Hannover 2016 – wissenschaftliches Programm

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Q: Fachverband Quantenoptik und Photonik

Q 30: Quantum Information: Concepts and Methods V

Q 30.6: Vortrag

Mittwoch, 2. März 2016, 12:15–12:30, e214

Mixing properties of local diffusion processes on the unitary group — •Emilio Onorati, Winton Brown, Oliver Buerschaper, Martin Kliesch, Albert Werner, and Jens Eisert — Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany

In recent years, random quantum processes have been the object of numerous investigations. Random quantum circuits are discrete processes of this type: unitary local gates are randomly chosen according to some distribution and repeatedly applied to quantum states. Continuous-time evolutions belong to this class too, e.g. the ones induced by fluctuating local Hamiltonians.

In this work, we prove that a diffusion process on the unitary group generated by a fluctuating local Hamiltonian has mixing properties analogous to those shown for random quantum circuits, hence providing a unifying picture for the two frameworks. More precisely, we show that local Wiener processes are approximate unitary k-designs after a polynomial run time. This result follows from previous techniques developed for random quantum circuits as well as new insights from representation theory.

In addition, we show that decoupling, a relevant concept for a large variety of applications in both physics and quantum information, can be obtained with almost linear scaling in the system size in the setting of fluctuating local Hamiltonians. To prove this, we construct an abstract continuous-time random walk over Pauli strings and show that it satisfies a certain mixing criterion which then implies decoupling.