Quantum phase estimation of multiple eigenvalues for small-scale (noisy) experiments
Quantum phase estimation of multiple eigenvalues for small-scale (noisy) experiments
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DOI：
10.1088/1367-2630/aafb8e
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发表时间：
2019-02-28
影响因子：
3.3
通讯作者：
Terhal, Barbara M.
中科院分区：
文献类型：
--
作者：
O'Brien, Thomas E.;Tarasinski, Brian;Terhal, Barbara M.
量子相位估计（QPE）是任何量子算法背后的主力，也是确定强关联量子系统基态能量的一种有前途的方法。低成本QPE技术利用仅使用单个辅助量子位的电路，需要经典的后处理来提取系统的特征值细节。我们研究了具有低深度无噪声或噪声电路的酉矩阵的相位估计的选择，改变相位估计电路本身以及经典的后处理以确定特征值相位。我们工作的情况下，当输入状态是不是一个酉矩阵的本征态。我们开发了一种新的后处理技术来提取特征值的相位估计数据的基础上，一个经典的时间序列（或频率）分析和对比，通过贝叶斯方法的分析。我们通过时间序列分析计算估计单个特征值的方差，发现它在进行的实验数量上扩展到一阶，在电路深度上扩展到一阶或二阶（取决于实验设计）。数值模拟证实了这两个估计缩放。我们试图用两种经典的后处理技术来补偿噪声，在存在去极化噪声的情况下找到了很好的结果，但是在9量子比特电路级模拟超导量子比特中的改进较小，目的是解决H-4分子的电子基态。
Quantum phase estimation (QPE) is the workhorse behind any quantum algorithm and a promising method for determining ground state energies of strongly correlated quantum systems. Low-cost QPE techniques make use of circuits which only use a single ancilla qubit, requiring classical post-processing to extract eigenvalue details of the system. We investigate choices for phase estimation for a unitary matrix with low-depth noise-free or noisy circuits, varying both the phase estimation circuits themselves as well as the classical post-processing to determine the eigenvalue phases. We work in the scenario when the input state is not an eigenstate of the unitary matrix. We develop a new post-processing technique to extract eigenvalues from phase estimation data based on a classical time-series (or frequency) analysis and contrast this to an analysis via Bayesian methods. We calculate the variance in estimating single eigenvalues via the time-series analysis analytically, finding that it scales to first order in the number of experiments performed, and to first or second order (depending on the experiment design) in the circuit depth. Numerical simulations confirm this scaling for both estimators. We attempt to compensate for the noise with both classical post-processing techniques, finding good results in the presence of depolarizing noise, but smaller improvements in 9-qubit circuit-level simulations of superconducting qubits aimed at resolving the electronic ground state of a H-4-molecule.