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.

中文翻译：

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用于量子化学的通用量子电路

用于量子计算的通用门集已为人所知数十年，但尚未提出用于粒子守恒酉的通用门集，这是量子化学中感兴趣的操作。在这项工作中，我们表明以 Givens 旋转形式的受控单激发门对于粒子守恒酉是普遍的。单激发门描述了由状态 $|01\rangle、|10\rangle$ 跨越的两个量子位子空间上的任意 $U(2)$ 旋转，同时保持其他状态不变——这种转换类似于单-双轨量子比特上的量子比特旋转。证明是建设性的，因此我们的结果还提供了一种编译任意粒子守恒酉的显式方法。此外，我们描述了一种使用受控单激发门来准备固定数量粒子的任意状态的方法。我们推导出 Givens 旋转的解析梯度公式以及分解成单量子位和 CNOT 门。我们的结果为量子计算化学提供了一个统一的框架，其中每个算法都是由相同的通用成分构建的独特配方：吉文斯旋转。