Heidelberg 2015 – wissenschaftliches Programm
Q 18.1: Vortrag
Dienstag, 24. März 2015, 11:00–11:15, K/HS1
Random Hamiltonians, random circuits and unitary designs — •Emilio Onorati1, Martin Kliesch1, Albert Werner1, Winton Brown2, and Jens Eisert1 — 1Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany — 2Département de Physique, Université de Sherbrooke
Randomness has proven to be a useful tool for a large variety of tasks in quantum information and physics, e.g. tomography and gate benchmarking, decoupling and thermalization making use of unitary designs, i.e. the application of random unitaries chosen according to the uniform Haar distribution. A known method to realise such unitary designs is provided by suitable random quantum circuits, where two-qubit gates are taken from a given distribution and repeatedly applied to a quantum state.
In this work, we provide a general picture of such designs, and specifically show that a continuous-time process with a local fluctuating Hamiltonian is able to mimic the properties of the Haar measure. In this spirit, we divide the total time in small steps; for each of these we generate a Hamiltonian composed of local terms weighted by gaussian coefficients, then we apply the corresponding unitary evolution.
The principal mathematical tool to the proof involves Markov chain theory. In particular, the continuous-time process defines a random walk over Pauli matrices, which converges to the same stationary distribution of the analogous walk induced by the Haar measure.