Quantum Matter in Mathematics and Physics Seminar

Speaker: Anurag Anshu (Harvard)

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

Abstract: 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.