Achieving Utility-Scale Applications through Full Stack Co-Design of Fault Tolerant Quantum Computers

TL;DR

This work tackles the problem of delivering utility-scale quantum advantage for a real-world chemical application: estimating the ground-state energy of a Ru-based CO2 hydrogenation catalyst (complex XVIII) with chemical accuracy. By performing a full-stack co-design across algorithm, logical processing, quantum error correction, and distributed hardware, and by integrating open-source tools (pyLIQTR, Bench-Q, pyZX) into a unified Quantum Resource Estimation workflow, the authors demonstrate a dramatic runtime reduction from 22 years to about one day for a representative system and extend the analysis to larger systems. They show that classical methods struggle to converge to chemical accuracy for this problem, while the quantum approach achieves polynomial scaling with system size and a linear scaling of runtime with orbitals, delivering robust evidence for quantum advantage. The results also reveal how multi-layer innovations interact across the FTQC stack and highlight the potential for applying the methodology to other applications and hardware platforms, including neutral-atom implementations, thereby advancing the path to practical quantum-accelerated catalysis and green-energy technologies. The study thus combines algorithmic advances (DFTHC+BLISS+SA, ZX-calculus), resource-aware compilation (GSC), and realistic hardware models (inter-ELU entanglement, surface-code cycles) to connect quantum algorithms with impactful real-world problems.

Abstract

Quantum computing promises revolutionary advances in modeling materials and molecules. However, the up-to-date runtime estimates for utility-scale applications on certain quantum hardware systems are in the order of years rendering quantum computations impractical. Our work incorporates state-of-the-art innovations in all key aspects of the fault-tolerant quantum computing (FTQC) stack to show how quantum computers could realistically and practically tackle CO$_2$ utilization for green energy production. We bring down the quantum computation runtime from 22 years to just 1 day, achieving a significant 7.9e03 reduction from previous state-of-the-art work. This reduction renders the quantum computation feasible, challenges state-of-the-art classical methods and results to a predicted run-time quantum advantage. We provide a rigorous analysis of how different innovations across the stack combine to provide such reductions. Our work provides strong evidence that all layers of FTQC are crucial in the quest for quantum advantage. Our analysis can be applied to related problems on FTQC and for any type of quantum architecture. Our methodology connects quantum algorithms to applications of positive real-world impact and leads to compelling evidence of achievable quantum advantage.

Figures (23)

• Figure 1: Examples of Ru-based catalyst structures that are relevant in the carbon capture catalytic cycle.
• Figure 2: Quantum Benchmarking Graph (QBG) of the proposed computational workflow.
• Figure 3: The computation of accurate electronic energies on fault-tolerant quantum computers (FTQC) will help to accurately predict chemical reaction rates. This will unlock the understanding on reaction mechanisms that determine the catalytic process and allow effective CO$_2$ utilization for green energy production. FTQC is an issue of great complexity with different layers involved and many choices available on all these layers of computation. Our full-stack co-design provides a rigorous analysis on the interplay of improvements across the stack for an achievable quantum advantage.
• Figure 4: This figure shows in a nutshell all the advancements from different layers of the FTQC incorporated in this work that were necessary to reduce the runtime estimate by $7.3e03$.
• Figure 5: We plot the estimated reaction energy of Eq. \ref{['Eq:DE']} using the XVIII and I calculated classical energies from Table \ref{['Table XVIII classical']}. For the rest of the systems involved in the reaction we used the energies reported in Table \ref{['Table Small molecules']} (in Sec. \ref{['Sec:Evidence_classical_benchmarking']}). For the explicit values of $\Delta E^{\mathrm{el}}_{\mathrm{XVIII}}$ see Table \ref{['Table DE']} in Sec. \ref{['Sec:Evidence_classical_benchmarking']}. For better visibility, the DFT method is shown in the subplot in mHa. The region $\pm$ 1mHa indicates that even the more closely aligned relative energies in absolute value still differ by more than the desired accuracy of 1mHa challenging the reliability of the methods.