We propose a novel deterministic method for preparing arbitrary quantum states, and we show that it requires asymptotically fewer quantum resources than previous methods. When our protocol is compiled into CNOT and arbitrary single-qubit gates, it prepares an $N$-dimensional state in depth $O(\log(N))$ and spacetime allocation (a metric that accounts for the fact that oftentimes some ancilla qubits need not be active for the entire protocol) $O(N)$, which are both optimal and not simultaneously achieved by previous methods. When compiled into the $\{\mathrm{H,S,T,CNOT}\}$ gate set, it prepares an arbitrary state up to error $\epsilon$ in depth $O(\log(N/\epsilon))$ and spacetime allocation $O(N\log(\log(N)/\epsilon))$, improving over $O(\log(N)\log(N/\epsilon))$ and $O(N\log(N/\epsilon))$, respectively. We illustrate how the reduced spacetime allocation of our protocol enables rapid preparation of many disjoint states with only constant-factor ancilla overhead -- $O(N)$ ancilla qubits are reused efficiently to prepare a product state of $w$ $N$-dimensional states in depth $O(w + \log(N))$ rather than $O(w\log(N))$, achieving effectively constant depth per state. We highlight several applications where this ability would be useful, including quantum machine learning, Hamiltonian simulation, and solving linear systems of equations. We provide quantum circuit descriptions of our protocol along with detailed pseudocode.

翻译：我们提出一种新的确定性方法用于制备任意量子态，并证明其渐近所需的量子资源少于现有方法。当我们的协议编译为CNOT门和任意单量子比特门时，它能在深度$O(\log(N))$和时空分配（一种衡量部分辅助量子比特无需全程参与协议的指标）$O(N)$下制备一个$N$维量子态，这两项指标均为最优且未被现有方法同时实现。当编译为$\{\mathrm{H,S,T,CNOT}\}$门集时，该协议可在深度$O(\log(N/\epsilon))$和时空分配$O(N\log(\log(N)/\epsilon))$下制备误差不超过$\epsilon$的任意量子态，相比现有方法分别从$O(\log(N)\log(N/\epsilon))$和$O(N\log(N/\epsilon))$得到改进。我们展示了协议中减少的时空分配如何仅需常数因子辅助量子比特开销即可快速制备多个不相关的量子态——通过高效复用$O(N)$个辅助量子比特，可在深度$O(w + \log(N))$而非$O(w\log(N))$下制备$w$个$N$维量子态的乘积态，实现每个态的有效常数深度。我们重点介绍了该能力在量子机器学习、哈密顿量模拟及线性方程组求解等多个领域的潜在应用，并提供了协议的量子电路描述及详细伪代码。