论文标题
量子力量法通过随时间发展的状态叠加
Quantum Power Method by a Superposition of Time-Evolved States
论文作者
论文摘要
We propose a quantum-classical hybrid algorithm of the power method, here dubbed as quantum power method, to evaluate $\hat{\cal H}^n |ψ\rangle$ with quantum computers, where $n$ is a nonnegative integer, $\hat{\cal H}$ is a time-independent Hamiltonian of interest, and $|ψ\rangle$ is a量子状态。我们表明，近似$ \ hat {\ cal h}^n $所需的门数在功率和量子数上线性缩放，这使其成为近任期量子计算机的有希望的应用程序。 Using numerical simulation, we show that the power method can control systematic errors in approximating the Hamiltonian power ${\hat{\cal H}^n}$ for $n$ as large as 100. As an application, we combine our method with a multireference Krylov-subspace-diagonalization scheme to show how one can improve the estimation of ground-state energies and the ground-state fidelities found using a变性 - 量子质溶剂方案。最后，我们概述了量子功率方法的其他应用，包括几种基于力矩的方法。我们从数值上证明了虚构的时间扩展，以进行假想时间的演化，并将结果与多射krylov-subspace对角度进行比较。
We propose a quantum-classical hybrid algorithm of the power method, here dubbed as quantum power method, to evaluate $\hat{\cal H}^n |ψ\rangle$ with quantum computers, where $n$ is a nonnegative integer, $\hat{\cal H}$ is a time-independent Hamiltonian of interest, and $|ψ\rangle$ is a quantum state. We show that the number of gates required for approximating $\hat{\cal H}^n$ scales linearly in the power and the number of qubits, making it a promising application for near term quantum computers. Using numerical simulation, we show that the power method can control systematic errors in approximating the Hamiltonian power ${\hat{\cal H}^n}$ for $n$ as large as 100. As an application, we combine our method with a multireference Krylov-subspace-diagonalization scheme to show how one can improve the estimation of ground-state energies and the ground-state fidelities found using a variational-quantum-eigensolver scheme. Finally, we outline other applications of the quantum power method, including several moment-based methods. We numerically demonstrate the connected-moment expansion for the imaginary-time evolution and compare the results with the multireference Krylov-subspace diagonalization.
