Quantum simulation of quantum phase transitions using the convex geometry of reduced density matrices
Quantum simulation of quantum phase transitions using the convex geometry of reduced density matrices
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DOI：
10.1103/physreva.106.012434
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发表时间：
2022-07
影响因子：
2.9
通讯作者：
Samuel Warren;LeeAnn M. Sager-Smith;D. Mazziotti
中科院分区：
文献类型：
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作者：
Samuel Warren;LeeAnn M. Sager-Smith;D. Mazziotti
绝对零温度下多粒子量子系统在不同相之间的转变（称为量子相变）需要严格处理粒子相关性。在这项工作中，我们提出了一种利用约化密度矩阵的几何结构来处理量子相变的通用量子计算方法。虽然量子相变的典型方法检查序参数的不连续性，但相变的起源——它们的序参数和对称性破缺——可以用双粒子约化密度矩阵（2-RDM）集来几何地理解。 2-RDM 的凸集提供了量子系统的全面图，包括其不同的相以及连接这些相的转变。由于 2-RDM 可以在量子计算机上以非指数成本进行计算，即使量子系统强相关，它们也非常适合量子相变的量子计算方法。我们计算 IBM 超导量子位量子处理器上 Lipkin-Meshkov-Glick 自旋模型的 2-RDM 凸集。尽管由于设备噪声，计算仅限于少粒子模型，但与经典可解的 1000 粒子模型的比较表明，有限粒子量子解捕获了相变的关键特征，包括强相关性和对称性破缺。
Transitions of many-particle quantum systems between distinct phases at absolute-zero temperature, known as quantum phase transitions, require an exacting treatment of particle correlations. In this work, we present a general quantum-computing approach to quantum phase transitions that exploits the geometric structure of reduced density matrices. While typical approaches to quantum phase transitions examine discontinuities in the order parameters, the origin of phase transitions -- their order parameters and symmetry breaking -- can be understood geometrically in terms of the set of two-particle reduced density matrices (2-RDMs). The convex set of 2-RDMs provides a comprehensive map of the quantum system including its distinct phases as well as the transitions connecting these phases. Because 2-RDMs can potentially be computed on quantum computers at non-exponential cost, even when the quantum system is strongly correlated, they are ideally suited for a quantum-computing approach to quantum phase transitions. We compute the convex set of 2-RDMs for a Lipkin-Meshkov-Glick spin model on IBM superconducting-qubit quantum processors. Even though computations are limited to few-particle models due to device noise, comparisons with a classically solvable 1000-particle model reveal that the finite-particle quantum solutions capture the key features of the phase transitions including the strong correlation and the symmetry breaking.