Exponential-in-$N_c^2$ cost reduction of product-formula-based quantum simulations of quantum chromodynamics

• URL: http://arxiv.org/abs/2608.21258v1
• Date: Fri, 21 Aug 2026 16:16:09 GMT
• Title: Exponential-in-$N_c^2$ cost reduction of product-formula-based quantum simulations of quantum chromodynamics
• Abstract summary: We show that a factor of size $O(24(N_c2-1))$ can be removed from the per-Trotter-step cost estimate by Kan and Nam.<n>Our method reduces the T-gate cost estimate of QCD simulations using a second-order product formula by a factor of nearly $1014$, independent of simulation parameters and sizes.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum algorithms for simulating quantum chromodynamics (QCD) have matured steadily since the pioneering work of Byrnes and Yamamoto [PRA 73, 022328 (2006)]. The most popular strategies for Hamiltonian simulation involve product-formula decompositions. However, the application of product-formula methods to SU($N_c$) lattice gauge theories by Byrnes and Yamamoto leads to $O(Λ^{8(N_c^2-1)})$ gate complexity per Trotter step, where $Λ$ is the bosonic cutoff in the electric (i.e., irreducible-representation) basis. A seminal work by Kan and Nam [arXiv:2107.12769 (2021)] significantly improves over such an undesirable cost and reports an $O\big(Λ\text{polylog}(Λ)\big)$ scaling, yet it still calls for an unrealistically large number of quantum gates. Here, we illuminate one of the reasons behind this high cost estimate and show that a factor of size $O(2^{4(N_c^2-1)})$ can be removed from the per-Trotter-step cost estimate by Kan and Nam. We specifically show that, by using methods developed in our past works [PRD 112, 014508 (2025); Quantum 7, 1213 (2023)], exponentiated-Hamiltonian decomposition---a necessary step in the application of product-formula algorithms---can be performed far more efficiently than previously thought. Our method reduces the T-gate cost estimate of QCD simulations using a second-order product formula by a factor of nearly $10^{14}$, independent of simulation parameters and sizes. Focusing on simulations in the electric basis, we further contrast our results with other methods: the local-multiplet basis approach of Ciavarella, Klco, and Savage [PRD 103, 094501 (2021)] and the near-optimal algorithm of Rhodes, Kreshchuk, and Pathak [PRX Quantum 5, 040347 (2024)]. This work highlights the importance of continued algorithmic improvement to bringing the quantum-simulation cost of QCD within reach of realistic quantum computers.

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