发表机构
Tencent Quantum Laboratory; T Lab（腾讯量子实验室; T实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种精确酉合成方法，利用高斯包络编码与坐标变换，在最优电路尺寸下同时实现渐近最优的深度-辅助量子比特权衡。
AI 中文摘要
酉合成是通用量子计算的基础，它将酉变换转化为基本门电路。我们证明，对于任意辅助量子比特预算 $m\geq 0$，每个 $n$ 量子比特的酉变换都可以通过包含 $O(4^n)$ 个 CNOT 门和单量子比特门的量子电路精确实现，电路层数为 $O(n+4^n/(n+m))$，达到渐近最优的深度-辅助量子比特权衡，同时实现最优的电路尺寸。关键思想是将计算基态编码为共享高斯包络的波函数，将振幅上的酉作用转化为坐标变换，从而允许浅电路实现。随后对连续编码进行离散化，并通过精确残差校正消除近似误差。深度-辅助量子比特权衡通过递归应用量子香农分解、合成其较小的酉因子并重用辅助量子比特来获得。
英文摘要
Unitary synthesis underlies universal quantum computation by translating unitary transformations into circuits of elementary gates. We show that for any budget $m\geq 0$ of ancilla, every $n$-qubit unitary can be exactly implemented using a quantum circuit consisting of $O(4^n)$ CNOT and single-qubit gates in $O(n+4^n/(n+m))$ layers attaining the asymptotically optimal depth--ancilla tradeoff while simultaneously achieving optimal circuit size. The key idea is to encode computational basis states as wavefunctions sharing a Gaussian envelope, converting unitary action on amplitudes into coordinate transformations that admit shallow circuit implementations. The continuous encoding is then discretized, with approximation errors removed by exact residual correction. The depth-ancilla tradeoff follows by recursively applying the quantum Shannon decomposition, synthesizing its smaller unitary factors, and reusing ancillary qubits.
