Quantum Circuits to local Hamiltonian: role in quantum complexity and new constructions

CMSA EVENTS: CMSA QUANTUM MATTER IN MATH & PHYSICS SEMINAR

When: February 2, 2024
10:00 am - 11:30 am
Where: CMSA, 20 Garden St, G10
Address: 20 Garden Street, Cambridge, MA 02138, United States
Speaker: Anurag Anshu - Harvard University

At the heart of the theory of NP completeness lies a mapping from classical circuits to constraint satisfaction problems (classical local Hamiltonians).
The 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.

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