Circuit-To-Hamiltonian Mapping Using Tensor Networks and Fault Tolerance

Explore a groundbreaking approach to quantum circuit-to-Hamiltonian mapping in this 36-minute lecture by Quynh Nguyen from Harvard University. Delve into a novel construction that utilizes injective tensor networks and parent Hamiltonians, eliminating the need for a clock register traditionally used in Feynman-Kitaev constructions. Discover how quantum fault tolerance techniques can enhance the robustness of this method, allowing for the encoding of quantum computations within the ground state. Examine the implications of this approach for states with varying energy densities and their ability to encode quantum computations with different noise models. Learn about the BQP-hardness of contracting injective tensor networks to additive error and consider the potential impact on the quantum PCP conjecture. Gain insights into the intersection of quantum complexity, area laws, and quantum gravity through this innovative research presented at the Simons Institute.