发表机构
Shanghai Jiao Tong University; Zhejiang University（上海交通大学; 浙江大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出共享相位算术方法，通过相干计算旋转参数加权和并一次性加到相位梯度态，实现并行量子旋转，分离表示与应用成本，并给出门计数界限。
AI 中文摘要
一层对角量子门可以通过计算基态上的整数值函数来指定。这一描述暗示了通过可逆地评估该函数并使用共享量子寄存器将其值转换为相位来实现该层。我们为并行相位回踢（PPK）发展了这一观点：多个旋转参数的加权和被相干地计算，一次性地加到相位梯度态上，然后进行反计算。该构造将表示相位函数的成本与应用它的成本分开。我们证明了正确性，给出了显式误差界，并分析了通用权重、旋转对和具有不相交二进制支持的权重的逻辑门计数。仅使用Clifford编码时，一批在b位相位分辨率下最多使用4(b-1)个T门，不包括初始化。第一个相位参考通过Gridsynth合成的独立旋转制备；额外的相位梯度态随后通过不相交支持构造，每个使用O(b)个T门。所得界限确定了共享相位算术何时降低摊销旋转成本，以及编码开销何时限制该优势。
英文摘要
A layer of diagonal quantum gates can be specified by an integer-valued function on computational basis states. This description suggests implementing the layer by evaluating that function reversibly and translating its value into a phase using a shared quantum register. We develop this viewpoint for parallel phase kickback (PPK): the weighted sum of several rotation parameters is computed coherently, added once to a phase-gradient state, and then uncomputed. The construction separates the cost of representing a phase function from the cost of applying it. We prove correctness, give explicit error bounds, and analyze logical gate counts for general weights, pairs of rotations, and weights with disjoint binary support. With Clifford-only encoding, a batch uses at most $4(b-1)$ T gates at $b$-bit phase resolution, excluding initialization. The first phase reference is prepared with independent rotations synthesized by Gridsynth; additional phase-gradient states then follow from the disjoint-support construction with $O(b)$ T gates each. The resulting bounds identify when shared phase arithmetic reduces amortized rotation cost and when encoding overhead limits that advantage.
