Universal Hamiltonians for Exponentially Long Simulation
Abstract: In this talk we address the problem of how to build a "simple" universal, local, translation-invariant, and time independent Hamiltonian whose time evolution can efficiently simulate the time evolution of any other Hamiltonian for up to exponentially long times. While this is a result about Hamiltonian simulation, this construction was partly motivated by a conjecture by Susskind which proposes a possible role of a quantum state's circuit complexity in the context of the AdS/CFT duality. In the first half of the talk, we will discuss this motivating background at a simple level and the related results that follow from our construction. In the second half of the talk, I will describe the construction of our universal Hamiltonian that achieves our results by using the ideas of a Hamiltonian Quantum Cellular Automaton (HQCA) and a continuous-time quantum walk on a line.
The IQIM Seminar Committee is excited to announce that the IQIM seminar will have a new format this year. Seminars will take place at lunch on Fridays, with food served beginning at 12 noon. There will not be a break halfway through the talk. More details on the mission of the seminars and the new format can be found on the IQIM website