基于核函数的有限温度量子模拟量子算法
Kernel-Function Based Quantum Algorithms for Finite Temperature Quantum Simulation
AI总结：
本文提出QKFE量子算法，利用核–傅里叶展开、随机态采样与量子干涉测量计算有限温度多体热力学，并以THEI解决低温低效问题。
摘要：
计算量子多体系统的有限温度性质，是描述从量子化学、凝聚态物理到热量子场论等广泛关联量子多体物理的关键。近年来快速发展的量子计算在影响量子热力学计算方面具有巨大潜力。为实现这种潜在影响，设计能够利用量子计算设备算力的量子算法至关重要。本文提出一种量子核函数展开（QKFE）算法，用于求解量子多体系统的热力学性质。在该量子算法中，多体态密度通过核–傅里叶展开进行近似，其展开矩通过随机态采样和量子干涉测量获得。与其经典对应方法，即核多项式方法（KPM）相比，QKFE在时间和内存成本上均具有指数优势。在计算低温性质时，QKFE会变得低效，这与经典KPM类似。为解决这一困难，我们进一步构造了一个热系综，并逐步逼近低温区域。对于其基态可通过多项式规模量子电路制备的量子哈密顿量，THEI具有总体多项式复杂度。我们通过将其应用于一维和二维量子自旋模型以及一个费米子晶格，证明了其效率。结合我们对利用数字和模拟量子器件实现该算法的分析，我们预计该量子算法可被当前量子技术所采用。
英文摘要：
Computing finite temperature properties of a quantum many-body system is key to describing a broad range of correlated quantum many-body physics from quantum chemistry and condensed matter to thermal quantum field theories. Quantum computing with rapid developments in recent years has a huge potential to impact the computation of quantum thermodynamics. To fulfill the potential impacts, it is crucial to design quantum algorithms that utilize the computation power of the quantum computing devices. Here we present a quantum kernel function expansion (QKFE) algorithm for solving thermodynamic properties of quantum many-body systems. In this quantum algorithm, the many-body density of states is approximated by a kernel-Fourier expansion, whose expansion moments are obtained by random state sampling and quantum interferometric measurements. As compared to its classical counterpart, namely the kernel polynomial method (KPM), QKFE has an exponential advantage in the cost of both time and memory. In computing low temperature properties, QKFE becomes inefficient, as similar to classical KPM. To resolve this difficulty, we further construct a thermal ensemble and approaches the low temperature regime step-by-step. For quantum Hamiltonians, whose ground states are preparable with polynomial quantum circuits, THEI has an overall polynomial complexity. We demonstrate its efficiency with applications to one and two-dimensional quantum spin models, and a fermionic lattice. With our analysis on the realization with digital and analogue quantum devices, we expect the quantum algorithm is accessible to current quantum technology.
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