Universal quantum circuits for quantum chemistry

Juan Miguel Arrazola, Olivia Di Matteo, Nicolás Quesada, Soran Jahangiri, Alain Delgado, and Nathan Killoran

Xanadu, Toronto, ON, M5G 2C8, Canada

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Universal gate sets for quantum computing have been known for decades, yet no universal gate set has been proposed for particle-conserving unitaries, which are the operations of interest in quantum chemistry. In this work, we show that controlled single-excitation gates in the form of Givens rotations are universal for particle-conserving unitaries. Single-excitation gates describe an arbitrary $U(2)$ rotation on the two-qubit subspace spanned by the states $|01\rangle, |10\rangle$, while leaving other states unchanged – a transformation that is analogous to a single-qubit rotation on a dual-rail qubit. The proof is constructive, so our result also provides an explicit method for compiling arbitrary particle-conserving unitaries. Additionally, we describe a method for using controlled single-excitation gates to prepare an arbitrary state of a fixed number of particles. We derive analytical gradient formulas for Givens rotations as well as decompositions into single-qubit and CNOT gates. Our results offer a unifying framework for quantum computational chemistry where every algorithm is a unique recipe built from the same universal ingredients: Givens rotations.

This work shows that a special type of gate, known as a controlled single-excitation gate, can be used to build any quantum circuit that preserves the number of particles in a fermionic system. These are the main transformations of interest in quantum chemistry. Controlled single-excitation gates are examples of Givens rotations, which therefore can be seen as the universal building blocks of quantum circuits for quantum chemistry.

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[3] Kaining Zhang, Min-Hsiu Hsieh, Liu Liu, and Dacheng Tao, "Gaussian initializations help deep variational quantum circuits escape from the barren plateau", arXiv:2203.09376.

[4] Daniel Huerga, "Variational Quantum Simulation of Valence-Bond Solids", arXiv:2201.02545.

[5] Juan Miguel Arrazola, Soran Jahangiri, Alain Delgado, Jack Ceroni, Josh Izaac, Antal Száva, Utkarsh Azad, Robert A. Lang, Zeyue Niu, Olivia Di Matteo, Romain Moyard, Jay Soni, Maria Schuld, Rodrigo A. Vargas-Hernández, Teresa Tamayo-Mendoza, Cedric Yen-Yu Lin, Alán Aspuru-Guzik, and Nathan Killoran, "Differentiable quantum computational chemistry with PennyLane", arXiv:2111.09967.

[6] Jack Ceroni, Alain Delgado, Soran Jahangiri, and Juan Miguel Arrazola, "Tailgating quantum circuits for high-order energy derivatives", arXiv:2207.11274.

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The above citations are from SAO/NASA ADS (last updated successfully 2022-08-14 11:09:11). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref's cited-by service no data on citing works was found (last attempt 2022-08-14 11:09:09).