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Explore a groundbreaking approach to quantum circuit mapping in this 37-minute conference talk presented by Anurag Anshu from Harvard University at IPAM's Topology, Quantum Error Correction and Quantum Gravity Workshop. Delve into a novel method for transforming arbitrary quantum circuits into local Hamiltonians, bypassing the traditional Feynman-Kitaev construction and its reliance on clock registers. Discover how this innovative technique leverages injective tensor networks and parent Hamiltonians to encode quantum computations, albeit with inherent stochastic noise. Learn about the integration of quantum fault tolerance to enhance robustness and examine the implications for states with varying energy densities. Gain insights into the BQP-hardness of contracting injective tensor networks and explore the potential impact on the quantum PCP conjecture. Uncover the possibilities of performing QMA verification in logarithmic depth and broaden your understanding of cutting-edge quantum computing concepts.
