Ground States of Local Hamiltonians and Quantum PCPs

PI计划将这笔资金用于对加州大学伯克利分校进行为期一年的访问，在那里他打算与Umesh Vazirani及其同事和学生密切合作，研究关于局部哈密顿量基态的两个基本问题——它们是否满足PCP定理的量子模拟，以及它们是否满足面积定律。为了深入了解局部哈密顿量的基态，PI将运用他在经典PCP理论方面的知识，这是他帮助开发的计算机科学中的一个深奥理论，并将其与伯克利同事在量子信息理论方面的专业知识结合起来。PCP定理的量子类比将会说明量子系统的一些深刻问题。除了它在量子信息理论中的含义，它在物理学中也有更直接的含义，比如实现量子系统在高温下保持其指数复杂性。此外，面积定律可以解释多体系统中波函数的局部行为。如果PI及其同事的努力取得成功，这将是一个类似于经典PCP理论发明的发展，它将吸引许多计算复杂性理论家，并将他们与量子计算联系起来。对局部哈密顿量基态行为的更深入理解应该会影响从量子化学到黑洞物理等学科。

The PI plans to apply the grant money towards a one-year visit to UC-Berkeley, where he intends to closely collaborate with Umesh Vazirani and his colleagues and students on two fundamental issues about ground states of local Hamiltonians - whether they satisfy the quantum analog of the PCP theorem, and whether they satisfy an area law. To gain the needed insight into the ground states of local Hamiltonians, the PI will employ his knowledge of classical PCP theory, a deep theory in computer science that he helped develop, and couple it with the expertise of the colleagues in Berkeley on quantum information theory.A quantum analog of the PCP theorem would say something profound about quantum systems. Besides its implications in quantum information theory, it would also have more direct implication in physics, such as the realization, that quantum systems retain their exponential complexity at high temperature. In addition, an area law would explain the often localized behavior of wave functions for many-body systems.If the PI and colleagues are successful in their efforts, this would be a development akin to the invention of classical PCP theory, that should attract a number of computational complexity theorists, and connect them with quantum computing. A deeper understanding of the behavior of ground states of local Hamiltonians should effect disciplines ranging from quantum chemistry to black hole physics.