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方法,用于编制任意量子状态,并且我们表明它需要的量子资源比以前的方法少。当我们的协议被汇编成CNOT和任意的单方位门时,它会准备一个以美元为单位的高度状态,深度为美元(log(n)美元)和空间时间分配(一个衡量标准,它考虑到经常需要用一些正方位来计算整个协议的运行效率)$(N)美元,这是最佳的,而不是用以往的方法同时达到的深度。当我们将协议汇编成美元(mathrm{H,S,T,CNOT)的量子门设置时,它会准备一个任意的状态,深度为美元(eepslon),深度为美元($(log(N/\log))和时空位分配美元(opslon) 美元(nlog(N/w) 美元)和美元(N\log(n)的深度值(n),它会有效地将多少美元(N/epslon)的内值(n) 的内值(n) 水平(nc) 美元),我们的内值的内数数据配置可以用来进行一个稳定的空间分配。</s>