Ground States of Local Hamiltonians and Quantum PCPs

PI计划将这笔赠款用于对加州大学伯克利分校为期一年的访问，他打算在那里与乌梅什·瓦兹拉尼及其同事和学生密切合作，讨论关于局部哈密顿人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。为了获得对局部哈密顿的基态所需的洞察，PI将利用他对经典PCP理论的知识，这是他帮助开发的计算机科学中的一种深刻理论，并将其与伯克利的同事在量子信息理论方面的专业知识结合起来。PCP定理的量子类比将说明量子系统的一些深刻的东西。除了它在量子信息论中的含义外，它还将在物理学中有更直接的含义，例如实现量子系统在高温下保持其指数复杂性。此外，面积定律将解释多体系统波函数的局域化行为。如果Pi和他的同事们的努力成功，这将是一个类似于经典PCP理论的发明的发展，应该会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。对局域哈密顿的基态行为的更深入的理解应该会影响从量子化学到黑洞物理的各种学科。

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.