2021/06/30 by Juan Miguel Arrazola, Olivia Di Matteo, Nicolás Quesada +3 · 1 citation
Physics and Astronomy · #quant-ph
paper · pdf · doi:10.22331/q-2022-06-20-742
published as Quantum 6, 742 (2022) · 11 pages, 12 figures
arxiv created 2022/06/10 · arxiv updated 2022/06/22
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⟩, |10⟩, 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.