Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
167 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
42 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

Hardware-efficient ansatz without barren plateaus in any depth (2403.04844v1)

Published 7 Mar 2024 in quant-ph and cond-mat.stat-mech

Abstract: Variational quantum circuits have recently gained much interest due to their relevance in real-world applications, such as combinatorial optimizations, quantum simulations, and modeling a probability distribution. Despite their huge potential, the practical usefulness of those circuits beyond tens of qubits is largely questioned. One of the major problems is the so-called barren plateaus phenomenon. Quantum circuits with a random structure often have a flat cost-function landscape and thus cannot be trained efficiently. In this paper, we propose two novel parameter conditions in which the hardware-efficient ansatz (HEA) is free from barren plateaus for arbitrary circuit depths. In the first condition, the HEA approximates to a time-evolution operator generated by a local Hamiltonian. Utilizing a recent result by [Park and Killoran, Quantum 8, 1239 (2024)], we prove a constant lower bound of gradient magnitudes in any depth both for local and global observables. On the other hand, the HEA is within the many-body localized (MBL) phase in the second parameter condition. We argue that the HEA in this phase has a large gradient component for a local observable using a phenomenological model for the MBL system. By initializing the parameters of the HEA using these conditions, we show that our findings offer better overall performance in solving many-body Hamiltonians. Our results indicate that barren plateaus are not an issue when initial parameters are smartly chosen, and other factors, such as local minima or the expressivity of the circuit, are more crucial.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (34)
  1. A. Krizhevsky, I. Sutskever, and G. E. Hinton, Imagenet classification with deep convolutional neural networks, Communications of the ACM 60, 84 (2017).
  2. M. Schuld, I. Sinayskiy, and F. Petruccione, An introduction to quantum machine learning, Contemporary Physics 56, 172 (2015).
  3. E. C. Martín, K. Plekhanov, and M. Lubasch, Barren plateaus in quantum tensor network optimization, Quantum 7, 974 (2023).
  4. T. Barthel and Q. Miao, Absence of barren plateaus and scaling of gradients in the energy optimization of isometric tensor network states, arXiv preprint arXiv:2304.00161  (2023).
  5. H.-K. Zhang, S. Liu, and S.-X. Zhang, Absence of barren plateaus in finite local-depth circuits with long-range entanglement, arXiv preprint arXiv:2311.01393  (2023).
  6. R. D. East, G. Alonso-Linaje, and C.-Y. Park, All you need is spin: Su (2) equivariant variational quantum circuits based on spin networks, arXiv preprint arXiv:2309.07250  (2023).
  7. X. Glorot and Y. Bengio, Understanding the difficulty of training deep feedforward neural networks, in Proceedings of the thirteenth international conference on artificial intelligence and statistics (JMLR Workshop and Conference Proceedings, 2010) pp. 249–256.
  8. C.-Y. Park and N. Killoran, Hamiltonian variational ansatz without barren plateaus, Quantum 8, 1239 (2024).
  9. J. Preskill, Quantum computing in the NISQ era and beyond, Quantum 2, 79 (2018).
  10. K. Fujii, Quantum Computation with Topological Codes: from qubit to topological fault-tolerance, Vol. 8 (Springer, 2015).
  11. D. A. Huse, R. Nandkishore, and V. Oganesyan, Phenomenology of fully many-body-localized systems, Phys. Rev. B 90, 174202 (2014).
  12. J. I. Cirac and P. Zoller, Quantum computations with cold trapped ions, Phys. Rev. Lett. 74, 4091 (1995).
  13. The IBM Quantum heavy hex lattice, https://research.ibm.com/blog/heavy-hex-lattice.
  14. L. F. Wessels and E. Barnard, Avoiding false local minima by proper initialization of connections, IEEE transactions on neural networks 3, 899 (1992).
  15. M. Serbyn, Z. Papić, and D. A. Abanin, Quantum quenches in the many-body localized phase, Phys. Rev. B 90, 174302 (2014).
  16. T. B. Wahl, A. Pal, and S. H. Simon, Signatures of the many-body localized regime in two dimensions, Nat. Phys. 15, 164 (2019).
  17. D. Wecker, M. B. Hastings, and M. Troyer, Progress towards practical quantum variational algorithms, Phys. Rev. A 92, 042303 (2015).
  18. C.-Y. Park, Efficient ground state preparation in variational quantum eigensolver with symmetry breaking layers, APL Quantum 1, 016101 (2024).
  19. C. O. Marrero, M. Kieferová, and N. Wiebe, Entanglement-induced barren plateaus, PRX Quantum 2, 040316 (2021).
  20. J. H. Bardarson, F. Pollmann, and J. E. Moore, Unbounded growth of entanglement in models of many-body localization, Phys. Rev. Lett. 109, 017202 (2012).
  21. X. Shi and Y. Shang, Avoiding barren plateaus via gaussian mixture model, arXiv preprint arXiv:2402.13501  (2024).
  22. S. Bravyi, D. Gosset, and R. Movassagh, Classical algorithms for quantum mean values, Nat. Phys. 17, 337 (2021).
  23. N. J. Coble and M. Coudron, Quasi-polynomial time approximation of output probabilities of geometrically-local, shallow quantum circuits, in 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS) (IEEE, 2022) pp. 598–609.
  24. T. Kuwahara, T. Mori, and K. Saito, Floquet–Magnus theory and generic transient dynamics in periodically driven many-body quantum systems, Annals of Physics 367, 96 (2016).
  25. J. Eisert, M. Friesdorf, and C. Gogolin, Quantum many-body systems out of equilibrium, Nat. Phys. 11, 124 (2015).
  26. R. Nandkishore and D. A. Huse, Many-body localization and thermalization in quantum statistical mechanics, Annu. Rev. Condens. Matter Phys. 6, 15 (2015).
  27. B. L. Altshuler, A. G. Aronov, and P. Lee, Interaction effects in disordered fermi systems in two dimensions, Phys. Rev. Lett. 44, 1288 (1980).
  28. F. Alet and N. Laflorencie, Many-body localization: An introduction and selected topics, Comptes Rendus Physique 19, 498 (2018).
  29. M. Žnidarič, T. Prosen, and P. Prelovšek, Many-body localization in the Heisenberg XXZ magnet in a random field, Phys. Rev. B 77, 064426 (2008).
  30. I. H. Kim, A. Chandran, and D. A. Abanin, Local integrals of motion and the logarithmic lightcone in many-body localized systems, arXiv preprint arXiv:1412.3073  (2014).
  31. L. Zhang, V. Khemani, and D. A. Huse, A floquet model for the many-body localization transition, Phys. Rev. B 94, 224202 (2016).
  32. J. A. Kjäll, J. H. Bardarson, and F. Pollmann, Many-body localization in a disordered quantum ising chain, Phys. Rev. Lett. 113, 107204 (2014).
  33. T. Cubitt and A. Montanaro, Complexity classification of local hamiltonian problems, SIAM Journal on Computing 45, 268 (2016).
  34. M. Schuld and F. Petruccione, Supervised learning with quantum computers, Vol. 17 (Springer, 2018).
Citations (12)
View on Semantic Scholar

Summary

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

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