauvage and F. Mintert, Optimal quantum control with poor statistics, Phys. Rev. X Quantum 1, 020322 (2020).
  34. E. Boros and P. L. Hammer, Pseudo-boolean optimization, Disc. Appl. Math. 123, 155 (2002).
  35. J. R. Johansson, P. D. Nation, and F. Nori, Qutip: An open-source python framework for the dynamics of open quantum systems, Comput. Phys. Commun. 183, 1760 (2012).
  36. F. L. Lewis, D. Vrabie, and V. L. Syrmos, Optimal control (John Wiley & Sons, 2012).
  37. J. Werschnik and E. Gross, Quantum optimal control theory, J. Phys. B 40, R175 (2007).
  38. C. Winterfeldt, C. Spielmann, and G. Gerber, Colloquium: Optimal control of high-harmonic generation, Rev. Mod. Phys. 80, 117 (2008).
  39. E. Polak, Optimization: algorithms and consistent approximations, Vol. 124 (Springer Science & Business Media, 2012).
  40. A. R. Conn, K. Scheinberg, and L. N. Vicente, Introduction to derivative-free optimization (SIAM, 2009).
  41. W. Hare, J. Nutini, and S. Tesfamariam, A survey of non-gradient optimization methods in structural engineering, Adv. Engineer. Software 59, 19 (2013).
  42. C. G. Broyden, The convergence of a class of double-rank minimization algorithms 1. general considerations, IMA J. Appl. Math. 6, 76 (1970).
  43. R. Fletcher, A new approach to variable metric algorithms, The Comp. J. 13, 317 (1970).
  44. D. Goldfarb, A family of variable metric updates derived by variational means, v. 24, Math. Comp.  (1970).
  45. D. F. Shanno, Conditioning of quasi-newton methods for function minimization, Math. Comp. 24, 647 (1970).
  46. J. A. Nelder and R. Mead, A simplex method for function minimization, The Comp. J. 7, 308 (1965).
  47. D. Bertsimas and J. Tsitsiklis, Simulated annealing, Stat. Science 8, 10 (1993).
Citations (9)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now