Averaging gate approximation error and performance of Unitary Coupled Cluster ansatz in Pre-FTQC Era

Kohdai Kuroiwa; Yuya O. Nakagawa

doi:10.22331/q-2025-07-21-1800

Averaging gate approximation error and performance of Unitary Coupled Cluster ansatz in Pre-FTQC Era

Kohdai Kuroiwa^1,2,3,4 and Yuya O. Nakagawa⁴

¹Institute for Quantum Computing, University of Waterloo, Ontario, Canada, N2L 3G1
²Department of Combinatorics and Optimization, University of Waterloo
³Perimeter Institute for Theoretical Physics, Ontario, Canada, N2L 2Y5
⁴QunaSys Inc., Aqua Hakusan Building 9F, 1-13-7 Hakusan, Bunkyo, Tokyo 113-0001, Japan

Published:	2025-07-21, volume 9, page 1800
Editor:	Krishna Kumar Sabapathy
Eprint:	arXiv:2301.04150v3
Doi:	https://doi.org/10.22331/q-2025-07-21-1800
Citation:	Quantum 9, 1800 (2025).

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Abstract

Fault-tolerant quantum computation (FTQC) is essential to implement quantum algorithms in a noise-resilient way, and thus to enjoy advantages of quantum computers even with presence of noise. In FTQC, a quantum circuit is decomposed into universal gates that can be fault-tolerantly implemented, for example, Clifford+$T$ gates. Here, $T$ gate is usually regarded as an essential resource for quantum computation because its action cannot be simulated efficiently on classical computers and it is experimentally difficult to implement fault-tolerantly. Practically, it is highly likely that only a limited number of $T$ gates are available in the near future. Pre-FTQC era, due to the constraint on available resources, it is vital to precisely estimate the decomposition error of a whole circuit. In this paper, we propose that the Clifford+$T$ decomposition error for a given quantum circuit containing a large number of quantum gates can be modeled as the depolarizing noise by averaging the decomposition error for each quantum gate in the circuit, and our model provides more accurate error estimation than the naive estimation. We exemplify this by taking unitary coupled-cluster (UCC) ansatz used in the applications of quantum computers to quantum chemistry as an example. We theoretically evaluate the approximation error of UCC ansatz when decomposed into Clifford+$T$ gates, and the numerical simulation for a wide variety of molecules verified that our model well explains the total decomposition error of the ansatz. Our results enable the precise and efficient usage of quantum resources in the early-stage applications of quantum computers and fuel further research towards what quantum computation can achieve in the upcoming future.

Popular summary

Quantum computers use elementary gates to build up more complex tasks. In the near future, before full-scale fault-tolerant quantum computers arrive, we will be limited in how many of an indispensable yet costly gate type (called T gates) we can reliably perform. This paper addresses the question: How much error does this limited use of T gates introduce—especially when translating important quantum routines into these basic gates?

Conventionally, one estimates the overall error by summing gate-by-gate errors, which can wildly overestimate the total. In this paper, we propose that, on average, the error behaves like a special and well-known type of noise called depolarizing noise. This makes it possible to better assess overall quantum-circuit performance, greatly simplifying error estimates without sacrificing accuracy.

We apply this improved error model to circuits used in quantum chemistry—a leading candidate for early quantum advantage—specifically the "unitary coupled‑cluster" (UCC) ansatz. Our simulations numerically validate our proposal of averaging errors, and demonstrate precisely how many T gates are needed to hit a given accuracy level. This gives practical guidance for quantum hardware design and software planning at their early stages.

Thus, we deliver a smarter and more precise way to forecast errors in quantum programs when T gate usage is limited—an essential piece for steering early quantum devices toward scientifically meaningful tasks.

► BibTeX data

@article{Kuroiwa2025averaginggate,
  doi = {10.22331/q-2025-07-21-1800},
  url = {https://doi.org/10.22331/q-2025-07-21-1800},
  title = {Averaging gate approximation error and performance of {U}nitary {C}oupled {C}luster ansatz in {P}re-{FTQC} {E}ra},
  author = {Kuroiwa, Kohdai and Nakagawa, Yuya O.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1800},
  month = jul,
  year = {2025}
}

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[2] Hasan Sayginel, Francois Jamet, Abhishek Agarwal, Dan E. Browne, and Ivan Rungger, "A fault-tolerant variational quantum algorithm with limited T-depth", Quantum Science and Technology 9 1, 015015 (2024).

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[8] Yuya O. Nakagawa and Yasunori Lee, "Application of resource theory based on free Clifford+kT computation to early fault-tolerant quantum computing", arXiv:2508.14546, (2025).

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