Molecular Quantum Circuit Design: A Graph-Based Approach

Jakob S. Kottmann

Institute of Computer Science, University of Augsburg, Germany

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Science is rich in abstract concepts that capture complex processes in astonishingly simple ways. A prominent example is the reduction of molecules to simple graphs. This work introduces a design principle for parametrized quantum circuits based on chemical graphs, providing a way forward in three major obstacles in quantum circuit design for molecular systems: Operator ordering, parameter initialization and initial state preparation. It allows physical interpretation of each individual component and provides an heuristic to qualitatively estimate the difficulty of preparing ground states for individual instances of molecules.

An integral part of science is the formulation of abstract concepts capable to capture the essential aspects of complex processes while remaining as simple as possible. For the construction of quantum circuits, such concepts are in high demand as most methodologies often lack simplicity and interpretability.

In Chemistry, one of the most prominent examples is the reduction of molecules to simple graphs with the atomic nuclei as vertices connected by edges representing so-called chemical bonds. In this work circuit designs based on chemical graphs are developed. This allows to construct quantum circuits that prepare electronic states of molecules, form two types of primitive elements: Orbital rotations and pair-correlators. The chemical graph is employed as a guiding heuristic to correctly arrange and initialize these building blocks.

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Cited by

[1] Seyed Ehsan Ghasempouri, Gerhard W. Dueck, and Stijn De Baerdemacker, "Modular Cluster Circuits for the Variational Quantum Eigensolver", The Journal of Physical Chemistry A 127 39, 8168 (2023).

[2] Xiaoxiao Xiao, Hewang Zhao, Jiajun Ren, Wei-Hai Fang, and Zhendong Li, "Physics-Constrained Hardware-Efficient Ansatz on Quantum Computers That Is Universal, Systematically Improvable, and Size-Consistent", Journal of Chemical Theory and Computation acs.jctc.3c00966 (2024).

[3] Manuel S. Rudolph, Jacob Miller, Danial Motlagh, Jing Chen, Atithi Acharya, and Alejandro Perdomo-Ortiz, "Synergistic pretraining of parametrized quantum circuits via tensor networks", Nature Communications 14 1, 8367 (2023).

[4] Manuel S. Rudolph, Jacob Miller, Danial Motlagh, Jing Chen, Atithi Acharya, and Alejandro Perdomo-Ortiz, "Synergy Between Quantum Circuits and Tensor Networks: Short-cutting the Race to Practical Quantum Advantage", arXiv:2208.13673, (2022).

[5] Philipp Schleich, Joseph Boen, Lukasz Cincio, Abhinav Anand, Jakob S. Kottmann, Sergei Tretiak, Pavel A. Dub, and Alán Aspuru-Guzik, "Partitioning Quantum Chemistry Simulations with Clifford Circuits", arXiv:2303.01221, (2023).

[6] Jakob S. Kottmann and Francesco Scala, "Compact Effective Basis Generation: Insights from Interpretable Circuit Design", arXiv:2302.10660, (2023).

The above citations are from Crossref's cited-by service (last updated successfully 2024-02-26 06:28:15) and SAO/NASA ADS (last updated successfully 2024-02-26 06:28:16). The list may be incomplete as not all publishers provide suitable and complete citation data.