Quantum computing enhanced computational catalysis (2007.14460v2)

Abstract: The quantum computation of electronic energies can break the curse of dimensionality that plagues many-particle quantum mechanics. It is for this reason that a universal quantum computer has the potential to fundamentally change computational chemistry and materials science, areas in which strong electron correlations present severe hurdles for traditional electronic structure methods. Here, we present a state-of-the-art analysis of accurate energy measurements on a quantum computer for computational catalysis, using improved quantum algorithms with more than an order of magnitude improvement over the best previous algorithms. As a prototypical example of local catalytic chemical reactivity we consider the case of a ruthenium catalyst that can bind, activate, and transform carbon dioxide to the high-value chemical methanol. We aim at accurate resource estimates for the quantum computing steps required for assessing the electronic energy of key intermediates and transition states of its catalytic cycle. In particular, we present new quantum algorithms for double-factorized representations of the four-index integrals that can significantly reduce the computational cost over previous algorithms, and we discuss the challenges of increasing active space sizes to accurately deal with dynamical correlations. We address the requirements for future quantum hardware in order to make a universal quantum computer a successful and reliable tool for quantum computing enhanced computational materials science and chemistry, and identify open questions for further research.

Quantum Computing Enhanced Computational Catalysis

The paper "Quantum computing enhanced computational catalysis" explores the innovative application of quantum computing to computational catalysis, with a focus on the prediction of chemical reaction mechanisms by accurately assessing electronic energies. This research presents a novel approach that significantly improves the efficiency of quantum algorithms used in quantum chemistry, thereby reducing computational costs and enabling enhanced simulations of complex catalytic processes.

Key Contributions and Methodology

1. Improved Quantum Algorithms: The authors introduce new quantum algorithms that demonstrate more than an order of magnitude improvement in computational efficiency over previous methods. These advances are essential for dealing with the strong electron correlations in quantum mechanical systems that pose challenges to traditional computational approaches.
2. Double-Factorized Representation: The paper highlights the use of double-factorized representations for four-index integrals in quantum chemistry calculations. This approach significantly reduces computational complexity, making the process more scalable and feasible for larger molecular systems.
3. Electronic Energy Measurement: The focal point of the paper is the measurement of electronic energies in a quantum computer to simulate the catalytic cycle of a ruthenium catalyst involved in transforming carbon dioxide into methanol. This process is crucial for functionalized carbon capture and conversion technologies, offering a pathway to mitigate greenhouse gas emissions.

Results and Implications

• Numerical Results:

The quantum algorithms proposed provide strong numerical results, indicating significant reductions in Toffoli gate counts necessary for achieving chemical accuracy in calculations. For example, a reduction from $1.5 \times 10^{14}$ to $1.2 \times 10^{10}$ Toffoli gates showcases the efficiency of these new approaches in chemical systems with moderate active space sizes.

• State Preparation and Overlap:

The paper confirms that preparing a single-determinant initial state is sufficient for the catalytic structures examined, which generally do not exhibit strong multi-configurational character. High success probabilities in quantum phase estimation highlight the robustness of the proposed algorithms.

• Active Space Size Scalability:

By exploring active spaces of varying sizes, the paper demonstrates that the scaling of computational costs follows a favorable $N^{3.25}$ trend for fixed atomic systems and improves understanding of the scalability limits of quantum computing in chemistry.

Challenges and Future Directions

Despite the advancements presented, further development in quantum algorithms is necessary to handle larger active spaces effectively, allowing quantum computing to achieve competitive advantage over classical methods. Future research should focus on understanding dynamical correlations and exploring alternative formulations to cope with electron density complexity.

Additionally, advancing quantum computing hardware to support fast gate operations and large qubit counts is crucial for achieving practical runtimes that can outperform the classical computational methods, as current estimates suggest that realistic runtimes may still extend to days or weeks.

In conclusion, this paper presents significant strides in quantum computing for chemical catalysis, demonstrating potential transformative impacts in material science and quantum chemistry. Continued innovation in quantum algorithms and hardware capabilities will further solidify quantum computing's role in addressing complex chemical phenomena and contributing to sustainable technological advancements.