On proving the robustness of algorithms for early fault-tolerant quantum computers

Rutuja Kshirsagar; Amara Katabarwa; Peter D. Johnson

doi:10.22331/q-2024-11-20-1531

On proving the robustness of algorithms for early fault-tolerant quantum computers

Rutuja Kshirsagar, Amara Katabarwa, and Peter D. Johnson

Zapata Computing Inc., 100 Federal Street, Boston, MA 02110, USA

Published:	2024-11-20, volume 8, page 1531
Eprint:	arXiv:2209.11322v3
Doi:	https://doi.org/10.22331/q-2024-11-20-1531
Citation:	Quantum 8, 1531 (2024).

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Updated after initial publication: This publication was updated to version v3 after the initial publication. The authors left the following comment on the arXiv:

27 pages, 3 figures, 1 table, 1 algorithm. Submitted to QIP 2023, APS March Meetings 2023, Quantum

Abstract

The hope of the quantum computing field is that quantum architectures are able to scale up and realize fault-tolerant quantum computing. Due to engineering challenges, such ``cheap'' error correction may be decades away. In the meantime, we anticipate an era of ``costly'' error correction, or {early fault-tolerant quantum computing}. Costly error correction might warrant settling for error-prone quantum computations. This motivates the development of quantum algorithms which are robust to some degree of error as well as methods to analyze their performance in the presence of error. Several such algorithms have recently been developed; what is missing is a methodology to analyze their robustness. To this end, we introduce a randomized algorithm for the task of phase estimation and give an analysis of its performance under two simple noise models. In both cases the analysis leads to a noise threshold, below which arbitrarily high accuracy can be achieved by increasing the number of samples used in the algorithm. As an application of this general analysis, we compute the maximum ratio of the largest circuit depth and the dephasing scale such that performance guarantees hold. We calculate that the randomized algorithm can succeed with arbitrarily high probability as long as the required circuit depth is less than $0.916$ times the dephasing scale.

Featured image: This figure depicts a successful instance of the randomized Fourier estimation algorithm in the frequency domain. The green dots represent the estimated values of the time signal in the Fourier spectrum. The blue dots and blue curves denote the ideal values and continuous functions that define them, respectively.

Popular summary

Near future quantum computers hold promise for useful applications even before idealized, fully error-corrected quantum systems are achieved. However, these early devices will be limited in their error-reduction capabilities, meaning they cannot completely eliminate noise. To make the best use of these machines, researchers will need algorithms that are inherently robust to some level of error. This demands new methodologies for designing noise-resilient quantum algorithms and analyzing their robustness under realistic conditions. This work provides insights and tools for evaluating these algorithms' performance in the presence of noise, helping to unlock the potential of early fault-tolerant quantum devices.

► BibTeX data

@article{Kshirsagar2024provingrobustnessof,
  doi = {10.22331/q-2024-11-20-1531},
  url = {https://doi.org/10.22331/q-2024-11-20-1531},
  title = {On proving the robustness of algorithms for early fault-tolerant quantum computers},
  author = {Kshirsagar, Rutuja and Katabarwa, Amara and Johnson, Peter D.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {8},
  pages = {1531},
  month = nov,
  year = {2024}
}

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