Alex Kerzner, Vlad Gheorghiu, Michele Mosca, Thomas Guilbaud, Federico Carminati, Fabio Fracas and Luca Dellantonio
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引用次数: 0
摘要
我们描述了一种求赫米矩阵最小特征值的量子算法。该算法结合了量子相位估计和量子振幅估计,与矩阵维度方面的最佳经典算法(即对矩阵编码的神谕进行 9 次黑盒查询,其中 N 是矩阵维度,ɛ 是所需精度)相比,速度提高了四倍。相比之下,相同任务的最佳经典算法需要查询。此外,该算法允许用户选择任意恒定的成功概率。我们还提供了一种运行时间相同的类似算法,它允许我们准备一个主要位于矩阵低能子空间的量子态。我们实现了这两种算法的模拟,并演示了它们在量子化学和材料科学问题中的应用。
A square-root speedup for finding the smallest eigenvalue
We describe a quantum algorithm for finding the smallest eigenvalue of a Hermitian matrix. This algorithm combines quantum phase estimation and quantum amplitude estimation to achieve a quadratic speedup with respect to the best classical algorithm in terms of matrix dimensionality, i.e. 9black-box queries to an oracle encoding the matrix, where N is the matrix dimension and ɛ is the desired precision. In contrast, the best classical algorithm for the same task requires queries. In addition, this algorithm allows the user to select any constant success probability. We also provide a similar algorithm with the same runtime that allows us to prepare a quantum state lying mostly in the matrix’s low-energy subspace. We implement simulations of both algorithms and demonstrate their application to problems in quantum chemistry and materials science.
期刊介绍:
Driven by advances in technology and experimental capability, the last decade has seen the emergence of quantum technology: a new praxis for controlling the quantum world. It is now possible to engineer complex, multi-component systems that merge the once distinct fields of quantum optics and condensed matter physics.
Quantum Science and Technology is a new multidisciplinary, electronic-only journal, devoted to publishing research of the highest quality and impact covering theoretical and experimental advances in the fundamental science and application of all quantum-enabled technologies.