发表机构
HK Institute of Quantum Science \& Technology, The University of Hong Kong, Hong Kong, China
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种利用中间测量与前馈的确定性构造，将精确n量子比特酉合成的量子深度从Θ(n)降至O(1)，并给出深度-宽度权衡，在恒定深度内实现任意酉变换。
AI 中文摘要
带前馈的中间线路测量将精确的 $n$ 量子比特酉合成的量子最坏情况深度从 $\Theta(n)$ 降低到 $O(1)$，使用任意单比特和双比特门以及不受限制的辅助空间。不带前馈的测量和重置仍然受限于线路因果锥边界。我们的确定性构造使用单比特测量、$O(1)$ 轮奇偶校验前馈，以及总共 $O(n4^n\log(n+2))$ 个量子比特，所有辅助比特初始和结束于 $|0\rangle$。经典处理不计入量子深度。我们仅传送 Nehoran 和 Yuen 近似中的矩阵误差。一个精确制备的辅助态编码此误差，其作用通过相干干涉加回。在算子范数误差 $2^{-n}$ 下，一步振幅放大就足够了。相干扇出电路达到相同的恒定深度界限，而仅使用单比特和双比特门的电路达到深度 $\Theta(n)$，门数为 $O(4^n\log^2(n+2))$。通用目标在深度 $h$ 下需要 $\Omega(4^n/(h+1))$ 个量子比特，即使不受限制的经典控制下也是如此。我们的深度-宽度权衡在 $1\le h\le2^n$ 范围内满足此界限，因子为 $O(n^2)$。
英文摘要
Mid-circuit measurements with feedforward reduce the optimal worst-case quantum depth for exact $n$-qubit unitary synthesis from $Θ(n)$ to $O(1)$, using arbitrary one- and two-qubit gates and unrestricted ancillary space. Measurements and resets without feedforward remain subject to the circuit causal-cone bound. Our deterministic construction uses single-qubit measurements, $O(1)$ rounds of parity feedforward, and $O(n4^n\log(n+2))$ total qubits, with all ancillas starting and ending in $|0\rangle$. Classical processing is not counted in quantum depth. We teleport only the matrix error of an approximation by Nehoran and Yuen. An exactly prepared ancillary state encodes this error, whose action is added back by coherent interference. At operator-norm error $2^{-n}$, one step of amplitude amplification suffices. Coherent fanout circuits achieve the same constant-depth bound, while circuits using only one- and two-qubit gates attain depth $Θ(n)$ with $O(4^n\log^2(n+2))$ gates. Generic targets require $Ω(4^n/(h+1))$ qubits at depth $h$, even under unrestricted classical control. Our depth-width trade-offs meet this bound within a factor $O(n^2)$ for $1\le h\le2^n$.
Comments23 pages, 3 figures
