Bootstrapping the Future: From Resource Estimation to Quantum Advantage

By Eric Arnold on

August 20, 2025

Use quantum instruction set architectures to translate high-level code into a logical representation.

Transform the logical representation into a low-level physical representation.

Estimate runtime under specific parameters such as the number of T gates and corresponding T factories (a bottleneck in quantum architecture), and the number of logical qubits and corresponding physical qubits.

These parameters describe the circuit in terms of its depth (gates/factories) and width (qubits), as in circuit complexity theory, with the added abstraction of logical to physical qubits to account for the cost of error correction. These estimates can provide stakeholders with a better understanding of how quantum computing will actually perform by 2030 and beyond.

Limitations

While RE is certainly useful, the methodology currently has two aspects that limit its generalizability and predictive power:

Specificity of Results

Estimates are technology and context dependent. Because tools rely on intermediate representations and instruction sets, their results pertain to the capabilities of specific physical modalities that are in constant flux. Estimates are also influenced by error budget parameters (specific to application). Exploring the impact of these parameters in a quantum chemistry simulation on a hypothetical fault-tolerant device, Quetschlich et al. varied operation speed (time regime), error rate, and factory number to obtain physical qubit estimates ranging from 6.04 million (non-Majorana) to 1.30 million (Majorana). Furthermore, varying the number of factories reduced physical qubit requirement to 1.08 million (Majorana), though with a significant increase in runtime.

Ancillary Code Limitations

Resource estimates may misrepresent true requirements for the following reasons:

A source of computational overhead that may inflate the resource estimate is the error correction method. Current RE tools rely on surface code for correcting errors resulting from environmental noise and qubit decoherence. As surface code is potentially less efficient than other methods, estimates incorporating this form of error correction may be significantly higher than necessary.
Initial state preparation is a computation necessary prior to simulating phenomena in a field such as quantum chemistry. The initial state and iterative optimizations incur computational cost that may significantly inflate estimates on near-term systems or may not be adequately included in fault-tolerant ones. Despite the efficiency of the actual simulation algorithms, preparing the initial state might incur so much overhead that quantum advantage could evaporate, particularly if the state is initialized on a hybrid classical-quantum system. In this vein, research skeptical of quantum advantage in chemistry has experimentally demonstrated that the states prepared by the variational quantum eigensolver, an algorithm for near-term systems, does not exhibit the time complexity necessary to achieve quantum advantage in that application. Further, the authors go on to argue that a reliance on state preparation in even advanced algorithms for fault-tolerant machines, such as phase estimation, will similarly dilute quantum advantage. Resource estimates such as those by Quetschlich et al., derived through qubitization and phase estimation, may not fully account for the computational cost of initial state preparation into their estimate. Together, surface code and initial state preparation dramatically affect current resource estimates.

Conclusion

It is important to note that the absence of evidence for quantum advantage in one area does not diminish its likelihood elsewhere, such as in finance, and that such advantage can only be demonstrated or disproven on a case-by-case basis. Additionally, more efficient error correction and initial state preparation methods could be developed as quantum computing scales, causing physical estimates to decrease significantly. Nevertheless, RE is useful for estimating algorithm performance on near-term systems and for setting the upper-bound for fault-tolerant system requirements (if costs such as initial state preparation are included). Researchers can use RE to compare algorithm performance within the limitations of ancillary code to develop better algorithms for future systems, and for stakeholders, it represents the best estimate of what will be possible under the future paradigm.

Works Cited

Bharti, K., Cervera-Lierta, A., Kyaw, T. H., Haug, T., Alperin-Lea, S., Anand, A., Degroote, M., Heimonen, H., Kottmann, J. S., Menke, T., Mok, W.-K., Sim, S., Kwek, L. C., & Aspuru-Guzik, A. (2021). Noisy intermediate-scale quantum (NISQ) algorithms. arXiv preprint arXiv:2101.08448. https://arxiv.org/abs/2101.08448

Chen, Z., Lu, Y., Wang, H., Liu, Y., & Li, T. (2025). Quantum Langevin dynamics for optimization. arXiv preprint arXiv:2311.15587. https://arxiv.org/abs/2311.15587

Elmegreen, B. G., Welser-Sherrill, L., Muller, A., Murayama, K., & Ziegelmayer, R. (2025). Integration of quantum accelerators into HPC: Toward a unified quantum platform. 2025 IEEE International Conference on Quantum Computing and Engineering (QCE), 1-10. https://www.computer.org/csdl/proceedings-article/qce/2024/413701a774/23oq5CvRekE

Google Quantum AI. (2024). Qualtran: Python library for expressing and analyzing fault tolerant quantum algorithms [Software]. GitHub. https://github.com/quantumlib/Qualtran

Han, J. Y., Cheng, B., Vu, D.-L., & Rebentrost, P. (2025). Quantum advantage for multi-option portfolio pricing and valuation adjustments. arXiv preprint arXiv:2203.04924. https://arxiv.org/abs/2203.04924

