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 $|01rangle, |10rangle$, 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.
Featured image: An example quantum circuit built from Givens rotations
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Cited by
[1] 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.
[2] I. Stetcu, A. Baroni, and J. Carlson, “Variational approaches to constructing the many-body nuclear ground state for quantum computing”, arXiv:2110.06098.
[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] Luogen Xu, Joseph T. Lee, and J. K. Freericks, “Decomposition of high-rank factorized unitary coupled-cluster operators using ancilla and multiqubit controlled low-rank counterparts”, Physical Review A 105 1, 012406 (2022).
[6] 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.
[7] Michael A. Jones, Harish J. Vallury, Charles D. Hill, and Lloyd C. L. Hollenberg, “Chemistry beyond the Hartree-Fock limit via quantum computed moments”, arXiv:2111.08132.
[8] Vlad Gheorghiu, Michele Mosca, and Priyanka Mukhopadhyay, “T-count and T-depth of any multi-qubit unitary”, arXiv:2110.10292.
[9] Davide Castaldo, Soran Jahangiri, Alain Delgado, and Stefano Corni, “Quantum simulation of molecules in solution”, arXiv:2111.13458.
The above citations are from SAO/NASA ADS (last updated successfully 2022-06-20 15:30:56). The list may be incomplete as not all publishers provide suitable and complete citation data.
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