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UID:10001318-1706868000-1706873400@cmsa.fas.harvard.edu
SUMMARY:Quantum Circuits to local Hamiltonian: role in quantum complexity and new constructions 
DESCRIPTION:Quantum Matter in Mathematics and Physics Seminar \nSpeaker: Anurag Anshu (Harvard) \nTitle: Quantum Circuits to local Hamiltonian: role in quantum complexity and new constructions \nAbstract: At the heart of the theory of NP completeness lies a mapping from classical circuits to constraint satisfaction problems (classical local Hamiltonians). \nThe quantum analogue of this is the remarkable history state construction of Kitaev (building upon Feynman’s work). This talk will provide an introduction to this mapping and its crucial role in bridging quantum computer science and quantum many-body physics research. Then\, we will describe a new mapping using tensor networks and quantum fault tolerance (https://arxiv.org/abs/2309.16475). Time permitting\, we will discuss the relevance of this mapping to the quantum PCP conjecture.
URL:https://cmsa.fas.harvard.edu/event/qm_2224/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-02.02.24.png
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UID:10000667-1706875200-1706878800@cmsa.fas.harvard.edu
SUMMARY:On complete Calabi-Yau metrics and Monge-Ampere equations
DESCRIPTION:CMSA Member Seminar \nSpeaker: Freid Tong (Harvard CMSA) \nTitle: On complete Calabi-Yau metrics and Monge-Ampere equations \nAbstract: Calabi-Yau metrics are central objects in K\”ahler geometry and also string theory. The existence of Calabi-Yau metrics on compact manifolds was answered by Yau in his solution of the Calabi conjecture\, but the situation in the non-compact setting is much more delicate\, and many questions related to the existence and uniqueness of non-compact Calabi-Yau metrics remain unanswered. I will give an introduction to this subject and discuss some ongoing joint work with T. Collins and S.-T. Yau\, on a new relationship between complete Calabi-Yau metrics and a new Monge-Ampere equation.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-2224/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Member-Seminar_2224.png
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