论文标题
能量过滤的随机相态作为微型典型热量子态
Energy-filtered random-phase states as microcanonical thermal pure quantum states
论文作者
论文摘要
我们提出了一种通过引入纯量子态来计算量子多体系统的有限温度多体系统的有限特性，此处称为纯量子态，此处称为能量过滤的随机相态，这也是近期量子计算机的潜在应用。在我们的形式主义中，微型典型合奏由两个参数（即系统的能量及其相关的能量窗口）指定。因此，状态的密度表示为以目标能量为中心的高斯人的总和，其扩展对应于能量窗口的宽度。然后，我们表明热力学数量（例如熵和温度）是通过评估时间进化运算符的痕迹以及时间进化运算符的痕迹来计算的。我们还描述了如何使用适合量子计算的随机对角线独立电路来评估这些轨迹。代表我们的微型典型合奏的纯量子状态与Wall和Neuhauser对过滤器对角线化方法引入的形式的状态有关[M. R. Wall和D. Neuhauser，J。Chem。物理。 102，8011（1995）]，因此我们将其称为能量过滤的随机相状状态。能量过滤的随机相状状态本质上是时间进化状态的傅立叶变换，其初始状态是作为随机相态制备的，而在傅立叶变换的时间积分时间中的截止时间则是能量窗口宽度的倒数。通过计算高达28吨的小簇上的一维自旋1/2 Heisenberg模型的热力学量来证明所提出的方法，这表明该方法对于围绕能量eigenstate的致密能量分布而言最有效。
We propose a method to calculate finite-temperature properties of a quantum many-body system for a microcanonical ensemble by introducing a pure quantum state named here an energy-filtered random-phase state, which is also a potentially promising application of near-term quantum computers. In our formalism, a microcanonical ensemble is specified by two parameters, i.e., the energy of the system and its associated energy window. Accordingly, the density of states is expressed as a sum of Gaussians centered at the target energy with its spread corresponding to the width of the energy window. We then show that the thermodynamic quantities such as entropy and temperature are calculated by evaluating the trace of the time-evolution operator and the trace of the time-evolution operator multiplied by the Hamiltonian of the system. We also describe how these traces can be evaluated using random diagonal-unitary circuits appropriate to quantum computation. The pure quantum state representing our microcanonical ensemble is related to a state of the form introduced by Wall and Neuhauser for the filter diagonalization method [M. R. Wall and D. Neuhauser, J. Chem. Phys. 102, 8011 (1995)], and therefore we refer to it as an energy-filtered random-phase state. The energy-filtered random-phase state is essentially a Fourier transform of a time-evolved state whose initial state is prepared as a random-phase state, and the cut-off time in the time-integral for the Fourier transform sets the inverse of the width of the energy window. The proposed method is demonstrated numerically by calculating thermodynamic quantities for the one-dimensional spin-1/2 Heisenberg model on small clusters up to 28 qubits, showing that the method is most efficient for the target energy around which the dense distribution of energy eigenstates is found.
