具有非局部驱动的SU(3)多重态空间中的量子退火
Quantum annealing in SU(3) multiplet space with nonlocal drivers
AI总结：
该研究提出基于\(\mathfrak{su}(3)\)代数的量子退火理论框架，用于克服崎岖能量景观中的一阶跃迁。通过数值研究具有两个量子驱动的哈密顿量，发现可规避能隙闭合，且\(\mathfrak{su}(3)\)驱动在达到全局最小值上更有效。
AI中文摘要：
提出了基于\(\mathfrak{su}(3)\)代数的量子退火理论框架，并将其应用于克服崎岖能量景观中的一阶跃迁问题。卡西米尔不变量的守恒意味着可以使用\(\mathfrak{su}(3)\)的不可约表示，避免自旋玻璃系统中指数级大的希尔伯特空间。在此框架中，量子驱动具有非局部性质，退火期间波函数可远离局部最小值传输，避免被困住。考虑了具有两个量子驱动的哈密顿量并进行数值研究，结果表明通过两个驱动参数空间中的合适路径可规避能隙闭合。与更传统的横向场和反铁磁算符驱动的退火相比，\(\mathfrak{su}(3)\)驱动在达到崎岖能量景观的全局最小值方面更有效。
英文摘要：
A theoretical framework for quantum annealing based on $\mathfrak{su}(3)$ algebra is proposed, and applied to the problem of overcoming first-order transitions in rugged energy landscapes. Conservation of the Casimir invariant means that one can work with irreducible representations of $\mathfrak{su}(3)$, avoiding the exponentially large Hilbert spaces of spin glass systems. In this framework, quantum drivers exhibit nonlocal properties in the sense that during annealing the wave function can be transported far away from a local minimum, thereby avoiding being trapped by it. We consider Hamiltonians with two quantum drivers and studied them numerically. It is shown that energy gap closures can be circumvented via a suitable path in the parameter space of the two drivers. Comparison with more traditional annealing driven by transverse field and antiferromagnetic operators suggests that $\mathfrak{su}(3)$ drivers are more effective in attaining the global minimum of rugged energy landscapes.