Harrigan, M. P., Khattar, T., Yuan, C., Peduri, A., Yosri, N., Malone, F. D., Babbush, R., & Rubin, N. C. (2024). Expressing and analyzing quantum algorithms with Qualtran. arXiv preprint arXiv:2409.04643. https://arxiv.org/abs/2409.04643

IBM Quantum. (2023). Charting the course to 100,000 qubits. IBM Quantum Computing Blog. https://www.ibm.com/quantum/blog/100k-qubit-supercomputer

ISI USC. (2024). pyLIQTR: Lincoln Laboratory Quantum Algorithm Test and Research [Software]. GitHub. https://github.com/isi-usc-edu/pyLIQTR

Kockum, A. F., Arvidsson-Shukur, D., Campbell, E., Cerezo, M., Cincio, L., Coles, P. J., & García-Pérez, G. (2025). Lecture notes on quantum computing. arXiv preprint arXiv:2311.08445. https://arxiv.org/abs/2311.08445

Lee, S., Lee, J., Zhai, H., Tong, Y., Dalzell, A. M., Kumar, A., Helms, P., Gray, J., Cui, Z.-H., Liu, W., Kastoryano, M., Babbush, R., Preskill, J., Reichman, D. R., Campbell, E. T., Valeev, E. F., Lin, L., & Chan, G. K.-L. (2023). Evaluating the evidence for exponential quantum advantage in ground-state quantum chemistry. Nature Communications, 14(1). https://doi.org/10.1038/s41467-023-37587-6

Lin, L., & Tong, Y. (2022). Heisenberg-limited ground state energy estimation for early fault-tolerant quantum computers. arXiv preprint arXiv:2102.11340. https://arxiv.org/abs/2102.11340

London, C., Brown, D., Xu, W., Vatansever, S., Langmead, C. J., Kartsaklis, D., Clark, S., & Meichanetzidis, K. (2023). Peptide binding classification on quantum computers. arXiv preprint arXiv:2311.15696. https://arxiv.org/abs/2311.15696

Low, G. H., & Chuang, I. L. (2019). Hamiltonian simulation by qubitization. Quantum, 3, 163. https://doi.org/10.22331/q-2019-07-12-163

McKinsey Digital. (2025). The year of quantum: From concept to reality in 2025. McKinsey & Company. https://www.mckinsey.com/capabilities/mckinsey-digital/our-insights/the-year-of-quantum-from-concept-to-reality-in-2025

Microsoft Azure Quantum. (2024). Azure Quantum Resource Estimation. Microsoft Corporation. https://quantum.microsoft.com/en-us/insights/education/concepts/resource-estimation

Peruzzo, A., McClean, J., Shadbolt, P., Yung, M.-H., Zhou, X.-Q., Love, P. J., Aspuru-Guzik, A., & O'Brien, J. L. (2014). A variational eigenvalue solver on a photonic quantum processor. Nature Communications, 5(1). https://doi.org/10.1038/ncomms5213

Quetschlich, N., Soeken, M., Murali, P., & Wille, R. (2025). Utilizing resource estimation for the development of quantum computing applications. 2025 IEEE International Conference on Quantum Computing and Engineering (QCE), 1-8. https://www.computer.org/csdl/proceedings-article/qce/2024/413701a232/23oq1tykVRC

Scholten, T. L., Williams, C. J., Moody, D., Mosca, M., Hurley, W., Zeng, W. J., Troyer, M., & Gambetta, J. M. (2024). Assessing the benefits and risks of quantum computers. arXiv preprint arXiv:2401.16317. https://arxiv.org/abs/2401.16317

Stamatopoulos, N., Egger, D. J., Sun, Y., Zoufal, C., Iten, R., Shen, N., & Woerner, S. (2020). Option pricing using quantum computers. Quantum, 4, 291. https://doi.org/10.22331/q-2020-07-06-291

van Dam, W., Mykhailova, M., & Soeken, M. (2024). Using Azure Quantum Resource Estimator for assessing performance of fault tolerant quantum computation. arXiv preprint arXiv:2311.05801. https://arxiv.org/abs/2311.05801

Whitfield, J. D., Zimborás, Z., Aspuru-Guzik, A., Berry, D., & Kivlichan, I. D. (2022). Quantum computing 2022. arXiv preprint arXiv:2201.09877. https://arxiv.org/abs/2201.09877

Yeter-Aydeniz, K., Siopsis, G., & Pooser, R. C. (2021). Scattering in the Ising model with the quantum Lanczos algorithm. New Journal of Physics, 23(4), 043033. https://doi.org/10.1088/1367-2630/abe63d

Zapata Computing. (2024). BenchQ: Resource estimation for fault-tolerant quantum computation [Software]. GitHub. https://github.com/zapatacomputing/benchq

Disclaimer: The author is completely responsible for the content of this article. The opinions expressed are their own and do not represent IEEE's position nor that of the Computer Society nor its Leadership.