论文标题
具有最佳电路深度的量子状态准备：实施和应用
Quantum State Preparation with Optimal Circuit Depth: Implementations and Applications
论文作者
论文摘要
量子状态制备是用于量子计算的重要子例程。我们证明，只要仅使用单Qubit大门和两倍的大门就可以使用$θ（n）$ - 深度电路准备任何$ n $ qubit的量子状态，尽管费用为指数级的辅助量子。另一方面，对于具有$ d \ geqslant2 $ non-Zero条目的稀疏量子状态，我们可以将电路深度降低到$θ（\ log（nd））$，带有$ O（nd \ log d）$辅助数端。稀疏状态的算法比最著名的结果要快，并且辅助量表的数量几乎是最佳的，并且仅随系统尺寸而多一级增加。我们讨论了结果在不同的量子计算任务中的应用，例如哈密顿模拟，求解方程式的线性系统以及实现量子随机访问记忆，并找到所有这三个任务的电路深度的指数减少的案例。特别是，使用我们的算法，我们发现了一个线性系统的系列，即使与最著名的量子和经典的去量化算法相比，也可以解决享受指数加速的问题。
Quantum state preparation is an important subroutine for quantum computing. We show that any $n$-qubit quantum state can be prepared with a $Θ(n)$-depth circuit using only single- and two-qubit gates, although with a cost of an exponential amount of ancillary qubits. On the other hand, for sparse quantum states with $d\geqslant2$ non-zero entries, we can reduce the circuit depth to $Θ(\log(nd))$ with $O(nd\log d)$ ancillary qubits. The algorithm for sparse states is exponentially faster than best-known results and the number of ancillary qubits is nearly optimal and only increases polynomially with the system size. We discuss applications of the results in different quantum computing tasks, such as Hamiltonian simulation, solving linear systems of equations, and realizing quantum random access memories, and find cases with exponential reductions of the circuit depth for all these three tasks. In particular, using our algorithm, we find a family of linear system solving problems enjoying exponential speedups, even compared to the best-known quantum and classical dequantization algorithms.
