Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
144 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 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

Benchmarking digital quantum simulations above hundreds of qubits using quantum critical dynamics (2404.08053v2)

Published 11 Apr 2024 in quant-ph, cond-mat.stat-mech, and cond-mat.str-el

Abstract: The real-time simulation of large many-body quantum systems is a formidable task, that may only be achievable with a genuine quantum computational platform. Currently, quantum hardware with a number of qubits sufficient to make classical emulation challenging is available. This condition is necessary for the pursuit of a so-called quantum advantage, but it also makes verifying the results very difficult. In this manuscript, we flip the perspective and utilize known theoretical results about many-body quantum critical dynamics to benchmark quantum hardware and various error mitigation techniques on up to 133 qubits. In particular, we benchmark against known universal scaling laws in the Hamiltonian simulation of a time-dependent transverse field Ising Hamiltonian. Incorporating only basic error mitigation and suppression methods, our study shows reliable control up to a two-qubit gate depth of 28, featuring a maximum of 1396 two-qubit gates, before noise becomes prevalent. These results are transferable to applications such as Hamiltonian simulation, variational algorithms, optimization, or quantum machine learning. We demonstrate this on the example of digitized quantum annealing for optimization and identify an optimal working point in terms of both circuit depth and time step on a 133-site optimization problem.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (32)
  1. H. E. Stanley, Phase transitions and critical phenomena, Vol. 7 (Clarendon Press, Oxford, 1971).
  2. S. Sachdev, Quantum Phase Transitions, 2nd ed. (Cambridge University Press, 2011).
  3. R. P. Feynman, Simulating physics with computers, Int. J. Theor. Phys. 21, 467 (1982).
  4. I. M. Georgescu, S. Ashhab, and F. Nori, Quantum simulation, Rev. Mod. Phys. 86, 153 (2014).
  5. M. Lewenstein, A. Sanpera, and V. Ahufinger, Ultracold Atoms in Optical Lattices: Simulating quantum many-body systems (OUP Oxford, 2012).
  6. D. S. Abrams and S. Lloyd, Quantum algorithm providing exponential speed increase for finding eigenvalues and eigenvectors, Phys. Rev. Lett. 83, 5162 (1999).
  7. A. Miessen, P. J. Ollitrault, and I. Tavernelli, Quantum algorithms for quantum dynamics: A performance study on the spin-boson model, Phys. Rev. Res. 3, 043212 (2021).
  8. T. Albash and D. A. Lidar, Adiabatic quantum computation, Rev. Mod. Phys. 90, 015002 (2018a).
  9. T. Kadowaki and H. Nishimori, Quantum annealing in the transverse ising model, Phys. Rev. E 58, 5355 (1998).
  10. S. Knysh, Zero-temperature quantum annealing bottlenecks in the spin-glass phase, Nat. Commun. 7, 12370 (2016).
  11. W. H. Zurek, U. Dorner, and P. Zoller, Dynamics of a quantum phase transition, Phys. Rev. Lett. 95, 105701 (2005).
  12. T. W. Kibble, Some implications of a cosmological phase transition, Phys. Rep. 67, 183 (1980).
  13. W. H. Zurek, Cosmological experiments in superfluid helium?, Nature 317, 505 (1985).
  14. E. Magesan, J. M. Gambetta, and J. Emerson, Characterizing quantum gates via randomized benchmarking, Phys. Rev. A 85, 042311 (2012).
  15. V. Zhang and P. D. Nation, Characterizing quantum processors using discrete time crystals, arXiv  (2023), arXiv:2301.07625 [quant-ph] .
  16. T. Albash and D. A. Lidar, Demonstration of a scaling advantage for a quantum annealer over simulated annealing, Phys. Rev. X 8, 031016 (2018b).
  17. E. Farhi, J. Goldstone, and S. Gutmann, A quantum approximate optimization algorithm, arXiv  (2014), arXiv:1411.4028 [quant-ph] .
  18. E. Farhi, D. Gamarnik, and S. Gutmann, The quantum approximate optimization algorithm needs to see the whole graph: A typical case, arXiv  (2020), arXiv:2004.09002 [quant-ph] .
  19. S. Morita and H. Nishimori, Mathematical foundation of quantum annealing, J. Math. Phys. 49, 125210 (2008).
  20. T. Caneva, R. Fazio, and G. E. Santoro, Adiabatic quantum dynamics of the lipkin-meshkov-glick model, Phys. Rev. B 78, 104426 (2008).
  21. A. Rajput, A. Roggero, and N. Wiebe, Hybridized methods for quantum simulation in the interaction picture, Quantum 6, 780 (2022).
  22. M. Motta and J. E. Rice, Emerging quantum computing algorithms for quantum chemistry, WIREs Comput Mol Sci. 12, e1580 (2022).
  23. Qiskit contributors, Qiskit: An open-source framework for quantum computing (2023).
  24. IBM Quantum, https://quantum-computing.ibm.com/ (2021).
  25. C. Rigetti and M. Devoret, Fully microwave-tunable universal gates in superconducting qubits with linear couplings and fixed transition frequencies, Phys. Rev. B 81, 134507 (2010).
  26. E. van den Berg, Z. K. Minev, and K. Temme, Model-free readout-error mitigation for quantum expectation values, Phys. Rev. A 105, 032620 (2022).
  27. N. Earnest, C. Tornow, and D. J. Egger, Pulse-efficient circuit transpilation for quantum applications on cross-resonance-based hardware, Phys. Rev. Res. 3, 043088 (2021).
  28. S. H. Sack and D. J. Egger, Large-scale quantum approximate optimization on nonplanar graphs with machine learning noise mitigation, Phys. Rev. Res. 6, 013223 (2024).
  29. S. H. Sack and M. Serbyn, Quantum annealing initialization of the quantum approximate optimization algorithm, Quantum 5, 491 (2021).
  30. IBM ILOG CPLEX Optimizer.
  31. ibm_auckland is one of IBM’s by now retired 27-qubit Falcon chips.
  32. G. Mazzola, Quantum computing for chemistry and physics applications from a monte carlo perspective, J. Chem. Phys. 160, 010901 (2024).
Citations (5)
View on Semantic Scholar

Summary

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

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