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Title:
Quantum Dynamics in Rugged Energy Landscapes
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Abstract:
We study the ability of quantum dynamics to navigate rugged energy landscapes, as appear both in long-range-interacting disordered systems and combinatorial optimization problems. From the non-equilibrium quantum mechanics perspective, the question is whether isolated unitary dynamics can bring such systems to equilibrium. From the quantum computation perspective, the question is whether quantum fluctuations can aid in "energy matching" problems, where one solution to an optimization problem is given and used as a starting point to find others. The existence of energy barriers and exponentially many "clusters" of states makes these tasks hard. Focusing on analytically tractable models in a transverse field, we find three sharp dynamical phases. At low fields, the system cannot tunnel out of its initial cluster (no equilibration, energy matching fails). At intermediate fields, the system does tunnel between states at the same classical energy (equilibration, energy matching succeeds). At high fields, the system escapes its cluster by being excited to higher classical energies (equilibration, yet energy matching fails).
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