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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Abstract

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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Cited by

[1] I. Stetcu, A. Baroni, and J. Carlson, "Variational approaches to constructing the many-body nuclear ground state for quantum computing", arXiv:2110.06098.

[2] Abhinav Anand, Philipp Schleich, Sumner Alperin-Lea, Phillip W. K. Jensen, Sukin Sim, Manuel Díaz-Tinoco, Jakob S. Kottmann, Matthias Degroote, Artur F. Izmaylov, and Alán Aspuru-Guzik, "A Quantum Computing View on Unitary Coupled Cluster Theory", arXiv:2109.15176.

[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.

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